Linguistic variable, hedges and several distances on complex fuzzy sets

Abstract

Complex fuzzy set (CFS) is a fuzzy set characterized by complex-valued membership function consisting of amplitude and phase terms, whose range of membership function extended to the unit circle in the complex plane. We often use words to describe variables in our daily life. Hence, the definition of linguistic variables and linguistic hedges on CFS are introduced. The most commonly used hedges are obtained. This paper also illustrates priority needs and advantages to introduce several distance measures in the case of complex fuzzy sets. Solutions to some problems in different fields are suggested through complex fuzzy distance measure and several distance measures between two complex fuzzy sets are introduced. The boundary for each distance of complex fuzzy sets is obtained.

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