The concept of linguistic variables was introduced by Zadeh in 1973. It is the most important and basic concept in fuzzy logic. But, it is not mentioned anywhere in literature that this paper introduces fuzzy logic.
An equivalent concept to fuzzy logic is approximate reasoning. Also, there are two versions of fuzzy logic; the extension of infinite valued logic and the other one is the broad one which says that fuzzy logic is synonymous with fuzzy sets.
The above observations lead to the confusion regarding the origin of fuzzy logic.
1. Exactly when fuzzy logic was introduced?
2. Who in which paper introduced this notion?
Fuzzy, or multi-valued logic was first introduced in the 1930s by Jan Lukasiewicz, a Polish logician and philosopher (Lukasiewicz, 1930). While classical logic operates with only two values 1 (true) and 0 (false), Lukasiewicz introduced logic that extended the range of truth values to all real numbers in the interval between 0 and 1. He used a number in this interval to represent the possibility that a given statement was true or false. For example, the possibility that a man 181cm tall is really tall might be set to a value of 0.86. It is likely that the man is tall. This work led to an inexact reasoning technique often called possibility theory.
Later, in 1937, Max Black, a philosopher, published a paper called ‘Vagueness: an exercise in logical analysis’ (Black, 1937). In this paper, he argued that a continuum implies degrees. He accepted vagueness as a matter of probability. However, Black’s most important contribution was in the paper’s appendix. Here he defined the first simple fuzzy set and outlined the basic ideas of fuzzy set operations.
In 1965 Lotfi Zadeh, Professor and Head of the Electrical Engineering Department at the University of California at Berkeley, published his famous paper ‘Fuzzy sets’. In fact, Zadeh rediscovered fuzziness, identified and explored it, and promoted and fought for it.
Zadeh extended the work on possibility theory into a formal system of mathematical logic, and even more importantly, he introduced a new concept for applying natural language terms. This new logic for representing and manipulating fuzzy terms was called fuzzy logic, and Zadeh became the Master of fuzzy logic.
Refs:
Lukasiewicz, J. (1930). Philosophical remarks on many-valued systems of propositional logic. Reprinted in Selected Works, L. Borkowski, ed., Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1970, pp. 153–179.
Black, M. (1937). Vagueness: An exercise in logical analysis, Philosophy of Science, 4, 427–455.
Zadeh, L. (1965). Fuzzy sets, Information and Control, 8(3), 338–353.
Zadeh, L. (1973). Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, and Cybernetics, SMC-3(1), 28–44.
This information must be available on Wikipedia. Usually, it is the most trustworthy source.
dear B.K. Tripathy ,
I am agree with C.P. Ravikumar and the conclusion there is:
The term fuzzy logic was introduced in 1965 by Lotfi Zadeh.
Dear Researchers,
Zadeh has mentioned in his 1994 paper on Fuzzy logic, Soft Computing and Neural networks that there are two approaches to fuzzy logic.
1. Extension of Multivalued logic (Lukasiewicz logic etc..)
2. Generalized sense (through linguistic variables...)
He had introduced linguistic variables long before that in 1974 may be. But, there also he has not claimed to have introducing fuzzy logic.
The first approach starts in 1930 with the introduction of 3-valued logic by Lukasiewicz and many others leading to multivalued logic, infinite valued logic and so on.
But, still when i tried to find the introduction of fuzzy logic through the second approach, i could not trace it back. That is where my confusion occurred. So, i wanted to put it in this forum to get the answer.
Thanks to all of you, who have participated in the conversation so far.
Expect a more pin-pointed answer. If i find one i shall put it here.
Professor Zadeh [1] introduced the fuzzy set theory and Following Zadeh's theory, Mamdani [2] introduced the fuzzy Inference system or FIS. (Mamdani FIS)
[1] L. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
[2] E. H. Mamdani, "Application of Fuzzy Algorithms for Control of Simple Dynamic Plant," Proc. Inst. Electr. Eng., vol. 121, no. 12, pp. 1585–1588, 1974.
Dear Professo,r B.K. Tripathy
This is a very interesting question and really not very clear in the literature. When I researched it I found that Zadeh with the publication of the article “Fuzzy Sets” introduced the fuzzy sets theory in 1965, but not the "fuzzy logic".
Zadeh (2008) points out that historically, the theory of fuzzy sets preceded fuzzy logic in its wide sense.
In this sense, I suspect that the first reference to "fuzzy logic" may have been in this article:
L.A. Zadeh, Fuzzy logic and approximate reasoning, Synthese 30 (1975) 407-428. https://doi.org/10.1007/BF00485052
In a complementary way, I think that section 2.1 of Zadeh (2008) might help you on investigation:
Zadeh, L.A., 2008. Is there a need for fuzzy logic?. Information Sciences 178, 2751– 2779. https://doi.org/doi:10.1016/j.ins.2008.02.012
Finally, if you can come to a conclusion, please share it with me. If you can't get these two articles, contact me and I can help you.
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