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Fuzzy systems: an overview.

Born in the United States around 1965, fuzzy set theory has grown to become a major scientific domain collectively referred to in this article as "fuzzy systems," which include fuzzy sets, logic, algorithms, and control. For the past few years, particularly in Japan, approximately 1,000 commercial and industrial fuzzy systems have been successfully developed. The number of industrial and commercial applications worldwide appears likely to increase significantly in the near future (see Table 1) [6, 18]. Interest in the U.S. and other countries has also been growing recently, as indicated by both the first IEEE conference on fuzzy systems held in March 1992 and the first IEEE Transactions on Fuzzy Systems, which premiered in February 1993 (see Table 2). This article presents an overview of fuzzy systems, covering issues such as basic concepts, currently successful areas and examples, and some fundamentals. Also included is a brief tutorial on fuzzy sets, logic, and control.

The most successful domain has been in fuzzy control of various physical or chemical characteristics such as temperature, electric current, flow of liquid/gas, motion of machines, etc. Also, fuzzy systems can be obtained by applying the principles of fuzzy sets and logic to other areas, for example, fuzzy knowledge-based systems such as fuzzy expert systems which may use fuzzy if-then rules; "fuzzy software engineering" which may incorporate fuzziness in programs and data; fuzzy databases which store and retrieve fuzzy information; fuzzy pattern recognition which deals with fuzzy visual or audio signals; applications to medicine, economics, and management problems which involve fuzzy information processing (see Tables 3 and 4).

Although there are numerous fuzzy systems in many application types and domains, most of them are based on a relatively simple idea. A fuzzy system allows a gradual and continuous transition, say, from 0 to 1, rather than a crisp and abrupt change between binary values of 0 and 1. (For more on the basics, see the sidebar "A Tutorial on Fuzzy Sets, Logic, and Control.")

There are certain particular characteristics of fuzzy systems that give them better performance for specific applications. In general, fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive. For example, the input and parameter values of a system may involve fuzziness, be inaccurate, or incomplete. Similarly, the formulas or inference rules to derive conclusions may be incomplete or inaccurate. Fuzzy logic allows decision making with estimated values under incomplete information. Note that the decision may not be correct and can be changed at a later time when additional information is available. Complete lack of information will not support any decision making using any form of logic. For difficult problems, conventional nonfuzzy methods are usually expensive and depend on mathematical approximations (e.g., linearization of nonlinear problems), which may lead to poor performance. Under such circumstances, fuzzy systems often outperform conventional methods such as a proportional, integral, and differential (PID) control.

Fuzzy system approaches also allow us to represent descriptive or qualitative expressions such as "slow" or "moderately fast," and these are easily incorporated with symbolic statements. These expressions and representations are more natural than mathematical equations for many human judgmental rules and statements.

When fuzzy systems are applied to appropriate problems, particularly the type of problems described previously, their typical characteristics are faster and smoother response than with conventional systems. This translates to efficient and more comfortable operations for such tasks as controlling temperature, cruising speed, for example. Furthermore, this will save energy, reduce maintenance costs, and prolong machine life. In fuzzy systems, describing the control rules is usually simpler and easier, often requiring fewer rules, and thus the systems execute faster than conventional systems. Fuzzy systems often achieve tractability, robustness, and overall low cost. In turn, all these contribute to better performance. In short, conventional methods are good for simpler problems, while fuzzy systems are suitable for complex problems or applications that involve human descriptive or intuitive thinking.

Fuzzy System Application Examples

In this section, sample fuzzy systems that set a trend in business thinking and adoption of fuzzy technology for industry are described to provide insight and background about the technology and its growth.

Historical Examples

Cement Kiln. Fuzzy techniques were used to implement an expert system, called Linkman, by Blue Circle Cement and SIRA in Denmark. The system incorporates the experience of operators in a cement production facility and has been in operation since 1982, making it the first major industrial fuzzy system application. A clinker, which mixes the ingredients of cement, grinds more efficiently with a smoother control. Conventional techniques were abandoned due to lack of a good mathematical model of a clinker kiln. This application has shown that fuzzy can be a money-making technology with many side benefits.

