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Multiple criteria decision making (MCDM) methods in economics: an overview/Daugiatiksliai sprendimu priemimo metodai ekonomikoje: apzvalga.

1. Introduction

Decision making problems are of crucial importance in economics. The main research activities in economics during the last five years have significantly increased. The main fields are operation research and sustainable development. Success in economics and business is a straightforward matter: focus on society, government, stakeholders, customers, and amaze them with experiences that exceed their expectations. Decision analysis is widely recognized as a sound prescriptive theory.

On the basis of intensive and productive scientific works and the high achievements, EURO Working Group OR in Sustainable Development and Civil Engineering (EWG-ORSDCE) was established in 2009 (

Publication in 1776 of The Wealth of Nations by Adam Smith has been described as the effective birth of economics as a separate discipline (Blaug 2007). Katona (1953) presented and contrasted the most common forms of methodologies of the economic principle of rationality in both psychology and economics, and a general discussion of the role of empirical research among psychologists in studies of economic behaviour was initiated.

Current economic models developed out of a broader field of political economy in the late 19th century, owing to a desire to use an empirical approach more akin to the physical sciences (Clark 1998). Rationality is a central principle in decision-making, where a rational agent is specifically defined as an agent who always chooses the action which maximises its expected performance (Johnson-Laird and Byrne 1991). Rational choice theory, also known as choice theory or rational action theory (Arrow 1989), is a framework for understanding and often formally modelling social and economic behaviour. The basic idea of rational choice theory is that patterns of behaviour in societies reflect the choices made by individuals as they act by comparing the costs and benefits of different courses of action. It is the main theoretical paradigm in the currently-dominant school of microeconomics.

The fact that people act rationally has been recognised by many scientists, but they have seen rational actions alongside other forms of action, seeing a human action as involving both rational and non-rational elements. Actions are often expressed as a set of actions. In rational choice theories, individuals are seen as motivated by the wants or goals that express their 'preferences'. Decision makers act within specific, given constraints and on the basis of the information that they have about the conditions under which they are acting. Durkheim in 1893 (Durkheim 1984) argued that all rational economic actions occur within an institutional framework of norms that cannot itself be explained as a result of rational action alone. Groups and organisations, business enterprises, and others may, then, all figure as collective actors whose individual intentions are aggregated and an agreed policy formulated (Hindess 1988). Individuals or organizations are called rational if they make optimal decisions in pursuit of their goals.

Von Winterfeldt's and Edwards works on multiple stakeholder decision analysis and behavioural decision theory generated a more formal approach to multiple attribute utility analysis (von Winterfeldt and Edwards 1986).

Perhaps the most important ideas are that a common value structure can be created even when stakeholders violently disagree about the issues at hand; that conflicts are often about specific value tradeoffs or facts; that conflicts about values can be expressed as different weights; and that conflicts about facts can be modelled by using judgments from different experts. Most importantly perhaps was the finding that decision analysis can be useful to help multiple stakeholders understand what they agree and disagree about, focus on the things that they disagree about and explore options that are better for everyone involved.

It is believed that a good rationale must be independent from personal emotions, feelings, instincts or culturally specific, moral codes and norms. If these minimum requirements are not satisfied, the analysis may be termed irrational. It is evident that no human has ever satisfied this criterion.

Weber (Max Weber (1864-1920) distinguished between four ideal-types of action (Weber 2011):

--Affectual, determined by an actor's specific affect, feeling, or emotion;

--Traditional action;

--Value-rational action. Here the action is undertaken for what one might call reasons intrinsic to the actor: some ethical, aesthetic, religious or other motive, independent of whether it will lead to success;

--Means-end rational action.

As expressed by Weintraub (2007), neoclassical economics rests on three assumptions:

--People have rational preferences among outcomes;

--Individuals maximize utility and firms maximize profits;

--People act independently on the basis of full and relevant information.

Bounded rationality is the idea that in decision-making rationality of individuals is limited according to the information they have, the cognitive limitations of their minds, and the finite amount of time they have to make decisions (Elster 1983). Another way to look at bounded rationality is that because decision-makers lack the ability and resources to arrive at the optimal solution; they instead apply their rationality only after having greatly simplified the choices available (Gigerenzer and Selten 2002).

Economists determine priorities of actors by strictly mathematical descriptions. They make a set of assumptions which are referred to as the assumptions of a human's rational behaviour.

Rational choice theory makes two assumptions about individuals' preferences for actions:

--Completeness: all actions can be ranked in order of preference (indifference between two or more is possible).

--Transitivity: if action [a.sub.1] is preferred to [a.sub.2], and action [a.sub.2] is preferred to [a.sub.3], then [a.sub.1] is preferred to [a.sub.3].

Together these assumptions form the result that given a set of exhaustive and exclusive actions to choose from, an individual can rank them in terms of his preferences, and that his preferences are consistent.

An individual's preferences can also take forms:

--Strict preference occurs when an individual prefers [a.sub.1] to [a.sub.2], but not [a.sub.2] to [a.sub.1].

--In some models, a weak preference occurs when an individual has a preference for at least [a.sub.j], similar to the mathematical operator [less than or equal to].

--Indifference occurs when an individual does not prefer [a.sub.1] to [a.sub.2], or [a.sub.2] to [a.sub.1].

--In more complex models, other assumptions are often incorporated, such as the assumption of independence axiom. Also, with dynamic models that include decision making over time, time inconsistency may affect an individual's preferences.

From the first days of the mankind on earth, there is evidence of countless human decision situations related to real life problems with many desirable attributes. These attributes are often referred to in literature as criteria or Performance Measures. All interested parties think about different touch points and allow them to rank feasible alternatives in importance, need for improvement, and overall criteria selection. The different touch points need to be reengineered to conduct the experience according to the criteria that the interested parties defined as important.

