A Novel Study on Complex Fuzzy Logic

K Rajesh, D. Rajeswara Rao

Abstract: Complex fuzzy logic is a generalization of traditional fuzzy logic, based on complex fuzzy sets. In complex fuzzy logic, inference rules, the novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets, characterized by complex-valued membership functions. Several mathematical properties of complex fuzzy sets, which serve as a basis for the derivation of complex fuzzy logic, are reviewed in this paper. These properties include basic set theoretic operations on complex fuzzy sets-namely complex fuzzy union and intersection, complex fuzzy relations and their composition, and a novel form of set aggregation-vector aggregation.

Keywords: Complex fuzzy logic, complex fuzzy relations, complex fuzzy sets