Fuzzy Soft Matrices Entropy: Application in Data-Reduction

Fuzzy Soft Matrices Entropy: Application in Data-Reduction

Omdutt Sharma (Maharshi Dayanand University, Rohtak, India), Pratiksha Tiwari (Delhi Institute of Advanced Studies, Delhi, India) and Priti Gupta (Maharshi Dayanand University, Rohtak, India)
Copyright: © 2018 |Pages: 20
DOI: 10.4018/IJFSA.2018070104

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 IJFSA.2018070104.m01 where IJFSA.2018070104.m02 is a set and IJFSA.2018070104.m03 for each IJFSA.2018070104.m04, the value IJFSA.2018070104.m05 is called the grade of membership of IJFSA.2018070104.m06 in IJFSA.2018070104.m07. For a finite set IJFSA.2018070104.m08 the fuzzy set IJFSA.2018070104.m09 is often denoted by IJFSA.2018070104.m10. Let IJFSA.2018070104.m11, then IJFSA.2018070104.m12 does not belong to the fuzzy set IJFSA.2018070104.m13 if IJFSA.2018070104.m14 and IJFSA.2018070104.m15 is called a fuzzy number if IJFSA.2018070104.m16. The set IJFSA.2018070104.m17 is called the support of IJFSA.2018070104.m18 and the set IJFSA.2018070104.m19 is called its kernel or core. The function m is called the membership function of the fuzzy set IJFSA.2018070104.m20

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