Parameter Reductions of Bipolar Fuzzy Soft Sets with Their Decision-Making Algorithms

Abstract

Parameter reduction is a very important technique in many fields, including pattern recognition. Many reduction techniques have been reported for fuzzy soft sets to solve decision-making problems. However, there is almost no attention to the parameter reduction of bipolar fuzzy soft sets, which take advantage of the fact that membership and non-membership degrees play a symmetric role. This methodology is of great importance in many decision-making situations. In this paper, we provide a novel theoretical approach to solve decision-making problems based on bipolar fuzzy soft sets and study four types of parameter reductions of such sets. Parameter reduction algorithms are developed and illustrated through examples. The experimental results prove that our proposed parameter reduction techniques delete the irrelevant parameters while keeping definite decision-making choices unchanged. Moreover, the reduction algorithms are compared regarding the degree of ease of computing reduction, applicability, exact degree of reduction, applied situation, and multi-use of parameter reduction. Finally, a real application is developed to describe the validity of our proposed reduction algorithms.

More General Form of Interval-Valued Fuzzy Ideals of BCK/BCI-Algebras

“…is concept has been studied from various points of view in different algebraic structures as BCK-algebras and some of its generalization (see, for example, [1][2][3][4][5]), groups (see for example, [6][7][8][9][10]), and rings (see, for example, [11][12][13]). Moreover, as novel approaches in decision-making, theoretical models were introduced based on (fuzzy) soft sets in [14][15][16][17][18][19]. In BCK/BCI-algebras and other related algebraic structures, different kinds of related concepts were investigated in various ways (see, for example, [20][21][22][23][24][25][26][27][28][29][30][31][32][33]).…”

Robust Aggregation Operators for Intuitionistic Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

“…Maji et al [7] established the notion of the fuzzy soft set (FSS) by merging FS and SS. Ali et al [8] proposed a novel decision-making approach for bipolar FSS utilizing different types of parameter reduction. Maji et al [9] developed the notion of IFSS and presented some fundamental operations with their desirable properties.…”

Parameter reductions in N‐soft sets and their applications in decision‐making

“…The theory of soft sets emerged as a way to escape from some of the weaknesses of previous models (Molodtsov, 1999) and is now playing a vital role in many fields including data analysis (Zou & Xiao, 2008) and decision‐making (Akram, Ali, & Alcantud, 2019; Ali, Akram, & Alcantud, 2019; Ali, Akram, Koam, & Alcantud, 2019; Feng, Jun, Liu, & Li, 2010; Ma, 2015; Maji, Biswas, & Roy, 2002; Roy & Maji, 2007). As to its theoretical development, Maji, Biswas, and Roy (2003) defined core algebraic operations for soft sets, which were complemented with additional operations in a study by Ali, Feng, Liu, Min, and Shabir (2009).…”