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State of art surveys of overviews on MCDM/MADM methods.

Introduction

Humans make decisions all the time. Decision-making is a very complex and difficult task. During the past decades, operations research (OR) has come a long way as a field that supports scientific management. OR mainly deals with model building and algorithmic optimization procedures that facilitate the analysis of complex real-world problems (Zopounidis, Pardalos 2010). Since von Neumann and Morgenstern (1947) and Savage (1954), this has become the dominant paradigm in decision analysis and decision support in the presence of multiple evaluation dimensions. Traditional OR techniques fit the same purpose: they maximise or minimize a utility function in the presence of constraints. Multi-Criteria Decision Making (MCDM) can be said to be both old and new part of OR, depending on one's frame of reference (Koksalan et al. 2011). MCDM has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria (Triantaphyllou 2010). Many modern researchers have considered MCDM problems. MCDM refers to making decisions in the presence of multiple, usually conflicting, criteria. The past decades have seen a dramatic increase on all main areas of MCDM:

--Formal models (algorithms, procedures and selection paradigms);

--Evaluation theories (assumptions about values or preferences and structured representations of values or preferences);

--Assessment methodologies (elicitation, estimation and scaling of individuals' preferences, utilities and subjective probabilities in MCDM situations) (Fishburn 1978).

There is no unique and well-defined methodology that one could follow step-by-step from the beginning to the end of a decision aiding process. When dealing with objects that can only be described and compared using several characteristics, aggregation is a major issue: it aims at operating a synthesis of the, usually contradictory, features of the objects, in view of achieving a goal such as choosing among the objects, rank ordering them, sorting them into categories and so on (Bouyssou et al. 2006).

MCDM methods cover a wide range of quite distinct approaches. MCDM methods can be broadly classified into two categories: discrete MCDM or discrete MADM (Multi-attribute Decision Making) and continuous MODM (Multi-Objective Decision Making) methods (Fig. 1). A dictionary definition of a "criterion" is "a means or standard of judging" by which one particular choice or course of action could be judged to be more desirable than another (h). Each problem has multiple, usually conflicting objectives/criteria. Each objective/criterion has a different unit of measurement. MCDM can be perceived as a process of evaluating real-world situations based on various qualitative/quantitative criteria in certain/uncertain/ risky environments in order to find a suitable course of action/choice/strategy/policy among several available options (Raju, Kumar 2013).

[FIGURE 1 OMITTED]

MODM methods are associated with problems where alternatives are non-predetermined and the aim of the problem under consideration is to design the best/optimal alternative by considering a set of well-defined design constraints, a set of quantifiable objectives. Thus, MODM methods deal with the design process and the number of alternatives is infinite (continuous). It is a constant challenge for designers to select the best materials and constructions to satisfy complex design problems (Jahan, Edwards 2013).

MADM art is interrelated with art of the Rational Choice Theory. It assumes that people are motivated by money and by the possibility of making a profit, and this has allowed constructing formal and often predictive models of human behaviour. They act rationally within specific given constraints and based on the information that they have about the conditions under which they are acting. Human actions involve both rational and non-rational elements (Scott 2000). Rational choice theories maintain that individuals must anticipate the outcomes of alternative courses of action and calculate that which will be best for them. As it is not possible for individuals to achieve everything they want, they must also make choices in relation to both their goals and means for attaining these goals. Rational individuals choose the alternative that is likely to give them the greatest satisfaction. Although the expected utility model has many possible founders, Von Neumann and Morgenstern (1947) are usually credited for the first axiomatic foundation of expected utility measurement. Today, the expected utility model is widely used as the normative cornerstone of decision analysis (Keeney, Raiffa 1976).

1. Main ideas of overview

Zavadskas and Turskis (2011) published a review of MCDM methods. This study looks at long known and relatively recently published methods. Liou and Tzeng (2012) published an article, which was intended to review the multi-criteria techniques that Zavadskas and Turskis (2011) did not mention in their article. Lately, Liou (2013) summarized the Tzeng's research work. Therefore, this gave rise to an idea to investigate the existing situation with reviews on MCDM/MADM methods.

