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Fifty Years of Fuzzy Logic and its Applications pp 661–681Cite as

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

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

Abstract

Fuzzy Logic, introduced by Zadeh along with his introduction of fuzzy sets, is a continuous multi-valued logic system. Hence, it is a generalization of the classical logic and the classical discrete multi-valued logic (e.g. Łukasiewicz’ three/many-valued logic). Throughout the years Zadeh and other researches have introduced extensions to the theory of fuzzy setts and fuzzy logic. Notable extensions include linguistic variables, type-2 fuzzy sets, complex fuzzy numbers, and Z-numbers. Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. This extension provides the basis for control and inference systems relating to complex phenomena that cannot be readily formalized via type-1 or type-2 fuzzy sets. Hence, in recent years, several researchers have used the new formalism, often in the context of hybrid neuro-fuzzy systems, to develop advanced complex fuzzy logic-based inference applications. In this chapter we reintroduce the concept of complex fuzzy sets and complex fuzzy logic and survey the current state of complex fuzzy logic, complex fuzzy sets theory, and related applications.

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Notes

  1. 1.

    The first documented reference by Zadeh to the concepts of Fuzzy Mathematics appeared in a 1962 paper.

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Acknowledgment

This work is based in part upon work supported by the National Science Foundation under grants I/UCRC IIP-1338922, AIR IIP-1237818, SBIR IIP-1330943, III-Large IIS-1213026, MRI (CNS-1429345, CNS-0821345, CNS-1126619), and CREST HRD-0833093 and by DHS S&T at TerraFly (http://terrafly.com) and the NSF CAKE Center (http://cake.fiu.edu).

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Authors and Affiliations

  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, USA

    Naphtali D. Rishe & Abraham Kandel

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  1. Dan E. Tamir
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  2. Naphtali D. Rishe
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  3. Abraham Kandel
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Correspondence to Dan E. Tamir .

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Editors and Affiliations

  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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Tamir, D.E., Rishe, N.D., Kandel, A. (2015). Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications. 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_31

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