Sendai Subway. The most celebrated fuzzy logic application, the Sendai Subway Automatic Train Operations Controller, captured the attention of all control engineers around the world. It challenged the common belief that the fuzzy logic-based approach could not be used in a safety-driven situation. The Hitachi team designed, developed, and compared fuzzy and conventional PID-type controllers in 300,000 simulation tests, as well as 3,000 riderless subway runs with real hardware. Strategies used by experienced train operators were implemented in fuzzy rules that performed a "predictive fuzzy control." Speed control during cruising, braking control near station zones, and switching of control were determined by fuzzy rules that processed sensor measurements and considered factors such as comfort and safety of travellers. In operation since 1986, this controller has reduced the stop-gap distance 2.5 times, doubled the comfort index, and reduced power consumption by 10%. Based on this successful experience, Hitachi is granted a license to implement a similar controller for the Tokyo subway.

Yamaichi Fuzzy Fund. This is a premier financial application for trading systems. It handles 65 industries and a majority of the stocks listed on Nikkei Dow and consists of approximately 800 fuzzy rules. Rules are determined monthly by a group of experts and modified by senior business analysts as necessary. The system was tested for two years, and its performance in terms of the return and growth exceeds the Nikkei Average by over 20%. While in testing, the system recommended "sell" 18 days before the Black Monday in 1987. The system went to commercial operations in 1988. All financial analysts including Western analysts will agree that the rules for trading are all "fuzzy."

Recent and Just-Around-The-Corner Examples

Home Appliances. In 1990, fuzzy logic was implemented in a wide range of home electric appliances in Japan, such as refrigerators, vacuum cleaners, washers, dryers, rice cookers, and air conditioners. "Fuzzy" became a commercial buzzword, and the year 1990 is called the "Fuzzy Logic Year" in Japan.

Video Cameras. Four video-camera applications based on fuzzy logic principles, the fuzzy automatic focusing, automatic exposure, automatic white balancing, and image stabilization systems, have been successfully implemented into products. The autofocus technique utilizes approximate measure of sharpness in fuzzy rules to control the motor speed, improves quality of focus, and reduces the focusing time. A total of 13 simple rules such as "If the sharpness is high and its differential is low then the focus motor speed is low" resulted in reduced hunting time, power savings, and motor wear and tear. The image stabilization successfully detects unwanted movements caused by bumping and bouncing of platforms and jitters caused by shaking hands, then corrects the shaken image as much as possible.

Automotive. Several fuzzy control applications to automobiles have been under way in Japan. The first fuzzy-controlled device on a car, a fuzzy cruise control, was marketed in May 1991. Others under study include fuel injection and transmission and brake systems. The transmission systems provide a smoother ride with a more human-like shifting pattern and reduce wear on the hardware. Testing and evaluation of fuzzy transmission is not complete, but initial results show a distinct reduction in the frequency of shifts in a varied terrain. U.S. automotive manufacturers are considering fuzzy concepts for cruise control, engine spark advance, engine idling, and active shock absorption.

Robotics. Fuzzy logic-based robotic control that can provide just-in-time manufacturing capability is expected soon, as evidenced by special sessions on robotic control at the FUZZ-IEEE 92 and FUZZ-IEEE 93 conferences. Robotic vision applications are expected to arrive in the near future and enhance our daily lives, especially from the viewpoint of security and crime detection.

Aerospace. Boeing, United Technology, and other aerospace companies have committed significant resources to become competitive in the marketplace. A number of fuzzy logic algorithms and applications to space-related control problems have been investigated at NASA in recent years. In NASA space shuttle flights during 1992 and 1993, experimental payloads flew with fuzzy logic-based temperature control devices. The requirement for these thermoelectric devices is to maintain temperature within 0.1[degree] Celsius accuracy over the operating range of 1 to 40. Conventional off-the-shelf hardware could not provide this accuracy because of long delay time and system behavior.

Other Applications. Research activities in the U.S., Europe, and Pacific Rim countries include control of alternating current induction motors for efficiency optimization and better control at lower speeds; audio and video data compression using fuzzy algorithms (e.g., HDTV); engine spark advance control; robotic arm movement control; and total coordination between visual sensors and mechanical motion. Computer vision, personal computing, telecommunication including mobile network, and just-in-time manufacturing are considered primary areas of focus for fuzzy logic applications. In the area of consumer appliances, suitability of fuzzy and neurofuzzy control for smart appliances and comfort maintenance for homes at a lower power consumption level have been investigated.

As the demand for computer information storage increases, hard disk drive manufacturers are pressed to bring high-performance gigabyte drives to the market. A conceptual fuzzy logic controller for a dual actuator servo for the optical disk has been developed and tested in simulation to achieve very high positioning accuracy [21,22]. Similar development for regular disk drives is forthcoming.

