In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, is given by linguistic values. It very awkward for the CFS describe this type of information. To overcome limitation, we first propose novel concept called complex set (LCFS) serve as an extension CFS. Then put forward some basic operational laws LCFSs. After t...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...

Type-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, ap...

In this paper, we introduce the concepts of fuzzy complex number, the operations of fuzzy complex number, the concepts of convergence for fuzzy complex number-valued sequence and the fuzzy complex numbervalued mapping. Then the fixed point of fuzzy complex number-valued mapping is discussed, some existent theorems of this mapping are given. It will establish a foundation for researching fuzzy c...

In this paper, the concept of fuzzy graph is extended to a complex fuzzy graph. Complex fuzzy graphs are encountered in complex fuzzy set theory. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thu...

This paper presents a method to construct more general fuzzy complex numbers and sets from ordinary fuzzy complex numbers by introduced the ordered sequences of membership functions. It is concluded that multifuzzy complex set is an extension of Buckley fuzzy complex set. Also, two types of multi-fuzzy complex numbers based on the forms z x iy = + and z re = θ are investigated. Multi-Fuzzy Comp...

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evo...