research-article

Fuzzy logic-a personal perspective

Author:

Lotfi A. ZadehAuthors Info & Claims

Fuzzy Sets and Systems, Volume 281, Issue C

Pages 4 - 20

https://doi.org/10.1016/j.fss.2015.05.009

Published: 15 December 2015 Publication History

Abstract

This paper marks the 50th anniversary of the publication of my first paper on fuzzy sets, "Fuzzy sets," Information and Control, 1965. What is of historical interest is that initially-and for some time thereafter-my paper was an object of indifference, skepticism and derision. A prominent school of thought claimed that fuzzy set theory is probability theory in disguise. Positive comments were few and far between. In contrast, my ideas were welcomed with open arms in Japan. In the seventies and eighties of last century, fuzzy set theory and fuzzy logic began to gain acceptance in Europe and, more particularly, in Eastern Europe and the Soviet Union. In part, many negative reactions to my papers reflected the fact that the word "fuzzy" has pejorative connotations. In large measure, science is based on the classical, Aristotelian, bivalent logic. Binarization-drawing a sharply defined boundary between two classes-is a deeply entrenched Cartesian tradition. What is not widely recognized is that this tradition has outlived its usefulness. One of the principal contributions of fuzzy logic is providing a basis for a progression from binarization to graduation, from binarism to pluralism, from black and white to shades of gray. Graduation involves association of a class which has unsharp (fuzzy) boundaries with degrees/grades of membership. Classes with unsharp boundaries are pervasive in human cognition. Most words in natural language are labels of such classes. This paper is a concise exposition of what I consider to be my principal contributions to the development of fuzzy set theory and fuzzy logic. Among the contributions which are discussed are: introduction of the concept of a fuzzy set, FL-generalization, the concept of a linguistic variable, information granulation, precisiation of meaning, generalized theory of uncertainty (GTU), the concept of a restriction, restriction-centered theory of truth and meaning, the information principle, and similarity-based definitions of possibility and probability.

References

[1]

L.A. Zadeh, J.R. Ragazzini, Probability criterion for the design of servomechanisms, J. Appl. Phys., 20 (1949) 141-144.

[2]

L.A. Zadeh, J.R. Ragazzini, An extension of Wiener's theory of prediction, J. Appl. Phys., 21 (1950) 645-655.

[3]

O. Lowenschuss, Non-binary switching theory, 1958 IRE National Convention Record Part 4, IRE National Convention, New York, NY, March 24-27, 1958, pp. 305-317.

[4]

W. Ulrich, Non-binary error correction codes, Bell Syst. Tech. J., 36 (1957) 1341-1388.

[5]

L.A. Zadeh, C.A. Desoer, Linear System Theory-the State Space Approach, McGraw-Hill Book Co., New York, 1963.

[6]

L.A. Zadeh, On the definition of adaptivity, Proc. IEEE, 51 (1963) 469-470.

[7]

L.A. Zadeh, From circuit theory to system theory, Proc. IRE, 50 (1962) 856-865.

[8]

L.A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965) 338-353.

[9]

J.F. Sowa, Review of logical foundations of artificial intelligence by Michael R. Genesereth & Nils J. Nilsson, Artif. Intell., 38 (1989) 125-131.

[10]

M.R. Genesereth, N.J. Nilsson, Logical Foundations of Artificial Intelligence, Morgan Kaufmann Publishers, Los Altos, CA, 1987.

[11]

L.A. Zadeh, Mathematics-a call for reorientation, in: Newsletter of the Conference Board on Mathematical Sciences, vol. 7, 1972, pp. 1-3.

[12]

L.A. Zadeh, Fuzzy sets and systems, in: Proc. Symp. on System Theory, Polytechnic Institute of Brooklyn, New York, 1965, pp. 29-39.

[13]

L.A. Zadeh, Shadows of fuzzy sets, Probl. Inf. Transm., 2 (1966) 37-44.

[14]

L.A. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl., 23 (1968) 421-427.

[15]

L.A. Zadeh, Quantitative fuzzy semantics, Inf. Sci., 3 (1971) 159-176.

Digital Library

[16]

L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Syst. Man Cybern., SMC-3 (1973) 28-44.

[17]

L.A. Zadeh, L.A. Zadeh, L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Part I, Inf. Sci., 8 (1975) 199-249.

[18]

L.A. Zadeh, PRUF-a meaning representation language for natural languages, Int. J. Man-Mach. Stud., 10 (1978) 395-460.

[19]

L.A. Zadeh, Test-score semantics for natural languages and meaning representation via PRUF, in: Empirical Semantics, Brockmeyer, Bochum, W. Germany, 1981, pp. 281-349.

[20]

L.A. Zadeh, A fuzzy-set-theoretic approach to the compositionality of meaning: propositions, dispositions and canonical forms, J. Semant., 3 (1983) 253-272.

[21]

L.A. Zadeh, A rationale for fuzzy control, J. Dyn. Syst. Meas. Control, 94 (1972) 3-4.

[22]

E. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man-Mach. Stud., 7 (1975) 1-13.

[23]

Z. Pawlak, Rough sets, Int. J. Parallel Program., 11 (1982) 341-356.

[24]

L.A. Zadeh, Fuzzy sets and information granularity, in: Advances in Fuzzy Set Theory and Applications, Publishing Co., North-Holland, Amsterdam, 1979, pp. 3-18.

[25]

G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, 1976.

[26]

L.A. Zadeh, On the validity of Dempster's rule of combination of evidence, University of California, Berkeley, 1979.