Hybrid Systems--Important Future Directions

The most active recent trend is various forms of hybrid systems of fuzzy logic and other areas such as neural networks and genetic algorithms.

Fuzzy-Neural Net Hybrid Systems

There have been many research works suggesting that various forms of combined uses of fuzzy logic and neural networks are complementary techniques [2, 7, 10, 14, 20]. The fundamental concept of such hybrid systems is to complement each other's weaknesses, thus creating new approaches to solve problems. For example, there are no capabilities of machine learning, memory, or pattern recognition in fuzzy systems. Fuzzy systems with neural networks may add such capabilities, and in fact recent commercial applications of neural networks in Japan are mostly tied to fuzzy control [1]. The current stage of such neural network systems is relatively simple for real-world applications, however, and some people say their functions are mostly "tuning" rather than "learning." Several applications have shown the advantages of neural networks in mapping nonlinear behavior of systems to predict future states, monitor the system behavior, and anticipate failures.

Fuzzy-Genetic Algorithm Hybrid Systems

Applications of genetic algorithms combined with fuzzy control are being investigated not only at the academic level but also at the commercial level. Genetic algorithms are particularly well suited for tuning the membership functions in terms of placing them in the universe of discourse. Properly configured genetic algorithm/fuzzy architectures search the complete universe of discourse and find adequate solutions according to the fitness function [5].

Fuzzy-PID Hybrid Systems

For certain applications, fuzzy and PID systems are employed together as a hybrid controller. A PID controller can be used for approximate and fast control, while a fuzzy system either tunes the PID gains or schedules the most appropriate PID controller for better performance.

Fundamental Issues

Problems and Limitations

Problems and limitations of fuzzy systems include:

(1) Stability: a major issue for fuzzy control. As described in the following text, there is no theoretical guarantee that a general fuzzy system does not go chaotic and stays stable, although such a possibility appears to be extremely slim from the extensive experience.

(2) Learning capability: Fuzzy systems lack capabilities of learning and have no memory as stated previously. This is why hybrid systems, particularly neurofuzzy systems, are becoming popular for certain applications.

(3) Determining or tuning good membership functions and fuzzy rules are not always easy. Even after extensive testing, it is difficult to say how many membership functions are really required. Questions such as why a particular fuzzy expert system needs so many rules or when can a developer stop adding more rules are not easily answered.

(4) There exists a general misconception of the term "fuzzy" as meaning imprecise or imperfect. Many professionals think that fuzzy logic represents some magic without firm mathematical foundation.

(5) Verification and validation of a fuzzy expert system generally requires extensive testing with hardware in the loop. Such luxury may not be affordable by all developers.

Stability, Controllability, and Observability

The notion of stability is well established in the classical control theory; and for a given linear system, several criteria of stability can be applied, and necessary computations can be performed. Similarly, the notion of controllability and observability is well established in the modern state-space theory. Using the linearized set of equations, proper parameters can be computed to show that the system behavior meets these criteria well. As a result of the complexity of mathematical analysis for fuzzy logic, stability theory requires further study, and issues such as controllability and observability have to be defined for fuzzy control systems.

Several techniques have been proposed for stability criteria for fuzzy systems [3, 8, 11, 16]. Importance of stability analysis is evident in a special session organized at the FUZZ-IEEE 93 conference, and we hope important results will appear soon that will establish fuzzy control at the same level as conventional control in terms of stability, observability, and controllability.

Fuzzy Versus Probability Theories

The continuous rather than crisp transition characteristics between 0 and 1 in fuzzy sets and logic is similar to probability theory. Additionally, the technique of deriving membership functions using the relative frequency distribution confuses developers and creates an impression that the fuzzy logic is another form of probability theory. This sometimes raises somewhat common and extensive debates of how fuzzy theory differs from probability. From a practical point of view, fuzzy systems have developed numerous new real-world applications, which would not have been realized by using probability theory. The most fundamental difference between fuzzy and probability theories is that the former deals with deterministic plausibility, while the latter concerns the likelihood of nondeterministic, stochastic events. For more on this subject, see [4], [10], and [25].