Discrete MCDM/MADM methods deal with discrete and predetermined alternatives, which are described by a determined discrete criteria set. The main task is:

--Rational selection among limited number of alternatives;

--Assessment and ranking of limited number of alternatives.

Recently, hundreds of publications have been published to provide information about MCDM methods, their development and application in different fields. This article provides an overview of the publication, which provides an overview of MCDM methods. The research is based on Web of Science database, which is a part of Thomson Reuters Web of Knowledge. The 1970s was an important decade for many seminal works. Foundations of modern MCDM were developed in 1950s and 1960s. Development of MCDM researches accelerated during the 80s and early 90s, and seems to have continued its exponential growth (Koksalan et al. 2011). Fig. 2 provides information about this from databases of reference for review of MCDM methods and their application.

The overview provides systematically classified information on MCDM reviews. They are grouped as shown in Fig. 3:

--Books on MCDM methods (Table 2);

--Articles on multi-criteria methods in scientific journals (Table 3);

--Articles on different MCDM approaches (Table 4);

--Comparative analysis of several MCDM methods (Table 5);

--MCDM review related with individual activity topics (Table 6).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

2. Main results

Table 1 provides information about the scope of the MCDM methods (Table 1). The total of 71 articles were found on the topic "MCDM review papers" in ISI Web of Science database (December 2013). However, there were only some articles that belonged to few different fields of the research area (Table 1).

The book by Koksalan et al. (2011) provides a brief history of the development of MCDM methods. It briefly describes the development of the area from ancient to modern times. Keeney and Raiffa (1976) formulated the basics of Decision with Multiple Objectives. Hwang and Masud (1979) provided review on development of MODM methods and applications in a relatively short period of time. Later, Hwang and Yoon (1981) reviewed the MADM methods (SAW, TOPSIS, ELECTRE, LINMAP).

Saaty (1980) published a detailed study on the analytic hierarchy process (AHP). Later, Saaty (1996) published a study on the further development of the Analytic Network Process (ANP) method. Zeleny (1982) published a book, which deals with the problem of compromise theory. Hwang and Lin (1987) published a study for Group Decision Making under multi-criteria. Roy (1996) summarized the information on ELECTRE group methods. Seminal studies have been prepared by Belton and Stewart (2002), Gal et al. (2009), Miettinen (2009). Brauers (2004) published a study on the basis of which MOORA and MULTIMOORA methods were developed. A great job was done by Figueira et al. (2005), Ehrgott et al. (2010), editing wide studies in which well-known scientists in this area published individual studies on different classes of MCDM methods.

Valuable studies were published by Triantaphyllou (2000, 2010). Hanne (2009) and Kaliszewski (2010) published a detailed study on soft computing intelligent strategies for Meta MCDM. Apparently, this is only a part of all existing noteworthy studies.

A number of books have been published, which contain detailed information about the MCDM approaches in separate specific areas of research. As an outcome of the development and growing application of MCDM methods, many specific subfields have emerged. Next, some of them are named: Ballestero and Romero (2009) analysed MCDM and its application to economic problems; Peldschus and Zavadskas (1997) analysed an application of discrete matrix games theory in construction and management; Chen and Li (2006) investigated applications of MCDM techniques in environmental management of construction; Zavadskas et al. (1994) applied MCDM in project construction; Venkata (2007) demonstrated how the graph theory and matrix approach as well as fuzzy MADM methods can be effectively used for decision-making in various situations of the manufacturing environment; Koo (2009) presented a study on the development of sustainability assessment model.

Table 3 provides information on reviews of general methods of MCDM. Only some have been listed. A seminal study by Bragge et al. (2012) has been recently published, which was carried out based on bibliometric study of MCDM methods prevalence. A large-scale survey was conducted by Toloie-Eshlaghy and Homayonfar (2011). It gives an overview of about 800 links. Zavadskas and Turskis (2011) provided an overview on MCDM methods based on the traditional classification (Hwang, Yoon 1981).