2. Operations research in economics

An Operations Research (OR) is the application of scientific method to the management of organized systems such as industrial production systems, government and social programs, and defence systems. OR (also referred to as decision science or management science) is the application of science to the solution of managerial and administrative problems; it focuses on the performance of organized systems taken as a whole rather than on their parts separately. Its techniques and methods, and the areas to which they are applied, can be expected to continue to expand rapidly (Industrial Engineering ... 2011). OR is an interdisciplinary mathematical science that focuses on the determination of the maximum or minimum of some real-world objectives. The environment in which decisions must be made is more complex than ever before. Companies use operations research to devise ways and means to maximize their profits and restrict their losses and risks. Also, they devise means to produce at lower costs or produce more quantities at the same costs.

Many years of research effort have been devoted to developing various mathematical models which could describe decision maker behaviour. These models are applied in OR. Some of the tools used by operational researchers are statistics, optimization, probability theory, queuing theory, game theory, graph theory, decision analysis, mathematical modelling and simulation.

The main stages of conventional OR are as follows:

--Creating the model, which is proper to the problem solution;

--Selecting the optimality criterion;

--Choosing preferable solution.

The primary step in many economical studies and in OR is the construction of models representing the reality. Typical decision making problems imply the creation of a subjective model representing personal perception of a decision problem. Decision making has two roots: economical utility theory and OR.

With expanded technologies and impact on environment, as well as sustainable development of economy, the use of OR is widely extending. Informed stakeholders, society, government and scientists require solving problems taking into account multiple criteria. Such problem solution approach enables taking high quality decisions. A distinction between OR and Decision making methods is that the latter have several different methods to evaluate quality of decisions made. Compromise among several criteria could be determined by the person (group of persons) who makes decisions.

There is a separated class of models for decision making methods which are of objective character (similar to the OR), but quality of the made decision is determined according to a several criteria. This class of problems is named multiple criteria models with objective described models. This class is position between OR and decision-making.

Forecasting is one of the most significant parts in decision-making. The reason of this is that decisions must be made before acting and it deals with future. Executives make forecasts as an essential part of their work. International institute of Forecasters sponsored classifying and the main forecasting principles are presented (Fig. 1). The Methodology Tree for Forecasting classifies all possible types of forecasting methods into categories and shows how they inter-relate.


Developing economics, changing environment, sustainability of decisions are the reasons for the rapid development of new OR techniques and many of those techniques were adopted for problem solution in economics. But in reality, the modelling of economical problems is based on a different kind of logics, taking into consideration the following elements (i.e. multiple criteria paradigm (Roy 1988)):

--The existence of multiple criteria;

--The conflicting situation between the criteria;

--The complex, subjective and ill-structured nature of the evaluation process;

--The introduction of financial decision makers in the evaluation process.

The main limitation of operations research is that it often ignores the human element in the production process. This science is technology driven and does not take into account the emotional factors and absenteeism of employees.

3. Multiple criteria decision making (MCDM) methods in economics

In the field of MCDM, there are two schools of thought that a human choice is based on: a French school and an American school (Lootsma et al. 1990). The French school mainly promotes the outranking concept for evaluating discrete alternatives (Roy 1968). The American school is based on multi-attribute value functions and multi-attribute utility theory (MAUT) (Keeny and Raiffa 1976).

Multiple criteria decision making, as described by Vincke (1992), is the most directly characterised by a set of multiple criteria method. From 1950s onwards, there had been a large number of refined MCDM methods developed and they differ from each other in the required quality and quantity of additional information, the methodology used, the user-friendliness, the sensitivity tools used, and the mathematical properties they verify. Vincke succinctly outlines a disaggregation of the overall of the multiple criteria decision into three components of multiple attribute utility theory, outranking methods and interactive methods.

Siskos and Spyridakos (1999) presented a survey of the history and the recent status of the multiple criteria decision support systems. Wang et al. (2009) in review of multi-criteria decision analysis aid in sustainable energy decision making pointed out that MCDM methods have become increasingly popular in decision-making for sustainability because of the multi-dimensionality of the sustainability goal and the complexity of socio-economic and biophysical systems.

Carlsson and Fuller (1996) stated that there are four quite distinct families of MCDM methods:

--The outranking;

--The value and utility theory based;

--The multiple objective programming;

--Group decision and negotiation theory based methods.

Fuzzy MCDM has basically been developed along the same lines, although with the help of fuzzy set theory a number of innovations have been made possible.

Utility theory is interested in people's preferences or values and with assumptions about a person's preferences and with judgements of preferability, worth, value, goodness or any of a number similar concept that enable them to be presented in numerically useful ways (Fishburn 1965, 1968). In decision theory, utility is a measure of the desirability of consequences of the courses of action that applies to decision making under the risk, i.e. under uncertainty within known probabilities.

The concept of utility applies to both single-attribute and multi-attribute consequences. The fundamental assumption in utility theory is that the decision maker always chooses the alternative for which the expected value of the utility is maximal. If that assumption is accepted, utility theory can be used to predict or prescribe the choice that the decision maker will make, or should make, among the available alternatives. For that purpose, a utility has to be assigned to each of the possible (and mutually exclusive) consequences of every alternative. A utility function is the rule by which this assignment is done and depends on the preferences of the individual decision maker. In utility theory, the utility measures of the consequences are assumed to reflect a decision maker's preferences in the following sense:

--The numerical order of utilities for consequences preserves the decision maker's preference order among the consequences;

--The numerical order of expected utilities of alternatives preserves the decision maker's preference order among these alternatives.

The art of applying multi-attribute utility has expanded since 1976. There should be significant interplay between descriptive studies of how people do process information and make decisions and prescriptive decision analysis to help people make decisions that are consistent with their values and understanding of the problem (Tsoukias and Vincke 2011).

Preferences are used in a lot of decision making problem situations in economics. The first attempt to give an account about preference relations can be referred to Von Neumann and Morgenstern (1944). Savage (1954) was the first to introduce the foundation of the subject. Most of the economical, industrial, financial or political decision problems are multiattribute. The problem to estimate utility function representing the actor's preferences in the multidimensional case (multiattribute utility theory) is very important. The problem of the selection or the ranking of alternatives submitted to a multicriteria evaluation is not an easy problem. Usually, there is no optimum solution; no alternative is the best one for each criterion. Better quality implies higher price. The criteria are conflicting. Compromise solutions have to be considered.

