Abstract
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex fuzzy relation are introduced.
Highlights
The notion of the fuzzy set was first introduced by Zadeh in a seminal paper in 1965 [7]
Ramot et al [5], extended the fuzzy set to complex fuzzy set with membership function, z = rseiws (x) where i = −1, which ranges in the interval [0,1] to a unit circle
Several set theoretic operations on complex fuzzy set were discussed with several examples, which illustrate the potential applications of complex fuzzy set in information processing
Summary
The notion of the fuzzy set was first introduced by Zadeh in a seminal paper in 1965 [7]. The notion of the fuzzy set A on the universe of discourse U is the set of order pair {(x, μA(x)), x ε U} with a membership function μA(x), taking the value on the interval [0,1]. Ramot et al [5], extended the fuzzy set to complex fuzzy set with membership function, z = rseiws (x) where i = −1 , which ranges in the interval [0,1] to a unit circle. The membership function defined for the complex fuzzy set z = rseiws (x) , which compromise an amplitude term rs(x) and phase term ws.
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