Notes on Developing Fuzzy Systems

Basic Steps for Developing a Fuzzy System

The basic steps are:

(1) Determine whether a fuzzy system is a right choice for the problem. If the knowledge about the system behavior is described in approximate form or heuristic rules, then fuzzy is suitable. Fuzzy logic is also useful in understanding and simplifying the processing when the system behavior requires a complicated mathematical model.

(2) Identify inputs and outputs and their ranges. Range of sensor measurements typically corresponds to the range of input variable, and the range of control actions provides the range of output variable.

(3) Define a membership function for each input and output parameter. How many membership functions are required is a choice of the developer and depends on the system behavior.

(4) Construct a rule base. It is up to the designer to determine how many rules are necessary and when to stop adding rules.

(5) Verify that the rule base output within its range for some sample inputs, and further validate that this output is correct and proper according to the rule base for the given set of inputs.

Common Development Methods

Many methods have been used to design, develop, and implement fuzzy systems--two common methods are described here. Researchers and application developers are now formulating methods that are based on system-engineering principles; however, the full development is expected to take some time.

Human Expert-Based Development.

Human expert-based development for fuzzy control systems is based on the observation that when a person who has operated (controlled) a system for a long time is asked about the methods he/she uses, the answers are frequently in a fuzzy rule form, such as:

If the pressure is too low, I increase the fuel flow.

This obviously maps well into a fuzzy rule with one input (pressure) and one output (fuel flow), each with one membership function defined on it (low (pressure) and increase (fuel flow)). These rules are formulated by the expert based on the experience in controlling the plant. If there are more parameters then the expert will enumerate them in some combination with some definition of the membership functions used. By interviewing an expert and gathering necessary information, a fuzzy system can be implemented to a) automate the control function, b) build an advisory system, or c) develop a monitoring system. This approach has been successfully used in many applications in Japan, particularly in those control functions which are very difficult to model. Experience gained by an operator in controlling a complex plant is easily transferred into an algorithm using fuzzy logic principles and its architecture. What is being exploited is the knowledge gained through long observation hours, its synthesis for plant behavior, and a controlling algorithm that provides adequate performance [15].

Cut-and-Try Development Method.

Cut-and-try is actually the most common approach used in the field to date. This approach breaks down into two distinct phases.

(1) Developer comes up with an initial control system that is an approximation of what is required.

(2) Developer then tunes this initial system to get a final fuzzy system.

In order to use this technique, a designer needs either a mathematical model of the system to be controlled or a large amount of historical data about the system. In either case, the first step is to analyze the model or data to find those regions of the input space where the "acceleration" is high--in other words, the bumps in the control surface.

Using graphical tools, a designer can generate appropriate charts and control surface plots and then determine the critical points in input space where acceleration is very high. On the control surface plot, the input values corresponding to bumps are critical input points, and bumps themselves are critical output points. Once the critical points are determined, appropriate membership functions can be formed. The belief value at the critical point is 1.0, and a suitable spread can be taken to drop the belief value to zero on both sides. For some membership spread, the belief value may remain at 1.0 and may not drop as it moves within the universe of discourse, thus, giving a "shouldered" membership function.

The next step is to form a grid of input membership functions, as done in the rule table. Then, an output membership function can be selected for each combination of input membership function. In short, one must fill the matrix. The result should be a fuzzy knowledge base that at least comes close to controlling the system.


The authors appreciate very much the support provided by Jack Aldridge, Hamid Berenji, Satoru Isaka, Michael Lembeck, Hideyuki Takagi, Kazuo Tanaka, and Lotfi A. Zadeh. Thanks also go to K. Hirota and M. Togai for helpful private communications to construct Table 1.

About the Authors:

TOSHINORI MUNAKATA is a professor of computer science in the Computer and Information Science department at Cleveland State University. Current research interests include applied artificial intelligence in the areas of fuzzy systems, neural networks, genetic algorithms and logic programming; and analysis of algorithms.

Author's Present Address: Computer and Information Science department, Cleveland State University, Cleveland, OH 44115; email:

YASHVANT JANI is the president of Togai InfraLogic. Current research interests include fuzzy systems, with emphasis on fuzzy control for industrial applications and governmental projects. Author's Present Address: Togai InfraLogic, 5 Vanderbilt, Irvine, CA 92718; email:


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Title Annotation:Cover Story; Artificial Intelligence; fuzzy logic-based systems
Author:Munakata, Toshinori; Jani, Yashvant
Publication:Communications of the ACM
Article Type:Technical
Date:Mar 1, 1994
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