The Combination of Soft Sets and -Structures with Applications

Kyoung Ja Lee,Seok Zun Song,Young Bae Jun

doi:10.1155/2013/420312

Abstract

Using the notions of soft sets and <svg style="vertical-align:-0.20474pt;width:16.612499px;" id="M2" height="12.0625" version="1.1" viewBox="0 0 16.612499 12.0625" width="16.612499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.738)"><use xlink:href="#x1D4A9"/></g> </svg>-structures, <svg style="vertical-align:-0.20474pt;width:16.612499px;" id="M3" height="12.0625" version="1.1" viewBox="0 0 16.612499 12.0625" width="16.612499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.738)"><use xlink:href="#x1D4A9"/></g> </svg>-soft set theory is introduced. We apply it to both a decision making problem and a <i >BCK/BCI</i> algebra.

Highlights

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems
There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties
Molodtsov [1] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties which is free from the difficulties that have troubled the usual theoretical approaches

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. There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties All these theories have their own difficulties. Uncertainties cannot be handled using traditional mathematical tools but may be dealt with using a wide range of existing theories such as the probability theory, the theory of (intuitionistic) fuzzy sets, the theory of vague sets, the theory of interval mathematics, and the theory of rough sets. All of these theories have their own difficulties which are pointed out in [1]. In this paper we introduce the notion of N-soft sets which are a soft set based on N-structures by using the notions of soft sets and N-structures, and we apply it to both a decision making problem and a BCK/BCI-algebra

Preliminaries

N-Soft Sets

Application in a Decision Making Problem

Conclusions