The subject was investigated in Keeney and Raiffa (1976), where the basic conditions under which their use is possible are introduced. Rough set theory is a tool for dealing with granularity, classification, vagueness and incompleteness in data analysis (Zhu 2009). In order to achieve this goal, researchers have proposed many methods other than classical logic, for example, fuzzy set theory, rough set theory, computing with words and granular computing, computational theory for linguistic dynamic systems.

It is obvious that uncertainty is a typical feature of preferences when it is necessary to define calculus so as to handle these situations operationally. Fuzzy set theory could then be a tool (Zadeh 1975a, b, c). The first fuzzy outranking relation is defined as theoretical background for the ELECTRE III method. Greco et al. (1999, 2000 and 2001); Pawlak et al. 1995) pointed at peculiarities of fuzzy sets and rough sets using in MCDM.

A linguistic variable is a variable whose values are expressed in linguistic terms (Zimmermann 1985). The concept of a linguistic variable is very useful in dealing with the situations which are too complex or not well-defined to be reasonably described in conventional quantitative expressions (Larichev and Moshkovich 1997; Larichev and Brown 2000; Ustinovichius et al. 2009, 2010, 2011). Fuzzy numbers are introduced to appropriately express linguistic variables. In the area of fuzzy reasoning, the two-tuple linguistic representation method (Herrera et al. 2000; Liu and Zhang 2011) is widely applied for computing with words.

Problem selection and alternative creation are critically important. Investigation and aggregation of values, which describe the reason actors are interested in decision situation, are referred to as value-focused thinking. The aim of this model is to create better alternatives and aggregation of individual preferences for any decision problem. Many of the complex problems faced by decision makers involve multiple conflicting objectives (Keeney 1982).

4. Classification of discrete multiple criteria methods

There are a lot of MCDM methods (Guitoni and Martel 1998). MCDM approaches are major parts of decision theory and analysis. Hwang and Yoon (1981) grouped the MCDM methods according to the available information. Real-world decision making problems are usually complex and no structures are to be considered through the examination of a single criterion, or point of view that will lead to the optimum decision. Operation in the marketplace requires some knowledge of areas generating critical situations and insolvency. It is necessary to learn the criteria determining both development and downfall of feasible alternatives (Kaplinski 2008a). In a mono-criterion approach, the analyst builds a unique criterion capturing all the relevant aspects of the problem. Such a one-dimensional approach is an oversimplification of the actual nature of the problem. In many real-world decision problems, the decision-maker has a set of multiple conflicting objectives. All new ideas and possible variants of decisions must be compared according to many criteria (Turskis et al. 2009). The problem of decisionmaker consists of evaluating a finite set of alternatives in order to find the best one, to rank them from the best to the worst, to group them into predefined homogeneous classes, or to describe how well each alternative meets all the criteria simultaneously. There are many methods for determining the ranking of a set of alternatives in terms of a set of decision criteria.


Over the past decades the complexity of economical decisions has increased rapidly, thus highlighting the importance of development and implementation of sophisticated and efficient quantitative analysis techniques for supporting and aiding economical decision-making. MCDM is an advanced field of OR; it provides decision makers and analysts with a wide range of methodologies, which are overviewed and well-suited to the complexity of economical decision problems (Hwang and Yoon 1981; Zopounidis and Doumpos 2002; Figueira et al. 2005). Over the last decade scientists and researchers have developed a set of new MCDM methods (Kaplinski and Tupenaite 2011; Kaplinski and Tamosaitiene 2010; Tamosaitiene et al. 2010). They modified methods and applied to solve practical and scientific problems.

Most of MCDM methods deal with discrete alternatives, which are described by a set of criteria. Criteria values can be determined as a cardinal or ordinal information. Information could be determined exactly or could be fuzzy, determined in intervals. Modern MCDM methods enable decision makers to deal with all above mentioned types of information. One of the problems encountered during multiple criteria decision making process is the choice of the aggregation procedure for solving the decision problem. However, multiple criteria decision analysts provide a variety of aggregation procedures. MCDM methods have become increasingly popular in decision making for economics because of the multi-dimensionality of the sustainability goal and the complexity of socio-economic, environment and government systems (Tables 1 and 2). Approximately one out of six scientific researches in MCDM deal with fuzzy sets or fuzzy relations (Table 2, Fig. 3).

In the multiple criteria approach, the analyst seeks to build several criteria using a few points of view. MCDM is one of the most widely used decision methodologies in science, business, and governmental worlds, which are based on the assumption of a complex world, and can help improve the quality of decisions by making the decision making process more explicit, rational, and efficient. In real life, a decision-maker first of all must understand and describe the situation. This stage includes the determination and assessment of the stakeholders, different alternatives of feasible actions, a large number of different and important decision criteria, type and quality of information, etc. It appears to be the key point defining MCDM as a formal approach. For Zeleny (1977, 1982) decision criteria are rules, measures and standards that guide decision-making. Bouyssou (1990) proposed a general definition of a criterion as a tool allowing comparison of alternatives according to a particular point of view. When building a criterion, the analyst should keep in mind that it is necessary for all the actors of the decision process to adhere to the comparisons that will be deduced from that model. Criteria (relatively precise, but usually conflicting) are measures, rules and standards that guide decision-making, which also incorporates a model of preferences between elements of a set of real or fictitious actions. Typical examples of MCDM problems are referred to as discrete MCDM problems, involve the selection among different investment projects, personnel ranking problem, and financial classification problem, and are decision-support oriented. The major strength of multiple criteria methods is their ability to address to the problems marked by various conflicting interests.