A number of publications can be found in regional journals, such as Alias et al. (2008), and several publications, which provide an overview on the theory of fuzzy MCDM applications, such as Chu, Lin (2009), El-Wahed (2008) and the analysis and classification of multi-criteria systems.

Significantly more review articles on separate MCDM methods (Table 4) have been published. Kaplinski and Tamosaitiene (2010) reviewed applications of discrete matrix game theory, Behzadian et al. (2010)--PROMETHEE method, and Behzadian et al. (2012)--TOPSIS method. Zopounidis and Doumpos (2002) conducted a review on a multi-criteria classification and sorting. Adler et al. (2002) reviewed the DEA method's applications. Shih (2008) conducted a review on TOPSIS group methods. Ishizaka, Labib (2011) and Ho (2008) publications were devoted to the analysis of AHP method. Jadhav and Rajendra Sonar (2009) overviewed MCDM software packages. Balezentis and Balezentis (2013) published a review article on MULTIMOORA method.

A significantly greater number of publications have been devoted to comparative analysis of separate MCDM methods (Table 5). Opricovic and Tzeng (2004) conducted a benchmarking on TOPSIS and VIKOR methods. Simanaviciene and Ustinovicius (2012) provided a benchmarking on TOPSIS, SAW and COPRAS methods. Podvezko (2011) conducted a comparative study of SAW and COPRAS methods and Podviezko (2012) provided a comparative study on SAW, PROMETHEE, TOPSIS, and COPRAS methods. Albinana and Vila (2012) conducted benchmarking on VIKOR, ELECTRE, COPRAS, and EVAMIX methods. A benchmarking MOORA, AHP, TOPSIS, VIKOR, ELECTRE and PROMETHEE methods has been provided by Chakraborty (2011). Interesting and valuable work in the field of MCDM benchmarking has been performed by Kou et al. (2012), Peng et al. (2011), Balezentis et al. (2012) and Stanujkic et al. (2012). Antucheviciene et al. (2011, 2012) carried out investigation on fuzzy MCDM methods (TOPSIS, VIKOR and COPRAS) and provided a comparative analysis. A large number of valuable works has been conducted, which enables us to evaluate the positive and negative characteristics of different MCDM methods and their ability to help solving real practical problems in different areas.

Reviews on topics of individual activities can be identified into a separate group of reviews on MCDM methods. Ehrgott et al. (2004), Xidonas and Psarras (2009) applied the MCDM methods to portfolio optimization and management; Jahan et al. (2010)--material choosing and screening; Diaz-Balteiro and Romero (2008)--forestry-related decisions; Ananda and Herath (2009)--forest management and planning. Greening and Bernow (2004) applied the MCDM methods to design of Coordinated Energy and Environmental Policy; Moffett and Sarkar (2006)--design of conservation area networks. Kaplinski and Tupenaite (2011) reviewed the latest MCDM applications in modern construction economics. Wang et al. (2009) and Yazdani-Chamzini et al. (2013) reviewed MCDM applications for energy systems assessment. Kaplinski and Peldschus (2011) and Tamosaitiene and Kaplinski (2013) reviewed the applications of MCDM methods in the social sciences; Zavadskas et al. (2008) reviewed the applications of MCDM methods in the area of bridge and road construction; and Huang et al. (2011)--MCDM methods in the social sciences.

Conclusions

The paper presents synopsis of numerous publications, which describe the use of traditional MCDM methods and some of the relatively recently developed methods. However, this review does not cover recent methods that have not yet been reviewed in articles or books. However, it is worth noting that publications reviewed in this article at least allow for a partial representation of the structure of those MCDM methods, which are gaining wider use.

Recently, development of hybrid and modular methods is becoming increasingly important. They are based on previously developed well-known methods, such as TOPSIS, SAW, DEA, AHP, ANP, VIKOR, DEMATEL, DEA, PROMETHEE, ELECTRE and their modification, by applying fuzzy and grey number theory. Relatively recently developed MCDM methods, such as COPRAS, ARAS, MOORA, MULTIMOORA, SWARA and WASPAS are rapidly developed and applied to solve real life problems. In order to help researchers and practitioners interested in hybrid MCDM techniques and applications of hybrid MCDM methods, it is necessary to publish reviews on these issues in future.

