Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

Abstract

Fuzzy Logic, introduced by Zadeh along with his introduction of fuzzy sets, is a continuous multi-valued logic system. Hence, it is a generalization of the classical logic and the classical discrete multi-valued logic (e.g. Łukasiewicz' three/many-valued logic). Throughout the years Zadeh and other researches have introduced extensions to the theory of fuzzy setts and fuzzy logic. Notable extensions include linguistic variables, type-2 fuzzy sets, complex fuzzy numbers, and Z-numbers. Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. This extension provides the basis for control and inference systems relating to complex phenomena that cannot be readily formalized via type-1 or type-2 fuzzy sets. Hence, in recent years, several researchers have used the new formalism, often in the context of hybrid neuro-fuzzy systems, to develop advanced complex fuzzy logic-based inference applications. In this chapter we reintroduce the concept of complex fuzzy sets and complex fuzzy logic and survey the current state of complex fuzzy logic, complex fuzzy sets theory, and related applications.

Comparison Study on Development Path for Small and Medium-sized Enterprises E-commerce Using Complex Fuzzy Sets

“…To clarify the necessity of a complex-valued membership degree, Ref. 28 presented a new interpretation of it from a complex fuzzy class which is embedded with the complex fuzzy set class operations.…”

PRASCAL: a pataphysical programming language

“…Computing struggles with illogicality, because the need for structured reasoning drives the algorithmic process itself. Standard solutions such as fuzzy logic introduce a degree of controlled variability into the reasoning process (Tamir et al, 2015). The balanced ternary places the zero sum on a sliding scale between 1 and -1, which is a way of introducing a certain degree of unpredictability into processes which nevertheless still accord with the fundamental principles of von Neumann binary architecture.…”

Evaluation of the Economic Relationships on the Basis of Statistical Decision-Making in Complex Neutrosophic Environment

“…According to CqROFSs, the degree of membership (m C ), the degree of nonmembership (n C ), and the sum (m C ) q + (n C ) q lie in a unit circle in a complex plane. Bi et al [30] defined CF arithmetic aggregation operators, and Tamir et al [31] presented an overview of theory and applications of CFSs and CF logic. Also, Tamir and Kandel [32] presented the axiomatic theory of CF logic and classes.…”