Classical methods of multiple criteria optimization and determination of priority and utility function were first applied by Pareto in 1896 (Pareto 1971). These methods were strongly related to economical theory, concerning the averages of thousands of decisions. Methods of multiple criteria analysis were developed to meet the increasing requirements of human society and the environment. Methods of multiple criteria analysis were developed in 1960s to meet the increasing requirements of human society and the environment. Keeney and Raiffa (1976) offered the representation theorems for determining multiple criteria utility functions under preferential and utility independence assumptions. Keeney (1982) outlined the essential features and concepts of decision analysis, formulated axioms and major stages. Seo (1981) suggested a multiple criteria decision making method that was concerned with balancing some conflicting objectives in a hierarchical structure. Saaty (1977) showed the global importance of solving problems with conflicting goals by using multiple criteria models and presented decision making models with incomplete information. In his latest works Saaty (Saaty et al. 2003) analyzed measuring problems in assignments associated with uncertainty conditions and applied the AHP method to solve different problems. Tanino et al (1981) analyzed the problem of the coordination of different goals and objectives of various interested parties. Keeney (1982) outlined the essential features and concepts of decision analysis, formulated axioms and major stages. Keeney and Winterfeldt (2001) suggested following the prudence principle in decision process, making decisions precisely and evaluating all possible alternatives, the aims of interested parties, subsequences of decision results and value changes, hereby minimizing the decision making risk.

There are lot of even sophisticated issues in collaboration with specialists representing other domains of science (e.g. mathematicians) (Kaplinski 2008a, b, c). Available wide range of MCDM problems solution techniques, varying complexity and possibly solutions, confuses potential users. Each method has own strengths, weaknesses and possibilities to be applied. It causes phenomena known as the inconsistent ranking problem and can be caused by different MCDM methods. A major criticism of MCDM methods is that due to the differences among different techniques, different results are obtained when applied to the same problem. These differences of algorithms are:

--Using weights differently;

--Different selection of the best solution;

--Attempt to scale objectives;

--Introducing additional parameters that affect solution.

The need of comparing MCDM methods and the importance of the selection problem were first recognized by MacCrimmon who suggested taxonomy of MCDM methods. There are many comparative studies presented in scientific research works. Guitoni and Martel (1998) proposed a methodological approach to select an appropriate MCDM method to a specific decision making situation. The selection may be done via comparing MCDM methods (Zanakis et al. 1998). A simulation by Zanakis et al. (1998) evaluated eight MCDM methods: SAW, multiplicative exponential weighting (MEW); ELECTRE, and AHPs: SAW and MEW performed best. Computations of different examples reveal the fact that evaluation outcome depends on both choice of utility function and its parameters (Podvezko and Podviezko 2010).

There are many ways to classify MCDM methods (Hwang and Yoon 1981; Larichev 2000; Figueira et al. 2005). For instance, Belton and Stewart (2002) offered the following classification of MCDM methods: 1) value measurement models; 2) goal, aspiration, and reference level models; 3) outranking models (the French school).

The classification of MCDM methods according to the type of information based on the Larichev's (Larichev 2000) proposal is given bellow:

--Methods based on quantitative measurements. The methods based on multiple criteria utility theory may be referred to this group (TOPSIS, LINMAP, MOORA, COPRAS, and its modification COPRAS-G).

--Methods based on qualitative initial measurements. These include two widely known groups of methods: AHP and fuzzy set theory methods (Zimmermann 2000).

--Comparative preference methods based on pair-wise comparison of alternatives. This group comprises the modifications of the ELECTRE, PROMETHEE, TACTIC, ORESTE and other methods (Turskis 2008).

--Methods based on qualitative measurements not converted into quantitative variables. This group includes methods of verbal decision making analysis (Berkeley et al. 1991) and uses qualitative data for decision environments involving high levels of uncertainty.

--MCDM problems can be categorized as continuous or discrete, depending on the domain of alternatives.

Hwang and Yoon (1981) classify them as:

--MCDM with discrete, usually limited, number of alternatives, requiring criterion comparisons, involving implicit or explicit tradeoffs;

--MODM (multiple objective decision-making), with decision variable values to be determined in a continuous or integer domain, of infinite on a large number of choices, to satisfy best the decision-maker constraints, preferences or priorities.

In particular, the main steps of multiple criteria decision making are the following:

--Determining the main goal of a problem;

--Establishing system of the main objectives or criteria by which the alternatives are to be judged;

--Generating feasible alternatives (a finite number of alternative plans or options) that can be implemented to achieve goals;

--Evaluating an impact of each criterion on the decision making function or weights of criteria. A decision-maker should express his / her preferences in terms of the relative importance of criteria, and one approach is to introduce criteria weights.

The weights in MCDM do not have a clear economic significance, but their use provides opportunity to model actual aspects of the preference structure:

--A set of performance evaluations of alternatives for each criterion;

--A method for ranking the alternatives based on how well they satisfy the criteria;

--Aggregating alternative evaluations (preferences);

--Accepting one alternative as the best (the most preferable);

--Gathering new information and the next iteration of MCDM if the final solution is not accepted;

--Making recommendations for decision-making.

An alternative in multiple criteria evaluation is usually described by quantitative and qualitative criteria. The criteria have different units of measurement. Normalization aims at obtaining comparable scales of the criteria values. Different techniques of criteria value normalization are used. The impact of the decision-matrix normalization methods on the decision results has been investigated by many authors (Juttler 1966; Korth 1969; Stopp 1975; Weitendorf 1976; Zavadskas 1987, 1990; Peldschus 2009; Ginevicius 2008; Zavadskas and Turskis 2008). There are still no rules determining the application of multiple criteria evaluation methods and interpretation of the results obtained.

The case study findings about pioneering studies in multiple criteria decision making paradigms and earliest application are summarized in Table 3.

5. Recent development and applications

Recent case study findings about the parallels between economics and multiple criteria decision making paradigms are summarized in Table 4. There, it is pointed at the methods applied by users except for authors of the paper. Authors of paper applied most of the methods listed in Table 4 in own researches, but they have not presented them.

6. Conclusions

Operations research is very beneficial in deciding upon what to produce, the quantities, the methods of production, which employees to engage in the production processes and the marketing schemes of the produced goods. In this survey a comprehensive view of problems that are open in the field of decision making in economics is given.

