articleIEEE Transactions on Fuzzy SystemsApr 1, 2002Closed access

Complex fuzzy sets

DRD. RamotRMRon MiloMFM. FriedmanAKAbraham Kandel

Tel Aviv University · Adama (Israel) · +1 more institution

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Abstract

The objective of this paper is to investigate the innovative concept of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. The inherent difficulty in acquiring intuition for the concept of complex-valued membership presents a significant obstacle to the realization of its full potential. Consequently, a major part of this work is dedicated to a discussion of the intuitive…

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Topics
Keywords
  • Fuzzy classification
  • Fuzzy number
  • Fuzzy set operations
  • Membership function
  • Defuzzification
  • Mathematics
  • Type-2 fuzzy sets and systems
  • Fuzzy set
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