From: rick@cs.arizona.edu (Rick Schlichting) Newsgroups: comp.research.japan,comp.ai.neural-nets,comp.ai Subject: Kahaner Report: Fuzzy-neural systems research in Asia. Message-ID: <28729@optima.cs.arizona.edu> Date: 22 Dec 92 03:49:07 GMT Followup-To: comp.research.japan [Dr. David Kahaner is a numerical analyst on sabbatical to the Office of Naval Research-Asia (ONR Asia) in Tokyo from NIST. The following is the professional opinion of David Kahaner and in no way has the blessing of the US Government or any agency of it. All information is dated and of limited life time. This disclaimer should be noted on ANY attribution.] [Copies of previous reports written by Kahaner can be obtained using anonymous FTP from host cs.arizona.edu, directory japan/kahaner.reports.] To: Distribution From: David K. Kahaner US Office of Naval Research Asia (From outside US): 23-17, 7-chome, Roppongi, Minato-ku, Tokyo 106 Japan (From within US): Unit 45002, APO AP 96337-0007 Tel: +81 3 3401-8924, Fax: +81 3 3403-9670 Email: kahaner@cs.titech.ac.jp Re: Fuzzy-neural systems research in Asia. 22 Dec 1992 This file is named "fuzzy.92" ABSTRACT. Overview of fuzzy-neural systems research based on examination of papers presented at three Asian conferences. A great deal of the current work is ad hoc and there is a need for more fundamental research to help explain and direct future activities. (Nguyen) This report was prepared by Prof Hung T. Nguyen LIFE Chair of Fuzzy Systems Department of Systems Science Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku Yokohama 227 JAPAN Tel: +81 45-922-1111 ext 2699; Fax: +81 45-922-1385 Prof Nguyen is on leave from the Mathematical Sciences Department of New Mexico State University. FUZZY-NEURO SYSTEMS: MAIN THRUST OF RESEARCH PRESENTED AT THREE CONFERENCES IN ASIA This report describes research trends surrounding the design of fuzzy-neuro systems as exemplified by works of Asian scientists presented at The International Symposium on Fuzzy Systems (Iizuka, Japan, July 1992), The 2nd International Conference on Fuzzy Logic and Neural Networks (Iizuka, Japan, July 1992) and The Korean Automatic Control Conference (Seoul, Korea, October 1992). By Hung T. Nguyen INTRODUCTION The papers presented at the above three Conference are published in (i) Proceedings of the International Symposium on Fuzzy Systems (July 12-15, 1992), Kyushu Institute of Technology, Iizuka, Fukuoka, Japan. Organizers: Takeshi Yamakawa and Eiji Uchino Kyushu Institute of Technology 680-4 Kawazu, Iizuka, Fukuoka 820, Japan. (2) Proceedings of the 2nd International Conference on Fuzzy Logic and Neural Networks (Iizuka '92), two volumes, published by Fuzzy Logic Systems Institute, 820-1 Yokota, Iizuka, Fukuoka 820, Japan. Organizer: Takeshi Yamakawa (3) Proceedings of the 1992 Korean Automatic Control Conference (International sessions), published by Korean Association of Automatic Control. General chairman of the Conference: Kyung-Gi Kim, Department of Electronics Engineering, Hanyang University, 17 Haendang-dong, Sungdong-ku, Seoul, Korea. The majority of papers were concerned with: Fuzzy Systems and Neural Networks, Fuzzy Logic Control, Fuzzy Modeling and Approximate Reasoning. In the following, we describe the above topics in some detail together with our comments. The general observation is this. Motivated by the industrial success of the fuzzy methodology in recent years, especially in Japan, researchers tend to look at practical problems in which ad-hoc design procedures can be proposed. We feel that this indicates a clear need for more basic research concerning general design methodology. FUZZY SYSTEMS AND NEURAL NETWORKS Neural networks process numerical information and exhibit learning capability. Fuzzy systems can process linguistic information and represent, say, experts' knowledge by fuzzy rules. Thus, it is not surprising that the fusion of these two technologies is the current research trend. The aim is to be able to create machines with more intelligent behavior. In the mentioned Conferences, one noticed the following motivation for considering both fuzzy systems and Neural Networks: (1) The Knowledge Base of a fuzzy system consists of a collection of "If... Then..." rules in which linguistic labels are modeled by membership functions. Neural Networks can be used to produce membership functions when available data are numerical. (2) Moreover, one can take advantage of the learning capability of neural networks to adjust membership functions, say in control strategies, to enhance control precision. (3) Neural Networks can be used to provide learning methods for fuzzy inference procedures. (4) In the opposite direction, one can use fuzzy reasoning architecture to construct new Neural Networks. (5) One can also fuzzify