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Fifty Years of Fuzzy Logic and its Applications pp 537–580Cite as

The Genesis of Fuzzy Sets and Systems – Aspects in Science and Philosophy

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

Abstract

In 1965 Lotfi A. Zadeh founded the theory of Fuzzy Sets and Systems. This chapter deals with developments in the history of philosophy, logic, and mathematics during the time before and up to the beginning of fuzzy logic and it also gives a view of its first application in control theory. Regarding the term “fuzzy” we note that older concepts of “vagueness” and “haziness” had previously been discussed in philosophy, logic, mathematics. This chapter delineates some specific paths through the history of the use of these “loose concepts ”. Haziness and fuzziness were concepts of interest in mathematics and philosophy during the second half of the 20th century. The logico-philosophical history presented here covers the work of Russell, Black, Hertz, Wittgenstein and others. The mathematical-technical history deals with the theories founded by Menger and Zadeh. Menger’s concepts of probabilistic metrics, hazy sets (ensembles flous) and micro-geometry as well as Zadeh’s theory of Fuzzy Sets paved the way for the establishment of Soft Computing methods. In the first decade of Fuzzy Sets and Systems, nobody thought that this theory would be successful in the field of applied sciences and technology. Zadeh expected that his theory would have a role in the future of computer systems as well as Humanities and Social Sciences. When Mamdani and Assilian picked up the idea of Fuzzy Algorithms to establish a first Fuzzy Control system for a small steam engine, this was the Kick-off for the “Fuzzy Boom” and Zadehs primary intention trailed away for years. Then in the new millennium a new movement for Fuzzy Sets in Social Sciences and Humanities was launched.

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Notes

  1. 1.

    Later Zadeh and also the whole “fuzzy community” made use of the greek letter \(\mu \) to mark the membership function in Fuzzy Set Theory.

  2. 2.

    In the original paper Menger wrote “\(>\)”. The present author thanks Erich Peter Klement for this correction.

  3. 3.

    In a footnote he named the works of \(1\)2 known philosophers, linguists or cognitive scientists.

  4. 4.

    PRUF is an acronym for “Possibilistic Relational Universal Fuzzy.”

  5. 5.

    For Soft Computing methods Social Sciences see also [58].

  6. 6.

    For more details on Abe Mamdani’s work see [59].

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Acknowledgments

The author wishes to thank Lotfi A. Zadeh for his generous help and unstinted willingness to support the author’s historical project on the theory of fuzzy sets and systems during the last \(15\) years. Many thanks go also to Claudio Moraga and Jim Bezdek who read this text and gave important hints to improve it. Work leading to this chapter was partially supported by the Foundation for the Advancement of Soft Computing Mieres, Asturias (Spain).

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  1. Friedrich Schiller University, Jena, Germany

    Rudolf Seising

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  1. Rudolf Seising
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Correspondence to Rudolf Seising .

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  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

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Seising, R. (2015). The Genesis of Fuzzy Sets and Systems – Aspects in Science and Philosophy. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_27

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_27

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  • Online ISBN: 978-3-319-19683-1

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