The fact that people act rationally and are independent of personal emotions, feelings, instincts or culturally specific, moral codes and norms has been recognised by many scientists in classical theories. It is evident that no human has ever satisfied this criterion. Groups and organisations, business enterprises, and others may, then, all figure as collective actors whose individual intentions are aggregated and an agreed policy formulated. There could be definitely stated that the "best" approach does not exist. The eventual choice of one is a multiple criteria problem and, therefore, it has no optimal solution. Economical decision making is extremely complex due to the intricacy of the systems considered and the competing interests of multiple stakeholders. Decision making theories and applications offer different modelling techniques, provide an appropriate approaches for modelling decision aiding, help in development of alternatives as they take into account the complexity of the process.

The selection of a model and problem solution approach depends on the desired goal, actors involved in the decision making process, available information, time, and etc. There are several branches of decision theory that depart from the stand expected utility paradigm. The major strength of multiple criteria methods is their ability to address problems marked by various conflicting interests.

There are a lot of open fields of future research as:

--Analysis of different scaling methods;

--Analysis of preference relations;

--Analysis of aggregation procedures;

--The study of grey relations;

--The study of fuzzy relations;

--The development and modification of new mathematical models to solve outranking problems.

Multiple criteria decision making provides powerful approaches to solve complicated problems in economics. These techniques allow actors to solve those problems which are impossible to solve by applying common optimisation models.

The main focus of this paper was to overview the use of decision support tools, such as recent developments of classical models of multicriteria decision analysis, which are being used increasingly for comparative analysis and assessment of alternatives.

doi: 10.3846/20294913.2011.593291


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Zavadskas, E. K.; Kaklauskas, A.; Turskis, Z.; Tamosaitiene, J. 2008. Selection of the effective dwelling house walls by applying attributes values determined at intervals, Journal of Civil Engineering and Management 14(2): 85-93. doi:10.3846/1392-3730.2008.14.3

Zavadskas, E. K.; Turskis, Z. 2008. A new logarithmic normalization method in games theory, Informatica 19(2): 303-314.

Zavadskas, E. K.; Turskis, Z. 2010. A new additive ratio assessment (ARAS) method in multicriteria decision-making, Technological and Economic Development of Economy 16(2): 159-172. doi:10.3846/tede.2010.10

Zeleny, M. 1977. Multidimensional measure of risk: the prospect ranking vector. In: Multiple Criteria Problem Solving, Zionts, S. (Ed.), Springer: Heidelberg; 529-548.

Zeleny, M. 1982. Multiple criteria decision making. New York: McGraw-Hill.

Zhu, W. 2009. Relationship among basic concepts in covering-based rough sets, Information Sciences 179(14): 2478-2486. doi:10.1016/j.ins.2009.02.013

Zimmermann, H. - J. 2000. An application-oriented view of modelling uncertainty, European Journal of Operational Research 122(2): 190-198. doi:10.1016/S0377-2217(99)00228-3

Zimmermann, H. J. 1985. Fuzzy set theory and its applications. Dordrecht: Kluwer Academic.

Zopounidis, C.; Doumpos, M. 2002. Multi-criteria Decision Aid in Financial Decision Making: Methodologies and Literature Review, Journal of Multi-Criteria Decision Analysis 11: 167-186. doi:10.1002/mcda.333

Zvirblis, A.; Buracas, A. 2010. The consolidated measurement of the financial markets development: the case of transitional economies, Technological and Economic Development ofEconomy 16(2): 266-279. doi:10.3846/tede.2010.17

Zvirblis, A.; Zinkeviciute, V. 2008. The integrated evaluation of the macro environment of companies providing transport services, Transport (23)3: 266-272. DOI: 10.3846/1648-4142.2008.23.266-272. doi:10.3846/1648-4142.2008.23.266-272

[TEXT NOT REPRODUCIBLE IN ASCII.]. (Vaigauskas, E.; Zavadskas, E. 1980. Use of utility function for an optimum variant of building choice. Vilnius Civil Engineering Institute, Vilnius.)

Edmundas Kazimieras Zavadskas (1), Zenonas Turskis (2)

Vilnius Gediminas Technical University, Faculty of Civil Engineering, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

E-mails: (1) (corresponding author); (2)

Received 10 January 2011; accepted 5 May 2011

Edmundas Kazimieras ZAVADSKAS. Prof., Head of the Department of Construction Technology and Management at Vilnius Gediminas Technical University, Vilnius, Lithuania. He has a PhD in Building Structures (1973) and Dr Sc. (1987) in Building Technology and Management. He is a member of the Lithuanian and several foreign Academies of Sciences. He is Doctore Honoris Causa at Poznan, Saint-Petersburg, and Kiev universities as well as a member of international organisations; he has been a member of steering and programme committees at many international conferences. E. K. Zavadskas is a member of editorial boards of several research journals. He is the author and co-author of more than 400 papers and a number of monographs in Lithuanian, English, German and Russian. Research interests are: building technology and management, decision-making theory, automation in design and decision support systems.

Zenonas TURSKIS has a PhD and is a chief research worker at Laboratory of Construction Technology and Management in Vilnius Gediminas Technical University, Lithuania. His research interests include building technology and management, decision-making theory, computer-aided automation in design and expert systems. He is the author of more than 80 research papers.
Table 1. Dynamics of multiple criteria decision making
applications in economics (this table is based on
the search in accessed on 9 May 2011)

                             & economics (keywords)

Year                          &          &           &
of                      multiple     multi       multi-
publication             criteria   criteria   attribute

                   A          B          C           D

2011             6688       2280        358         110
2010             9694       3119        316         101
2009             8965       2870        262          99
2008             8264       2498        242          89
2007             7284       2260        182          70
2006             6416       1866        123          51
2005             5294       1494        125          60
2004             5266       1360        102          55
2003             4510       1164         88          43
2002             3760        992         88          55
2001             3645        916         68          41
2000             3165        788         52          50
1999             2796        691         73          54
1998             2879        724         79          71
1997             2763        649         74          70
1996             2668        641         77          90
1996             2562        565         68          59
1994             2300        515         36          47
1993             1979        433         59          50
[less than
or equal
to] 1992        21914       4170        370         356
Total          112812      29995       2842        1621

                             & economics (keywords)

Year                  &            &           &     Total
of             multiple     multiple       multi-      B-G
publication   attribute    objective    objective

