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Fuzzy Soft Matrices Entropy: Application in Data-Reduction

Omdutt Sharma, Pratiksha Tiwari, Priti Gupta

Source Title: International Journal of Fuzzy System Applications (IJFSA) 7(3)

DOI: 10.4018/IJFSA.2018070104

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Abstract

This article describes how information technology and internet together infused organizations with huge amount of data. Consequently, accumulating, storing, understanding and analyzing data at a large scale is equally important and complex. Out of this data not all is information data, in order to extract information, one needs to discard redundant, irrelevant and unnecessary data. This article aims to introduce a data reduction technique which will be useful to discard irrelevant data. Here in data-reduction, the authors have used fuzzy-soft set techniques, namely fuzzy-soft information matrixes. Further, they have introduced a new fuzzy-soft information measure of fuzzy-soft matrixes.

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2. Preliminaries

In this section we describe the preliminary definitions, and results which will be required later in this paper.

2.1. Fuzzy Set

Zadeh (1965) commenced an extension of classical notion of a set known as fuzzy sets, fuzzy sets are the sets in which elements have degree of membership and degree of always belong to interval [0, 1]. Thus we say that a fuzzy set is a class of objects with a continuum of grades of membership. The indicator functions of classical sets are particular case of the membership functions of fuzzy sets where membership value is either 0 or 1. Thus we say that fuzzy sets are generalization of classical sets. In fuzzy set theory, classical bivalent set are usually called crisp sets.

Definition 2.1.1 A fuzzy set is a pair where is a set and for each , the value is called the grade of membership of in . For a finite set the fuzzy set is often denoted by . Let , then does not belong to the fuzzy set if and is called a fuzzy number if . The set is called the support of and the set is called its kernel or core. The function m is called the membership function of the fuzzy set