Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem

Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem

Chiranjibe Jana (Department of Applied Mathematics, Vidyasagar University, Midnapore, India) and Madhumangal Pal (Department of Applied Mathematics, Vidyasagar University, Midnapore, India)
Copyright: © 2018 |Pages: 24
DOI: 10.4018/IJFSA.2018070103

Abstract

This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.
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1. Introduction

Decision making is one of the most significant and useful thing in our day-to-day life. But with the growing complexities of the systems, it is difficult to the decision maker for making a correct decision under these environments. For handling it, the fuzzy set theory (Zadeh (1965)) and intuitionistic fuzzy set theory (Atanassov (1986)) have been defined for making a decision smother. After their development, researchers have work on it and present several algorithms for solving the decision-making problems by Garg (2016a, 2016b, 2016c, 2016d, 2016e).

The classical methods unable to modeling uncertain data in economics, engineering, environmental science, sociology and information sciences successfully, because they have inherent difficulties and that have troubled the usual theoretical approaches. To overcome these difficulties, (Molodtsov (1999)) introduced the concept of soft set theory as a new mathematical tool for dealing with uncertainties which is free from difficulties. In theoretical aspects, soft set theory has a rich application in different direction. Now, works on the soft set theory are progressing rapidly. Maji et al. (2002, 2003) described the application of soft set theory in a decision-making problem and studied several operations on the theory of soft sets. Then many researcher find tremendous works using soft set theory as they have foundation. Ali et al. (2009) studied some new operations on soft set theory, Acar et al. (2010) introduced soft set and soft ring, Aktas and Cağman (2007) introduced the definition of soft groups and derived some basic properties of it, Sezgin et al. (2012) introduced soft near ring, Jana and Pal (2016) provided new soft intersection set on groups, Feng et al. (2008) initiated the concept of soft semiring, soft ideals on semiring and soft idealistic semiring.

It is well known that soft set theory as a tool for applications in both theoretical areas as well as a technique for laying the foundations. Nowadays and upcoming days, it has been stimulated a breadth of the disciplines of Information Sciences with intelligent systems, expert and decision support systems, approximate reasoning, self-adaptation and self-organizational systems, information and knowledge, modeling and computing as seen in the following studies like decision making (Çağman and Enginoçglu, 2010; Zhan, Liu and Herawan, 2017).

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