Caption: Fig. 1. Broad classification of MCDM methods

Caption: Fig. 2. Number of publications on topic: review papers on MCDM methods (based on ISI Web of Science database)

Caption: Fig. 3. Five-step pyramid of MCDM reviews

doi:10.3846/20294913.2014.892037

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Wang, J.-J.; Jing, Y.-Y.; Zhang, C.-F.; Zhao, J.-H. 2009. Review on multi-criteria decision analysis aid in sustainable energy decision-making, Renewable and Sustainable Energy Reviews 13(9): 2263-2278. http://dx.doi.org/10.1016/j.rser.2009.06.021

Xidonas, P.; Psarras, J. 2009. Equity portfolio management within the MCDM frame: a literature review, International Journal of Banking, Accounting and Finance 1(3): 285-309.

Yazdani-Chamzini, A.; Fouladgar, M. M.; Zavadskas, E. K.; Moini, S. H. H. 2013. Selecting the optimal renewable energy using multi criteria decision making, Journal of Business Economics and Management 14(5): 957-978. http://dx.doi.org/10.3846/16111699.2013.766257

Zavadskas, E. K.; Liias, R.; Turskis, Z. 2008. Multi-attribute decision-making methods for assessment of quality in bridges and road construction: state-of-the-art surveys, The Baltic Journal of Road and Bridge Engineering 3(3): 152-160. http://dx.doi.org/10.3846/1822-427X.2008.3.152-160

Zavadskas, E.; Peldschus, F.; Kaklauskas, A. 1994. Multiple criteria evaluation of projects in construction. Vilnius: Technika. 226 p.

Zavadskas, E. K.; Turskis, Z. 2011. Multiple criteria decision making (MCDM) methods in economics: an overview, Technological and Economic Development of Economy 17(2): 397-427. http://dx.doi.org/10.3846/20294913.2011.593291

Zeleny, M. 1982. Multiple criteria decision making. New York: McGraw-Hill. 563 p.

Zopounidis, C.; Doumpos, M. 2002. Multicriteria classification and sorting methods: a literature review, European Journal of Operational Research 138(2): 229-246. http://dx.doi.org/10.1016/S0377-2217(01)00243-0

Zopounidis, C.; Pardalos, P. M. (Eds.). 2010. Handbook of multicriteria analysis. Berlin, Heidelberg: Springer-Verlag. 455 p. http://dx.doi.org/10.1007/978-3-540-92828-7

Received 31 December 2012; accepted 31 January 2014

Edmundas Kazimieras ZAVADSKAS, Zenonas TURSKIS, Simona KILDIENE

Department of Construction Technology and Management, Faculty of Civil Engineering, Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania

Corresponding author Simona Kildiene

E-mail: simona.kildiene@vgtu.lt

Edmundas Kazimieras ZAVADSKAS. PhD, DSc, h.c.multi. Prof., the Head of the Department of Construction Technology and Management of Vilnius Gediminas Technical University, Lithuania. Senior Research Fellow at the Research Institute of Smart Building Technologies. PhD in Building Structures (1973). Dr Sc. (1987) in Building Technology and Management. A member of Lithuanian and several foreign Academies of Sciences. Doctore Honoris Causa from Poznan, Saint Petersburg and Kiev universities. The Honorary International Chair Professor in the National Taipei University of Technology. A member of international organizations; a member of steering and programme committees at many international conferences; a member of the editorial boards of several research journals; the author and co-author of more than 400 papers and a number of monographs in Lithuanian, English, German and Russian. Editor-in-chief of journals Technological and Economic Development of Economy and Journal of Civil Engineering and Management. Research interests: building technology and management, decision-making theory, automation in design and decision support systems.

Zenonas TURSKIS. PhD from VISI (Vilnius Engineering Construction Institute, former name of Vilnius Gediminas Technical University). He works at the Construction Department of Vilnius Gediminas Technical University. He has more than 100 publications in journals such as International Journal of Information Technology & Decision Making, Economic Research, Journal of Economic Computation and Economic Cybernetics Studies and Research (ECECSR) and more. His research interests include automated programming, technological decision multicriteria evaluation in construction and investment areas.

