Elsevier

Fuzzy Sets and Systems

Volume 33, Issue 3, 15 December 1989, Pages 333-345
Fuzzy Sets and Systems

Fuzzy complex numbers

https://doi.org/10.1016/0165-0114(89)90122-XGet rights and content

Abstract

This paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations. It is shown that arithmetic of fuzzy complex numbers may be performed in terms of α-cuts. Next two special types of fuzzy complex numbers based on the forms z = x + iy and z = reiγ for regular complex numbers are investigated. Introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions.

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A preliminary version of this paper was presented at the International Symposium on Fuzzy Systems and Knowledge Engineering, July 10–16, 1987, Guangzhou-Guiyang, China

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