the Neural Networks architecture to enlarge the domain of applications. (6) The fusion of Neural Networks and Fuzzy Systems is essentially based upon the fact that Neural Networks can learn experts' knowledge (through numerical data) and Fuzzy Systems can represent experts' knowledge (through the representation of in-out relation by fuzzy reasoning). As in any science, practical successes call for theoretical justifications. While the above technologies have become firmly established in well defined domains of applications, only few theoretical results have been obtained. Theoretical results are needed, not only for explaining the successful results but also for guiding general design methodology for systems. The success of Neural Networks is explained by the universal approximation property (via Stove-Weierstrass theorem). However, there is no standard method for constructing the most suitable neural network structure, e.g. determining the number of neural units in hidden layers. Mathematically speaking, while the graphical form of Neural Networks indicates that such input-output maps can approximate continuous functions to any degree of accuracy, one still faces the practical problem: which specific network structure will actually do the job? reported by using simulations, either to demonstrate good performance or to make comparisons among various alternatives. The standard design of a fuzzy logic controller consists of selecting an suitable number of rules, assigning appropriate membership functions to linguistic labels (by various empirical techniques) and choosing an approximate reasoning procedure (i.e. choosing fuzzy logic connectives to combine evidence and a defuzzification mode to provide single output). (Results are also reported on the problem of stability of fuzzy feedback control). Some of the papers in these conferences emphasized the need for a clear design method for fuzzy controllers. Recall that when the controlled plant is too complex to postulate a mathematical model, but skilled human operators are available, one needs to represent experts' knowledge and reasoning for the purpose of automation. The fuzzy logic approach is attractive because of its ability to handle qualitative information. Again, various case-studies were reported, such as autonomous mobile robot, automatic combustion control systems, chemical control processes, batch culture, driving control of a car, etc. FUZZY MODELING By analogy with stochastic modeling, fuzzy modeling is referred to the art of systems modeling using Zadeh's theory of fuzzy sets and logic. For fuzzy systems in general, the situation is this. Consider an input-output map (a black box). Suppose we wish to describe this box by a set of "if... Then..." rules. Recall that fuzzy If... Then... rules are widely used in recent industrial applications because of their flexibility in representing the behavior of a complex system by using both qualitative experts' knowledge as well as numerical experimental data. First we have to identify the input and output variables. Next, we construct fuzzy rules. With regard to a dynamical system, this step is called identification. A theoretical question is: How many rules are needed to describe faithfully a system? Once a number of rules is fixed, one faces the problem of assigning membership functions to linguistic labels in rules. Here Neural Networks can be used to tune membership functions. From a commonsense viewpoint, membership functions can be modeled parametrically, i.e. they are known up to a finite number of numerical parameters. Thus, after the structural identification phase, one faces the parameter identification problem, i.e. determining (or estimating) the parameters involved in the membership functions. Some ad-hoc methods for identification of systems using fuzzy If... Then... rules were reported, for example fault diagnosis method, interior penalty method, fuzzy optimization method, etc.... Fuzzy modeling is particular important for designing control laws of dynamical plants without mathematical models. In such situations, one needs to identify the plant first and then derive control laws. This is referred to as fuzzy logic controllers based on fuzzy models (of the controlled plants). This important research area is still at its very beginning. It is anticipated that without fuzzy dynamical models, it is not clear how basic concepts such as stability and robustness in Fuzzy Control theory can be addressed. APPROXIMATE REASONING The inference engine of a fuzzy system is constructed using a logical process known as approximate reasoning. It is a generalization of classical deduction reasoning process. Basically an approximate reasoning procedure consists of the selection of an interpretation of "If... Then..." statements and a way to "fire" such rules. Unlike classical two-valued logic, a fuzzy implication can have various different interpretations, i.e. different mathematical "truth tables". Also, there are different ways to generalize the classical Modus Ponens. Even Zadeh's compositional rule of inference leaves room for various choices of fuzzy logical connectives. Thus the designer of a particular system always faces a choice problem. Papers presented in the area of approximate reasoning contained new methods such as fuzzy entropy method, linear revising method, approximate reasoning method with certainty factor, and Neural Networks based methods. OVERVIEW AND COMMENTS The papers presented at the three conferences covered a large spectrum of results obtained as well as problems in Neural Networks and Fuzzy technologies: Fuzzy Neural Networks, Chaos fuzzy systems, fuzzy neural computing, learning algorithms for fuzzy systems, approximate reasoning, fuzzy modeling, fuzzy logic control, neural chips, fuzzy hardware, fuzzy clustering.... Although Neural Networks and Fuzzy systems can be investigated separately, the majority of papers focused on the fusion of the two technologies in order to tackle more complex problems, and hence to create more intelligent machines. So far, empirical evidence is convincing for more research in this direction. In my view, the variety of design techniques is due to a lack of firm theoretical foundation. Of course, this is the area of "soft computing", and one should not expect a rigid theory like a conventional mathematical theory. However, theoretical results are already useful as general guide lines, namely specifying the structures of Neural Networks and fuzzy systems, the classes of inference procedures used in approximate reasoning. More basic research is needed in order to provide foundations for design methodology. In the near future, we will continue to see more applications of the fuzzy approach to the so-called friendly systems. Several questions remain: if a system is "successfully" designed, how to make it "better"?, can one specify a design technique for a class of systems rather than just for one given system? It was apparent that the Asian scientists pursued more research than US scientists in the fields of chaotic fuzzy systems and fuzzy measures and integrals for decision-making. The chaos in general systems results from non-linear dynamical systems and exhibits complicated and unpredictable behavior. Applications are considered for control problems, especially for systems sensitive to oscillations and chaostic instability. Typical papers to be looked at are: (1) "Chaos and Information loss in Fuzzy dynamical Systems" (P. Diamond, Australia, Proceedings of the International Symposium in Fuzzy Systems, p.17- 20) (2) "A chaostic chip for analyzing non-linear discrete dynamical systems" (T. Yamakawa, T. Miki and E. Uchino, Proceedings of the Second International Conference on Fuzzy Logic and Neural Networks, Vol. 1, p.563-566) As for the development of the mathematical theory of measures and integrals in a fuzzy setting is concerned, typical paper is: "Non-additivity of fuzzy measures representive preferential dependence" (T. Murofushi and M. Sugeno, Proceedings of the Second International Conference Fuzzy Logic and Neural Networks, Vol. 2, p.617-620) The invited section on this topic was devoted to new results and applications to reasoning in decision and control problems. Dealing with uncertainty in humanistic systems is a crucial problem. Besides the random uncertainty which can be captured by probabilistic laws (with the analytic tools of the well-established statistical decision theory), it has been recognized that other types of uncertainty, such as imprecision and ambiguity (vagueness), have also to be dealt with. The main feature of these uncertainties is the non-additivity property. In the Bayesian approach to reasoning in intelligent machines, upper and lower probabilities, or some more general axiomatic measures of imprecision, are non-additive. In a related vein, the concept of degrees of belief in the so-called theory of evidence exhibits also non-additivity. It turns out that a general framework for measuring non-additive uncertainties is the theory of fuzzy measures proposed by M. Sugeno in 1974. As a typical example of applications, the Choguet integral of utility functions, with respect to some fuzzy measure, can be used as a generalization of the ordinary concept of expected utilities in decision- making problems. Thus, in my view. a general theory of decisions based upon fuzzy measures and integrals will be useful for systems exhibiting various kinds of uncertainties. -------------------------------END OF REPORT----------------------------