[27]

L.A. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst., 90 (1997) 111-127.

Digital Library

[28]

L.A. Zadeh, Fuzzy logic and approximate reasoning, Synthese, 30 (1975) 407-428.

[29]

L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1 (1978) 3-28.

Digital Library

[30]

D. Dubois, H. Prade, Possibility Theory, Plenum Press, New York, 1988.

[31]

D. Dubois, H. Prade, Possibility theory, probability theory and multiple-valued logics: a clarification, Ann. Math. Artif. Intell., 32 (2001) 35-66.

[32]

D. Dubois, H. Prade, Possibilistic logic-an overview, in: Handbook of the History of Logic, vol. 9: Computational Logic, North-Holland, 2014, pp. 197-256.

[33]

L.A. Zadeh, Probability theory and fuzzy logic are complementary rather than competitive, Technometrics, 37 (1995) 271-276.

Digital Library

[34]

L.A. Zadeh, The information principle, Inf. Sci., 294 (2015) 540-549.

Digital Library

[35]

V.J. Loginov, Probability treatment of Zadeh membership functions and their use in pattern recognition, Eng. Cybern. (1966) 68-69.

[36]

E. Hisdal, Infinite-valued logic based on two-valued logic and probability - part 1.4. The TEE model for grades of membership, Int. J. Man-Mach. Stud., 25 (1990) 89-111.

Digital Library

[37]

G. Coletti, R. Scozzafava, Conditional probability, fuzzy sets, and possibility: a unifying view, Fuzzy Sets Syst., 144 (2004) 227-249.

[38]

B. Kovalerchuk, E. Triantaphyllou, A.S. Deshpande, E. Vityaev, Interactive learning of monotone Boolean functions, Inf. Sci., 94 (1996) 87-118.

Digital Library

[39]

L.A. Zadeh, A note on similarity-based definitions of possibility and probability, Inf. Sci., 267 (2014) 334-336.

Digital Library

[40]

A.I. Orlov, Fuzzy and random sets, Appl. Multivar. Stat. Anal. J. Acad. Sci. USSR (1978) 262-280.

[41]

I.R. Goodman, Identification of fuzzy sets with a class of canonically induced random sets, in: Proc. 19th IEEE Conf. Decis. & Cntrl., Dec. 1980, pp. 829-834.

[42]

P. Walley, Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London, 1991.

[43]

L.A. Zadeh, Toward a perception-based theory of probabilistic reasoning with imprecise probabilities, J. Stat. Plan. Inference, 105 (2002) 233-264.

[44]

L.A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inf. Sci., 172 (2005) 1-40.

Digital Library

[45]

L.A. Zadeh, Generalized theory of uncertainty (GTU)-principal concepts and ideas, Comput. Stat. Data Anal., 51 (2006) 15-46.

Digital Library

[46]

D.V. Lindley, The probability approach to the treatment of uncertainty in artificial intelligence and expert systems, Stat. Sci., 2 (1987) 17-24.

[47]

R. Aliev, O. Huseynov, Decision Theory with Imperfect Information, World Scientific, Hackensack, NJ, 2014.

[48]

J.F. Sowa, Knowledge Representation: Logical, Philosophical, and Computational Foundations, Brooks Cole Publishing Co., Pacific Grove, CA, 2000.

Digital Library

[49]

L.A. Zadeh, Precisiation of meaning via translation into PRUF, in: Cognitive Constraints on Communication, Reidel, Dordrecht, 1984, pp. 373-402.

[50]

L.A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Syst., 2 (1996) 103-111.

Digital Library

[51]

L.A. Zadeh, From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, IEEE Trans. Circuits Syst., 45 (1999) 105-119.

[52]

L.A. Zadeh, Computing with Words-Principal Concepts and Ideas, Springer, Berlin, 2012.

[53]

T. Yamakawa, Stabilization of an inverted pendulum by a high-speed fuzzy logic controller hardware system, Fuzzy Sets Syst., 32 (1989) 161-180.

Digital Library

[54]

L.A. Zadeh, Calculus of fuzzy restrictions, fuzzy sets and their applications to cognitive and decision processes, in: Proceedings of the U.S.-Japan Seminar on Fuzzy Sets and Their Applications, Academic Press, New York, 1975, pp. 1-39.

[55]

L.A. Zadeh, A note on Z-numbers, Inf. Sci., 181 (2011) 2923-2932.

Digital Library

[56]

L.A. Zadeh, Toward a restriction-centered theory of truth and meaning (RCT), Inf. Sci., 248 (2013) 1-14.

[57]

L.A. Zadeh, Similarity relations and fuzzy orderings, Inf. Sci., 3 (1971) 177-200.

Digital Library

[58]

L.A. Zadeh, A concept of probability based on similarity relations, in: Bayesian Research Conference on Uncertainty, University of Southern California, January 9, 1981.

[59]

A. Billot, I. Gilboa, D. Samet, D. Schmeidler, Probabilities as similarity-weighted frequencies, Econometrica, 73 (2005) 1125-1136.

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Pei ZDeng LXu YLi MXu LYan L(2024)Credibility of a Membership Function Related to a Linguistic Value to Improve Computing With WordsIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2024.337470432:6(3458-3470)Online publication date: 12-Mar-2024
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Index Terms

Fuzzy logic-a personal perspective
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic

Index terms have been assigned to the content through auto-classification.

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cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 281, Issue C

December 2015

308 pages

ISSN:0165-0114

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Elsevier North-Holland, Inc.

United States

Publication History

Published: 15 December 2015

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