Simona KILDIENE. PhD student at the Department of Construction Technology and Management of Vilnius Gediminas Technical University, Vilnius, Lithuania. Master of Science (construction engineering), VGTU, 2010. Bachelor of Science (construction management), VGTU, 2008. Research interests include construction economics, construction management, multiple criteria analysis and decision-making theories.
Table. 1. Number of publications by research area MCDM review papers
(from database ISI Web of Science)

                                                   Number of
MCDM review papers                                publications


Energy fuels                                           18
Operations research management science                 17
Management                                             12
Environmental sciences, Ecology                        10
Economics                                              5
Environmental sciences                                 5
Computer science artificial intelligence               3
Engineering Electrical Electronic                      3
Biodiversity Conservation                              2
Computer science information systems                   2
Ecology                                                2
Environmental studies                                  2
Geography                                              2
Geography physical                                     2
Agronomy                                               1
Business                                               1
Chemistry Physical                                     1
Computer Science interdisciplinary application         1
Computer Science Software Engineering                  1
Computer Science Theory Methods                        1
Construction Building Technology                       1
Engineering Civil                                      1
Engineering Industrial                                 1
Engineering Manufacturing                              1
Forestry                                               1
Forestry                                               1
Health Care Sciences Service                           1
Information Science Library Science                    1
Mathematics Applied                                    1
Metallurgy Metallurgical Engineering                   1
Mining Mineral Processing                              1
Obstetrics Gynaecology                                 1
Planning Development                                   1
Public Environmental Occupational Health               1
Statistics Probability                                 1
Urban Studies                                          1
Water Resources                                        1

Table 2. Books on MCDM methods

Reference                               Considered problem

Keeney, Raiffa 1976            Decision with MODM

Hwang, Masud 1979              MODM methods

Saaty 1980                     The analytic hierarchy process

Hwang, Yoon 1981               MADM

Zeleny 1982                    MCDM

Hwang, Lin 1987                Group MCDM

Zavadskas et al. 1994          Multi-criteria evaluation of projects
                               in construction

Roy 1996                       Multicriteria methodology for decision
                               aiding

Saaty 1996                     Decision making with dependence and
                               feedback

Peldschus, Zavadskas 1997      Matrix games in building technology and
                               management

Triantaphyllou 2000            MCDM methods

Belton, Stewart 2002           Multiple criteria decision analysis

Figueira et al. (Eds.) 2005    Multiple criteria decision analysis

Bouyssou et al. 2006           Evaluation and decision models with
                               multiple criteria: stepping stones for
                               the analyst

Chen, Li 2006                  Environmental management in
                               construction

Kahraman 2008                  Fuzzy MCDM

Gal et al. 2009                Multi-criteria decision making advances
                               in MCDM models, algorithms, theory and
                               applications

Hanne 2009                     Intelligent strategies for meta MCDM

Koo 2009                       Development of sustainability
                               assessment model

Miettinen 2009                 Nonlinear multi objective optimization

Ballestero, Romero 2010        MCDM and its applications to economic
                               problems

Ehrgott et al. 2010            Trends in multiple criteria decision
                               analysis

Kaliszewski 2010               Soft computing for complex multiple
                               criteria decision making

Pedrycz et al. 2010            Decision-making in system project,
                               planning, operation, and control:
                               motivation, objectives, and basic
                               concepts offuzzy MCDM

Triantaphyllou 2010            MCDM methods: a comparative study

Zopounidis, Pardalos 2010      Multi-criteria analysis

Koksalan et al. 2011           MCDM

Tzeng, Huang 2011              MADM

Doumpos, Grigoroudis 2013      Recent advances in intelligent decision
                               making and presentation of hybrid
                               models and algorithms for preference
                               modelling and optimisation problems

Ishizaka, Nemery 2013          Multi-criteria decision analysis

Larichev, Olson 2001           Multiple criteria analysis in strategic
                               siting problems