                      E            F           G

2011                4177         8429         453     15807
2010                5945        12165         497     22143
2009                5448        11441         451     20571
2008                4990        10185         375     18379
2007                4617         9197         364     16690
2006                3856         8054         280     14230
2005                3048         6562         228     11517
2004                2881         5953         193     10544
2003                2468         5056         164      8983
2002                1956         4121         132      7344
2001                1839         3838         127      6829
2000                1638         3380         135      6043
1999                1441         3000         119      5378
1998                1416         2968         142      5400
1997                1297         2688         151      4929
1996                1203         2520         180      4711
1996                1133         2246         140      4211
1994                1052         2079         165      3894
1993                 888         1835         132      3397
[less than
or equal
to] 1992            8708        17773        1101     32478
Total              60001       123490        5529    223478

Table 2. Dynamics of fuzzy multiple criteria decision making
applications in economics (this table is based on the search

(accessed on 9 May 2011))

                          Decision making (fuzzy)
                           economics (keywords)

Year of                    multiple     multi-      multi-
publication                criteria    criteria    attribute

                  A           B            C           D

2011             733        1,200         335         91
2010             827        1,295         344         91
2009             843        1,293         325         70
2008             601         936          288         54
2007             538         941          278         60
2006             432         702          214         57
2005             322         530          128         32
2004             248         466          122         39
2003             200         381          101         25
2002             159         332          77          28
2001             163         293          68          25
2000             156         283          82          19
1999             121         252          72          17
1998             139         241          88          23
1997             111         250          91          37
1996             127         238          62          28
1996             136         209          68          34
1994             120         224          63          35
1993             80          173          40          13
[less than
or equal
to] 1992         745        1,244         394         159
Total           6,801       11,483       3,240        937

                           Decision making (fuzzy)

                             economics (keywords)

Year of       multiple     multiple      multi       Total
publication   attribute   objectives   objective      B-G

                  E           F            G

2011             856        1,179         233        3,894
2010             885        1,315         238        4,168
2009             931        1,306         242        4,167
2008             666         952          178        3,074
2007             614         926          179        2,998
2006             450         695          139        2,257
2005             338         525          99         1,652
2004             292         475          84         1,478
2003             257         377          68         1,209
2002             202         339          58         1,036
2001             182         288          55          911
2000             172         281          55          892
1999             164         255          41          801
1998             145         252          65          814
1997             175         232          55          840
1996             137         234          53          752
1996             138         190          48          687
1994             138         224          73          757
1993             93          157          48          524
[less than
or equal
to] 1992         777        1,151         282        4,007
Total           7,612       11,353       2,293      36,918

Table 3. Backgrounds of multiple criteria decision making
approaches and the earliest applications

Multiple attribute utility theory (MAUT)

Methods                Studies
LOGICAL                Keeney and Raiffa      Background MAUT
DECISION               (1976)

                       Smith and Speiser      Decision support
                       (1991)                 system based on the

DECAID                 Pitz (1987)            Decision support
                                              system based on the

                       [TEXT NOT              Investigation of
                       REPRODUCIBLE IN        MAUT practical
                       ASCII] (1980)          applications

Simple Additive        MacCrimon (1968)       Author
Weighting (SAW)

Linear                 Srinivasan and         Authors
Programming            Shocker (1973)
Techniques for
Analysis of

Analytic Hierarchy     Saaty (1977, 1980);    Author of AHP
Process (AHP)

Analytic Hierarchy     Lootsma (1993)         Multiplicative AHP
Process (AHP)                                 is an exponential
                                              version of the
                                              simple multi-
                                              attribute rating
                                              technique (SMART)

Utility Theory         Jacquet-Lagreze and    Authors
Additive (UTA)         Siskos (1982)

TOPSIS                 Hwang and Yoon         Authors

TOPSIS                 Antucheviciene et      The case study
                       al. (2010)             proved that the
                                              proposed TOPSIS-M
                                              (TOPSIS applying
                                              Mahalanobis distance

Multicriterion         Matarazzo (1986,       Author
Analysis of            1988b)
Preferences by means
of Pairwise
Alternatives and
comparisons (MAPPAC)

PRAGMA                 Matarazzo (1988a,      Author

Measuring              Bana e Costa and       Authors
Attractiveness by a    Vansnick (1994)
Categorical Based
TecHnique. (MACBETH)

Complex Proportional   Zavadskas and          Authors
Assessment (COPRAS)    Kaklauskas (1996)

Complex Proportional   Zavadskas et al.       Authors. Ranking of
ASsessment method      (2008)                 alternatives
with Grey interval
numbers (COPRAS-G)

REMBRANDT              Lootsma (1992) Olson etAuthor Users

Multi-Objective        Brauers and            Authors
Optimization by        Zavadskas (2006)
Ratio Analysis
Method (MOORA)

MULTIMOORA             Brauers and            Authors. Full
                       Zavadskas (2010)       Multiplicative Form
                                              is added to MOORA.

Additive Ratio         Zavadskas and          Authors of new
Assessment method      Turskis (2010)         method

ARAS-F                 Turskis and            Authors. Fuzzy set
                       Zavadskas (2010a)      applied to location
                                              problem. ARAS-F

ARAS-G                 Turskis and            Authors. Grey
                       Zavadskas (2010b)      relations applied to
                                              problem solution.
                                              ARAS-G presented

Step-wise weight       Kersuliene et al.      Selection of
assessment ratio       (2010)                 rational dispute
analysis (SWARA)                              resolution method by
                                              applying new
                                              step-wise weight
                                              assessment ratio

Elimination Et Choix   Benayoun et al.        First publication
Traduisant la          (1966)                 Author Explains the
REalite (ELimination                          bases of general
and Choice             Roy (1968, 1991)       decision making
Expressing REality)                           methodology which
(ELECTRE)              Roy (1978, 1990,       took shape toward
                       1996)                  end of 1960s. The
                                              evolutions have
                                              continued with
                                              ELECTRE II, ELECTRE
                                              III, ELECTRE IV,
                                              ELECTRE IS and
                                              ELECTRE TRI.

