Introduction to fuzzy soft groups

Abstract

a b s t r a c tIn this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems of homomorphic image and homomorphic pre-image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.

A New Approach to Group Theory via Soft Sets and $L$-Fuzzy Soft Sets

“…Let G be a common universe, E be a set of parameters and A ⊆ E. Then a pair (F, A) is called a L-fuzzy soft set over G, where F is a mapping given by F : A → FL(G). 4 } be the set of four houses under consideration, E = {e 1 (costly), e 2 (beautiful), e 3 (green surroundings), e 4 (wooden), e 5 (luxurious be the set of parameters and A = {e 1 , e 2 , e 3 } ⊂ E. Let α i ∈ L, i ∈ {1, 2, ..., 9}, where…”

“…The notion of fuzzy soft groups was introduced in ( [4], [10]). In this section, we introduce the concept of L-fuzzy soft groups which extends the notion of group to include the algebraic structures of L-fuzzy soft sets, and give some new fundamental properties of L-fuzzy soft groups.…”

“…Jin-liang et al [10] defined the operations on fuzzy soft groups, and proved some results on them. Aygünoglu and Aygün [4] gave the concept of fuzzy soft group, and defined fuzzy soft function and fuzzy soft homomorphism. Majumdar and Samanta [15] defined generalised fuzzy soft sets, and studied some of their properties.…”

A new approach in handling soft decision making problems

“…They have also introduced the concept of fuzzy soft set, a more generalized concept, which is a combination of fuzzy set and soft set and also studied some of its properties. Soft set and fuzzy soft set theories have a rich potential for applications in several directions, few of which had been shown by some authors [1,2,5,6,7,8,12,14].…”

Fuzzy Soft Prime Ideals Over Right Ternary Near-Rings

“…They have applications in Medical diagnosis [3], decision making ( [9]) knowledge representation and retrieval [10] etc. Aygungolu and Aygun [2] generalized the notion of soft groups and introduced fuzzy soft groups in 2009. Thereafter many researchers are applying fuzzy soft tools to other algebraic structures.…”