Bipolar fuzzy soft sets and its applications in decision making problem

Abstract

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

An application of fuzzy soft multisets to algebra

“…Maji et al present the concept of fuzzy soft set [21] which is based on a combination of the fuzzy set and soft set models. Presentations of lots of methods which for solving some important problems of some fields such as medicine and decision making in the last decade [1,5,8,18,32,34,38] show that applied studies on soft set theory continue without slowing down. Moreover, theoretical studies on soft set theory have been continuing rapidly in recent years [2,4,6,7,11,12,33].…”

Fuzzy Parameterized Bipolar Fuzzy Soft Expert Set and Its Application in Decision Making

“…In this paper, we extend the concept of fuzzy parameterized fuzzy soft expert set to the bipolar-valued fuzzy set introduced by Lee [10], and we introduce the fuzzy parameterized bipolar fuzzy soft expert set (FPBFSES). We investigated the basic properties of this set such as De Morgan's law and applied it to a decision-making problem, i.e., the home buying process.…”

“…Definition 3.4 [10]. Consider a set of universe U and a set of parameter E. Suppose P (U ) represents the set of all bipolar fuzzy sets on U .…”

“…Definition 3.6 [10]. A BFSS (F, A) is called an absolute BFSS if F (e) = B U ∀e ∈ A, where B U is the collection of all bipolar fuzzy subset of U .…”

Inverse fuzzy soft set and its application in decision making

“…Yang et al (2009) used Kong's algorithm to solve a decision-making problem while Feng et al (2010) extended the level soft sets methods to interval-valued fuzzy soft sets, followed by Alhazaymeh and Hassan (2012a, 2012b, 2013a, 2013b, and Hassan and Alhazaymeh (2013) on vague soft sets, and trapezoidal fuzzy soft sets (Xiao et al, 2012;Khalil and Hassan, 2017a). Cagman and Karatas (2013) defined the intuitionistic fuzzy soft sets, followed by studies on generalised intuitionistic fuzzy soft sets (Agarwal et al, 2013;Khalil, 2015), multi Q-fuzzy parameterised soft sets (Adam and Hassan, 2014), possibility multi-fuzzy soft sets (Zhang and Shu, 2014;Khalil and Hassan, 2017b), bipolar fuzzy soft sets (Abdullah et al, 2014), trapezoidal interval type-2 fuzzy soft sets (Zhang and Zhang, 2013;Khalil and Hassan, 2017c) and vague soft set relations and functions (Alhazaymeh and Hassan, 2015). Since Zadeh (1965) introduced his model, fuzzy sets and fuzzy logic have been applied to many real life problems in uncertain, ambiguous environment (Alhazaymeh and Hassan, 2012c;Singh et al, 2014;Alhazaymeh et al, 2012) and further developed in decision-making processes (Tripathy and Arun, 2015;Tripathy et al, 2016;Sooraj et al, 2016Sooraj et al, , 2017, and neuro-fuzzy genetics Hassan, 2012, 2013).…”