ELECTRE III and IV     Vallee and             Practical
                       Zielniewicz (1994)     realization,
                                              provided with

Organization,          Roubens (1982)         Author
Rangement Et
Synthese de dones

Preference Ranking     Brans et al. (1984,    Authors
Organization Method    1986)
for Enrichment
Evaluation             Brans and Mareschal    PROMETHEE V method
(PROMETHEE)            (1992)                 presented

                       Zahedi (1986)          Reviewed the AHP and
                                              its applications in
                                              diverse decision
                                              problems. It
                                              addresses some of
                                              the major extensions
                                              and criticisms of
                                              the method, as well.

MELCHIOR                                      Authors
                       Leclercq (1984)
Tratement des                                 Author
Actions Compte Tenu    Vansnick (1986)
de l'Importance des
Crite'res (TACTIC)

ARGUS                  De Keyser and Peters   Author

VIP                    Dias and Clkmaco       Analysis software.
                       (2000)                 Authors

IRIS                   Dias et al. (2002)     Analysis software.

Compromise ranking     Opricovic (1998)       Author
method (VIKOR)

Table 4. Recent applications of multiple criteria decision
making approaches in economics

Method        Reference                   Considered problem

AHP           Ananda and Herath           AHP is used to
              (2008)                      synthesise
                                          preferences related
                                          to regional forest
                                          planning and to

              Cebeci (2009)               Presented an
                                          approach to select a
                                          suitable enterprise
                                          resource planning
                                          system for textile
                                          industry. Fuzzy AHP
                                          method is applied.

              Wu et al. (2009)            Fuzzy AHP (FAHP) and
                                          the three MCDM
                                          analytical tools of
                                          SAW, TOPSIS, and
                                          VIKOR were
                                          respectively adopted
                                          to rank the banking
                                          performance and
                                          improve the gaps
                                          with three banks.

              Podvezko (2009)             Application of AHP
                                          technique to more
                                          complicated cases is

              Colombo et al.              Proved that
              (2009)                      judicious use of AHP
                                          by experts can, in
                                          this instance, be
                                          used to represent
                                          citizens' views.

              Maskeliunaite et al.        Problem of quality
              (2009)                      of passenger

              Podvezko et al.             Contracts' ranking

              Stemberger et al.           Applied in business
              (2009)                      processes

              Sivilevicius and            Problem of improving
              Maskeliunaite (2010)        the quality for

              Bojovic et al.              Determination of an
              (2010)                      optimal rail freight
                                          car fleet

              Steuten et al.              AHP weights are used
              (2010)                      to fill missing gaps
                                          in Markov decision

              Hadi-Vencheh and            An improved voting
              Niazi--Motlagh              AHP-data envelopment
              (2011)                      analysis methodology
                                          for suppliers

              Yan et al. (2011)           Presented new
                                          developments and
                                          maintenances of the
                                          under limited
                                          government budget
                                          and time

UTA           Gomes and Rangel            An application of
              (2009)                      the UTA method and
                                          its variant UTA-CR
                                          to determine utility
                                          functions for the
                                          multiple criteria
                                          evaluation of
                                          residential real

COPRAS        Ginevicius and              Evaluation of banks
              Podvezko (2008)             from the Perspective
                                          of their reliability
                                          for clients

              Datta et al. (2009)         Determining
                                          compromise towards
                                          the selection of

              Bindu Madhuri et al.        Selection of
              (2010)                      alternatives based
                                          on COPRAS-G and AHP

              Uzsilaityte and             Comparison of
              Martinaitis (2010)          different
                                          alternatives for the
                                          renovation of
                                          buildings, taking
                                          into account energy,
                                          economic and
                                          criteria while
                                          evaluating impact of
                                          renovation measures
                                          during their life

              Chatterjee et al.           Material selection
              (2011)                      based on COPRAS and
                                          EVAMIX methods

              Karbassi et al.             Effectiveness
              (2011)                      problem of energy
                                          using in buildings

              Podvezko (2011)             The Comparative
                                          Analysis of MCDA
                                          Methods SAW and

TOPSIS        Jakimavicius and            Developed approach
              Bu-rinskiene (2007)         of automobile
                                          transport system

              Arslan and Aydin            Two real military
              (2009)                      problems are solved
                                          by an ideal point
                                          algorithm and an
                                          outranking method.
                                          Fuzzy sets are

              Jakimavicius and            Computed ranks for
              Burinskiene (2009)          transport zones of
                                          city according to
                                          accessibility and
                                          city statistics

              Liaudanskiene et al.        Selection of the
              (2009)                      most effective
                                          alternative in

              Wu et al. (2009)            Fuzzy AHP (FAHP) and
                                          the three MCDM
                                          analytical tools of
                                          SAW, TOPSIS, and
                                          VIKOR were
                                          respectively adopted
                                          to rank the banking
                                          performance and
                                          improve the gaps
                                          with three banks.

              Liu (2009)                  Explored the
                                          decision making
                                          problem based on the
                                          interval vague value

              Cokorilo et al.             Determining the
              (2010)                      optional solution
                                          from the existing

              Rudzianskaite              The problem of
              Kvaraciejiene et al.        selecting the most
              (2010)                      effective road
                                          investment projects.

              Ginevicus et al.           Formation of the
              (2010)                      integrated
                                          competitive strategy
                                          of an enterprise
                                          under the conditions
                                          of oligopoly market.
                                          SAW, VIKOR and
                                          TOPSIS are used.

              Jin and Liu (2010)          The extended TOPSIS
                                          method is proposed
                                          to solve
                                          group decision
                                          making problems when
                                          the attribute values
                                          take the form of
                                          interval grey
                                          linguistic variables
                                          and attribute weight
                                          is unknown.

              Liu and Liu (2010)          A relative approach
                                          degree method of
                                          grey relation
                                          projection is
                                          presented to deal
                                          with multiple
                                          attribute making, in
                                          which the attribute
                                          weight is unknown
                                          and attribute value
                                          is hybrid index.

