Fuzzy Sets and Systems 2 (1979) 1-3. © North Holland Publishing Company

GUEST EDITORIAL TO THE SPECIAL ISSUE ON FUZZY SETS A N D APPLICATIONS

Madan M. GUPTA

The problem of control and decision-making in a fuzzy environment presents one of the most fundamental and challenging issues in the design and analysis of man-machine systems. At present, the behavior of such systems is usually analyzed by the use of methods deeply rooted in classical mathematics. It is becoming increasingly clear, however, that classical mathematics, with a concep- tual structure that rests on two-valued logics, is not well-suited for dealing with systems that manifest a high degree of fuzziness. To deal with fuzziness effec- tively, we must be prepared to lower our standards of precision, and be tolerant of approaches that are approximate in nature. 1~is is the essence of fuzzy logic.

Advances in science and technology have made our modern society very complex, and with this our decision processes have become increasingly vague and fuzzy, and hard to analyze. "Fuzzy-ism" is a body of concept and techniques aimed at providing a systematic framework for dealing with this vagueness and imprecision.

"Fuzzy-ism" is young, and has just entered into the second decade of its existence, but its doctrine is having a profound impact on the development of the theory of decision-making. This International Journal on Fuzzy Sets and Systems is aimed to report the most recent developments, both in theory and applications, and provide a communication between scientists and practitioners.

Fuzzy set theory originated in the work of Lotfi A. Zadeh over a dozen years ago, and this decade has witnessed an exponential growth in the development of mathematical concepts and their applications. And these developments have provided a basis to new approaches to problems in engineering, management, social sciences, medicine, decision analysis, psychology, sociology, economics, and many more fields. During the past few years many informal and formal meetings were organized [1-6], and they provided a stimulating atmosphere for the discussion of key problems and developments in this fuzzy field. The first such meeting was held at the I F A C - H a g u e Symposium in 1973 [1], and recently a special one-day symposium on Fuzzy Set Theory and Applications was held under the auspices of the 16th IEEE Conference on Decision and Control at New Orleans [5].

Unlike other decision analysis field, the field of fuzzy set theory and their "real life" applications is still in its infancy. Thus, the papers that are included in this special issue do not represent a coordinated set of contributions that cover each

2 M. Gupta

and every important aspect of the area. It was felt, however, that fuzzy set theory represents the new frontier, and that a collection of some selected papers that were preseeted at the 1EEE--FuzTy Symposium at New Orleans could prov:,de a snapshot of the state-of-the-art that could be very useful to researchers in this important field. This first special issue of the Journal is the outcome of this effort. These papers were reviewed and re-written. Almost all manuscripts were revised to conform with the recommendations of the reviewers, and several other manuscripts were rejected on various technical grounds and suitability for this issue.

My persona[ overall impressions of the contributions that appear in this issue are in brief as follows. From a theoretical point of view, there is an introduction to some new ideas and expansion of the existing theories. From the applications point of view, we see a small sample from the many application areas which demand significant advances in fuzzy set theory. We are observing the formation of several schools of thought in regards to this fuzzy field, and I believe that ,~;ome of this has reflected into this issue.

The papers that are contained in this issue are described here briefly. Characterization of consensus in group decision making is an important topic,

and has been a subject of discussion in the past. Bezdek uses the fuzzy relation spaces in the characterization of "consensus". Gaines describes the methods of identification for systems whose behavior can be described only in fuzzy terms. In the third paper Kokawa, Nakamura and Oda describe the results of hint-effect experiments, and analyze the human decision-making process from fuzzy- theoretic and concept-formational viewpoints.

When problem situations are imprecise, people use mental processes closer to coping than to exact, logical-deductive reasoning. Kochen sketches new ways of explicating the process of coping. Nguyen proposes and develops some concepts and techniques useful for the theory of linguistic probabilities. He expresses these probabilities in linguistic rather than numerical terms. He bases this development on possibility theory introduced by Zadeh.

Chang and Pavlidis present several methods for functional approximation with variable-knot variable-degree splines, and with variable-knot first-order splines. Sanchez, in his paper explores the properties of lower and upper inverses of fuzzy relaUons. Then he relateg these notions to problems in medical diagnosis. In the last application oriented paper Tazaki and Amagasa propose a method for structuring hierarchy for complex problems. Their proposed procedure permits one to develop an automatic graphic structure that portrays the hierarchy.

The 1977 I E E E - F u z z y Symposium had a wide international participation, and many complex problems in many related fuzzy areas were discussed. This reflects the worldwide importance of complex process, and the recognition that they are receiving by the international scientific and engineering community via the fuzzy set theo~T.

As I pointed out earlier, this collection of articles is not intended to delineate

Guest Editorial 3

"Fuzzy set theory and applications", however, it illustrates a small sample of field of interest which involved the human-like decision making.

Of course, there will continue to be a variety of different developments both in theory and applications, and the fuzzy notion will continue to penetrate in humanistic processe~; and, I feel that fuzzy field will continue to be an exciting area for both theoretical and applied research in the decades to come.

To the reviewers who met impossible deadlines, I express my deep gratitude.

Madan M. GUPTA University of Saskatchewan Sasl~atoon & Regina, Sask., Canada

Reterences

[1] M.M. Gupta, IFAC Report on the Round Table Discussion on the Estimation and Control in a Fuzzy Environment, held at the IFAC-Hauge, June 1973, Automatica, 11 (1975) 209-212.

[2] M.M. Gupta and E.H. Maffldani, IFAC Report on the second IFAC Round Table Discussion on ~'Fuzzy Automata and Decision Processes", held at the Sixth Triennial IFAC World Congress, Boston/Cambridge. Also in Automatica, 12 (1975) 241-296.

[3] M.M. Gupta, G.N. Saridis, and B. Gaines, eds., Fuzzy Automata and Decision Processes, (North Holland, Amsterdam, 1977).

[4] M.M. Gupta, R.K. Ragade, and R. Yager, Report on the IEEE Special Symposium on Fuzzy Set Theory and Applications, at the 1977 CDC, New Orleans (December, 1978).

[5] Proc. 1977 IEEE Conference on Decision and ControlmSpecial Symposium on Fuzzy Set Theory and Applications, 2 (1977) 1300-1450. [Available from the IEEE Service Center, 445 Hoes Lane, Piscataway, NJ, 08856, USA; Cat. No. 77CH1269-0.]

[6] M.M. Gupta, IFAC Report on the Third IFAC Ro~,nd Table Discussion on Fuzzy Decision Making and Applications, held at the Seventh Triennial IFAC World Congress, He|sinki, June 12-16, 1978, Proc. IFAC World Congress, also to appear in Automatica.