Multi-fuzzy soft groups

The purpose of this study is to extend the multi-fuzzy soft sets to the theory of groups. The concept of multi-fuzzy soft sets is examined and some new definitions are introduced such as restricted and extended intersection, restricted and extended union, boolean AND-intersection and boolean OR-union of the family multi-fuzzy soft sets and also a definition of a multi-fuzzy soft function is given. In this paper, the concept of multi-fuzzy soft sets is applied to the theory of groups and a notion which is called a multi-fuzzy soft group is proposed. A definition of homomorphism of multi-fuzzy soft groups is presented. We obtain that the image (or pre-image) of a multi-fuzzy soft group is a multi-fuzzy soft group.

Automated summary

This study extends the concept of multi-fuzzy soft sets to group theory, introducing new definitions such as restricted and extended intersections, unions, boolean AND-intersections, and boolean OR-unions. The concept of multi-fuzzy soft sets is applied to groups, proposing the notion of a multi-fuzzy soft group and defining homomorphisms of multi-fuzzy soft groups. The study concludes that the image (or pre-image) of a multi-fuzzy soft group remains a multi-fuzzy soft group.