Table 3. General reviews on MCDM in articles of scientific journals

Reference                               Considered problem

Manouselis, Costopoulou 2007    Analysis and classification of
                                multi-criteria recommender systems

El-Wahed 2008                   Intelligent fuzzy MCDM

Chu, Lin 2009                   An extension to fuzzy MCDM

Zavadskas, Turskis 2011         Multiple criteria decision making
                                (MCDM) methods in economics

Bragge et al. 2012              Scholarly communities of research in
                                multiple criteria decision making: a
                                bibliometric research profiling study

Liou, Tzeng 2012                Multiple criteria decision making
                                (MCDM) methods in economics

Liou 2013                       New concepts and trends of MCDM

Aruldoss et al. 2013            A survey on multi criteria decision
                                making methods and its applications

Table 4. Overview on application of different MCDM methods

Reference                                Considered problem

Adler et al. 2002               Data Envelopment Analysis (DEA)

Zopounidis, Doumpos 2002        Multicriteria classification and
                                sorting methods

Ho 2008                         Integrated analytic hierarchy process

Shih 2008                       MCDM with an application to group
                                TOPSIS

Jadhav, Rajendra Sonar 2009     Software packages

Cook, Seiford 2009              Data envelopment analysis (DEA)

Kaplinski, Tamosaitiene 2010    Game theory application

Behzadian et al. 2010           PROMETHEE

Ishizaka, Labib 2011            Analytic hierarchy process

Behzadian et al. 2012           A state-of the-art survey of TOPSIS
                                applications

Balezentis, T.,                 Applications of the multi criteria
Balezentis, A. 2013             decision making method MULTIMOORA

Table 5. Comparative analysis of MCDM methods

Reference                              Considered problem

Kou et al. 2012              Evaluation of classification algorithms
                             using MCDM and rank correlation

Peng et al. 2011             FAMCDM

Podvezko 2011                Comparative analysis SAW and COPRAS

Antucheviciene et al. 2012   Comparative analysis of FTOPSIS, FVIKOR
                             and COPRAS-F

Antucheviciene et al. 2011   Measuring congruence of ranking results
                             applying particular MCDM methods

Opricovic, Tzeng 2004        TOPSIS and VIKOR

Simanaviciene,               TOPSIS, SAW, COPRAS
Ustinovicius 2012

Chakraborty 2011             MOORA, AHP, TOPSIS, VIKOR, ELECTRE,
                             PROMETHEE

Balezentis et al. 2012       VIKOR, TOPSIS, ARAS

Albinana, Vila 2012          VIKOR, ELECTRE, COPRAS, EVAMIX

Stanujkic et al. 2012        Comparative analysis of some prominent
                             MCDM methods

Table 6. MCDM review on topics of individual activities

Reference                                Considered problem

Greening, Bernow 2004           Design of coordinated energy and
                                environmental policies

Melo et al. 2009                Facility location and supply chain
                                management

Moffett, Sarkar 2006            Design of conservation area networks

Ananda, Herath 2009             Forest management and planning

Diaz-Balteiro, Romero 2008      Forestry decisions

Ehrgott et al. 2004             Portfolio optimization

Ho et al. 2010                  Supplier evaluation and selection

Jahan et al. 2010               Material screening and choosing

Xidonas, Psarras 2009           Equity portfolio management

Kaplinski, Tupenaite 2011       Modern construction economics

Wang et al. 2009                Sustainable energy

Kaplinski, Peldschus 2011       Social science

Huang et al. 2011               Environmental sciences

Zavadskas et al. 2008           Quality in bridges and road
                                construction

Yazdani-Chamzini et al. 2013    Selecting the optimal renewable energy

Tamosaitiene, Kaplinski 2013    Application of MCDM methods in social
                                sciences

Kabir et al. 2013               A review of multi-criteria
                                decision-making methods for
                                infrastructure management
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Title Annotation:multi-criteria decision making; multi-attribute decision making
Author:Zavadskas, Edmundas Kazimieras; Turskis, Zenonas; Kildiene, Simona
Publication:Technological and Economic Development of Economy
Article Type:Report
Geographic Code:1USA
Date:Mar 1, 2014
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