A new kind of fuzzy n-ary hypergroups in the framework of soft set theory.

Hongjie Li,Yunqiang Yin

doi:10.1155/2014/957391

Abstract

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈γ, ∈γ∨q δ)-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are introduced and some related properties and characterizations are obtained. The homomorphism properties of (∈γ, ∈γ∨q δ)-fuzzy soft (invertible) n-ary subhypergroups are also derived.

Highlights

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems
Molodtsov [1] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches
The goal is to explain new methodological development in n-ary hypergroups which will be of growing importance in the future

Summary

Introduction

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems. One major problem shared by those theories is their incompatibility with the parameterization tools To overcome these difficulties, Molodtsov [1] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Maji et al [10] introduced several algebraic operations in soft set theory and published a detailed theoretical study on soft sets. The purpose of this paper is to deal with the algebraic structure of n-ary hypergroups by applying fuzzy soft set theory. We introduce the concepts of (∈γ, ∈γ∨qδ)-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup and focus on investigating their characterization and algebraic properties. We discuss the homomorphism properties of (∈γ, ∈γ ∨ qδ)-fuzzy soft (invertible) n-ary subhypergroups

Preliminaries

A New Operation on Fuzzy Soft Sets over an n-Ary Hypergroupoid

Conclusions