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The Theory and Applications of Generalized Complex Fuzzy Propositional Logic

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Soft Computing: State of the Art Theory and Novel Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 291))

Abstract

The current definition of complex fuzzy logic has two limitations. First, the derivation uses complex fuzzy relations; hence, it assumes the existence of complex fuzzy sets. Second, current theory is based on a restricted polar representation of complex fuzzy proposition, where only one component of a complex fuzzy proposition carries fuzzy information. In this chapter we present a novel form of complex fuzzy logic. The new theory, referred to as generalized complex fuzzy logic, overcomes the limitations of the current theory and provides several advantages. First, the derivation of the new theory is based on axiomatic approach and does not assume the existence of complex fuzzy sets or complex fuzzy classes. Second, the new form supports Cartesian and polar representation of complex logical propositions with two components of fuzzy information. Hence, the new form significantly improves the expressive power and inference capability of complex fuzzy logic. Finally, the new form is compatible with (yet independent of) the definition of complex fuzzy classes; thereby providing further improvement in the expressive power and inference capability. The chapter surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides a new and generalized complex fuzzy propositional logic theory. The new theory has potential for usage in advanced complex fuzzy logic systems and latent for extension into multidimensional fuzzy propositional and predicate logic. Moreover, it can be used for inference with type 2 (or higher) fuzzy sets. Furthermore, the introduction of complex logic can be used for analysis of periodic temporal fuzzy processes where the period is fuzzy.

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Author information

Authors and Affiliations

  1. CS Department, Texas State University, 601 University Drive, San Marcos, Texas, 78666, USA

    Dan E. Tamir

  2. Faculty of Engineering Sciences, Department of Information Systems Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Mark Last

  3. CSE Department, University of South Florida, 4202 E. Fowler Ave, Tampa, Florida, 33620, USA

    Abraham Kandel

Authors
  1. Dan E. Tamir
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  2. Mark Last
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  3. Abraham Kandel
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Corresponding author

Correspondence to Dan E. Tamir .

Editor information

Editors and Affiliations

  1. , Iona College, Machine Intelligence Institute, New Rochelle, 10801, New York, USA

    Ronald R. Yager

  2. Information Technologies of the, Republic of Azerbaijan, Ministry of Communications and, Zarifa Aliyeva str. 33, Baku, AZ1000, Azerbaijan

    Ali M. Abbasov

  3. , Department of Electrical, University of Alberta, ECERF Building W5-023, Edmonton, T6G 2V4, Alberta, Canada

    Marek Z. Reformat

  4. , Department of Information Technology, Azerbaijan Technical University, 25 H.Cavid Ave., Baku, AZ1073, Azerbaijan

    Shahnaz N. Shahbazova

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Tamir, D.E., Last, M., Kandel, A. (2013). The Theory and Applications of Generalized Complex Fuzzy Propositional Logic. In: Yager, R., Abbasov, A., Reformat, M., Shahbazova, S. (eds) Soft Computing: State of the Art Theory and Novel Applications. Studies in Fuzziness and Soft Computing, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34922-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-34922-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34921-8

  • Online ISBN: 978-3-642-34922-5

  • eBook Packages: EngineeringEngineering (R0)

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