Fuzzy Sets and Systems
A novel framework of fuzzy complex numbers and its application to compositional modelling
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Complex neuro-fuzzy self-learning approach to function approximation
ACIIDS'10 Proceedings of the Second international conference on Intelligent information and database systems: Part II
Complex-fuzzy adaptive image restoration: an artificial-bee-colony-based learning approach
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Complex fuzzy computing to time series prediction: a multi-swarm PSO learning approach
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Knowledge discovery by an intelligent approach using complex fuzzy sets
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part I
Adaptive image restoration by a novel neuro-fuzzy approach using complex fuzzy sets
International Journal of Intelligent Information and Database Systems
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Complex fuzzy logic is a postulated logic system that is isomorphic to the complex fuzzy sets recently described in a previous paper. This concept is analogous to the many-valued logics that are isomorphic to type-1 fuzzy sets, commonly known as fuzzy logic. As with fuzzy logics, a complex fuzzy logic would be defined by particular choices of the conjunction, disjunction and complement operators. In this paper, an important assertion from a previous paper, that only the modulus of a complex fuzzy membership should be considered in set theoretic (or logical) operations, is examined. A more general mathematical formulation (the property of rotational invariance) is proposed for this assertion, and the impact of this property on the form of complex fuzzy logic operations is examined. All complex fuzzy logics based on the modulus of a vector are shown to be rotationally invariant. The case of complex fuzzy logics that are not rotationally invariant is examined using the framework of vector logic. A candidate conjunction operator was identified, and the existence of a dual disjunction was proven. Finally, a discussion on the possible applications of complex fuzzy logic focuses on the phenomenon of regularity as a possible fuzzification of stationarity.