              Han and Liu (2011)          Modified fuzzy
                                          TOPSIS is applied

ARAS          Bakshi and Sarkar           Performance
              (2011)                      evaluation of

              Balezentis and              Integrated
              Balezentis (2011)           assessment of
                                          economic sectors

SAW           Jakimavicius and            Developed mechanism
              Burinskiene (2007)          of automobile
                                          transport system

              Zvirblis and                Integrated
              Zinkeviciute (2008)         evaluation of the
                                          macro environment of
                                          companies was

              Jakimavicius and            Computed ranks for
              Burinskiene (2009)          transport zones of
                                          city according to
                                          accessibility and
                                          city statistics

              Shevchenko et al.           Comparative analysis
              (2008)                      (CLARA and SAW
                                          methods) of variants
                                          of investment
                                          classified risks

              Wu et al. (2009)            Fuzzy AHP (FAHP) and
                                          the three MCDM
                                          analytical tools of
                                          SAW, TOPSIS, and
                                          VIKOR were
                                          respectively adopted
                                          to rank the banking
                                          performance and
                                          improve the gaps
                                          with three banks.

              Zvirblis and Buracas        Research and
              (2010)                      evaluation of State
                                          financial markets

              Ginevicius et al.           Forming the
              (2010)                      integrated
                                          competitive strategy
                                          of an enterprise
                                          under the conditions
                                          of oligopoly market.
                                          SAW, VIKOR and
                                          TOPSIS are used.

              Podvezko (2011)             The Comparative
                                          Analysis of MCDA
                                          Methods SAW and

ELECTRE       Thiel (2008)                Peculiarities of
                                          method applying

              Ulubeyli and Kazaz          Selection problem

              Radziszewska-Zielina        Partner selection
              (2010)                      problem

              Wachowicz (2010)            ELECTRE-TRI method
                                          applied. Two authors
                                          introduced their own
                                          procedures that can
                                          be applied in the
                                          phase for eliciting
                                          preferences and
                                          building the offer
                                          scoring systems for
                                          the parties.

              Bojkovic et al.             Transport as an
              (2010)                      economic activity
                                          having complex
                                          interactions with
                                          the environment was

              Kaya and Kahraman           AHP and ELECTRE
              (2011)                      methods applied to
                                          assessment of
                                          E-banking Sector

PROMETHEE     Nowak (2005)                Investment evaluation

              Mitkova and                 The results from two
              Mlynarovic (2007)           methodological
                                          approaches to the
                                          analysis of
                                          performance and risk
                                          of private pension
                                          funds in the Slovak
                                          Republic are
                                          presented: (1)
                                          multiple criteria
                                          decision model, and
                                          methodology, (2)
                                          modern portfolio
                                          theory to analyze
                                          pension funds in a
                                          risk-return space.

              Palma et al. (2007)         Multi-criteria
                                          analysis was used to
                                          evaluate the
                                          performance of
                                          silvoarable agro
                                          forestry on
                                          hypothetical farms
                                          in nineteen
                                          landscape test sites
                                          in Spain.

              Ghazinoory et al.           Different areas of
              (2009)                      nanotechnology for
                                          Iranian economy
                                          considering other
                                          strategies and the
                                          results of PROMETHEE
                                          method are

              Tomic-Plazibat et           Assessed
              al. (2010)                  country-risk of
                                          sixteen Central,
                                          Baltic and
                                          South-East European
                                          countries, for 2005
                                          and 2007, using
                                          multivariate cluster

              Podvezko and                Reveals influence of
              Podviezko (2010)            the choice of
                                          preference functions
                                          and their parameters
                                          on the outcome of

              Juan (2010)                 Porter's diamond
                                          model of competitive
                                          advantage is applied
                                          to establish
                                          evaluating criteria
                                          on urban
                                          quality, and a fuzzy
                                          set theory combining
                                          the PROMETHEE method
                                          is used to determine
                                          the priority of

MOORA         Brauers and                 Robustness in
              Ginevicius (2009)           regional development

              Brauers et al.              Assessment of
              (2010)                      regional and

              Brauers and                 Example of project
              Zavadskas (2010)            management under
                                          multiple objectives
                                          and MULTIMOORA is

              Ivanov and Stanujkic        Software selection

              Brauers and                 The economy of the
              Ginevicius (2010)           Belgian regions is
                                          tested with

              Garcia Alcaraz et           Evaluation of
              al. (2010)                  feasible
                                          alternatives and
                                          selection problem

              Chakraborty (2011)          Applications of the
                                          method in

              Brauers et al.              MULTIMOORA with
              (2011)                      fuzzy number theory
                                          applied to EU member
                                          states assessment

VIKOR         Ginevicius and              Evaluated financial
              Podvezko (2006)             state of enterprises
                                          from various

              Antucheviciene and          Modelling
              Zavadskas (2008)            multidimensional
                                          redevelopment of
                                          derelict buildings.
                                          Fuzzy VIKOR is

              Wu et al. (2009)            Fuzzy AHP (FAHP) and
                                          the three MCDM
                                          analytical tools of
                                          SAW, TOPSIS, and
                                          VIKOR were
                                          respectively adopted
                                          to rank the banking
                                          performance and
                                          improve the gaps
                                          with three banks.

Game theory   Ginevicius et al.           Forming the
              (2010)                      integrated
                                          competitive strategy
                                          of an enterprise
                                          under the conditions
                                          of oligopoly market.
                                          SAW, VIKOR and
                                          TOPSIS are used.

              Ginevicius and              Duopoly market
              Krivka (2008)               analysis

              Zavadskas and               Peculiarities of
              Turskis (2008)              problem solution

              Stein (2010)                Determined agents'
                                          strategies based on
                                          intended but bounded

              Stein and Ginevicius        Presented round
              (2010)                      based games in which
                                          the present values
                                          change and influence
                                          the cooperative

              Kaplinski and               Game theory
              Tamosaitiene                applications for
                                          management problems
                                          solution (2010)
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Author:Zavadskas, Edmundas Kazimieras; Turskis, Zenonas
Publication:Technological and Economic Development of Economy
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Geographic Code:4EXLT
Date:Jun 1, 2011
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