Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications推荐.pdf

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications Dan E. Tamir, Naphtali D. Rishe and Abraham Kandel 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 exten- sions 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 com- plex fuzzy logic, complex fuzzy sets theory, and related applications. Keywords Fuzzy set theory ⋅ Fuzzy class theory ⋅ Fuzzy logic ⋅ Complex fuzzy sets ⋅ Complex fuzzy classes ⋅ Complex fuzzy logic ⋅ Neuro-fuzzy systems D.E. Tamir (✉) Department of Computer Science, Texas State University San Marcos, Texas, USA e-mail: dt19@ N.D. Rishe ⋅ A. Kandel School of Computing and Information Sciences, Florida International University, Miami, USA e-mail: rishe@cs.fi A. Kandel e-mail: Abraham.Kandel.FIU@ © Springer International Publishing Switzerland 2015 661 D.E