A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System

Abstract

The basic idea underneath the generalized intuitionistic fuzzy soft set is very constructive in decision making, since it considers how to exploit an extra intuitionistic fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is redefined and clarified by F. Feng. In this paper, we introduced a method to solve decision making problems using an adjustable weighted soft discernibility matrix in a generalized intuitionistic fuzzy soft set. We define the threshold functions like mid-threshold, top-bottom-threshold, bottom-bottom-threshold, top-top-threshold, med-threshold function and their level soft sets of the generalized intuitionistic fuzzy soft set. After, we proposed two algorithms based on threshold functions, a weighted soft discernibility matrix and a generalized intuitionistic fuzzy soft set and also to show the supremacy of the given methods we illustrate a descriptive example using a weighted soft discernibility matrix in the generalized intuitionistic fuzzy soft set. Results indicate that the proposed method is more effective and generalized over all existing methods of the fuzzy soft set. Mathematics 2019, 7, 742 2 of 21 such as economics, medical science, social science, environmental science and engineering. In recent years, model vagueness has become interested in many authors. Many classical theories such as fuzzy set theory [1], probability theory, vague set theory [2], rough set theory [3], intuitionistic fuzzy set [4] and interval mathematics [5] are well known and effectively model uncertainty. These approaches show their inherent difficulties as pointed out by Molodtsov [6], because of intensive quantity and type of uncertainties. In Reference [6], Molodtsov defines the soft set which is a new logical instrument for dealing uncertainties.Soft set theory attracts many authors because it has a vast range of applications in many areas like the smoothness of functions, decision making, probability theory, data analysis, measurement theory, forecasting and operations research [6][7][8][9][10]. Nowadays, many authors work to hybridize the different models with soft set and achieved results in many applicable theories. Maji defines the fuzzy soft set and intuitionistic fuzzy soft set [11,12]. Then the further extensions of soft sets like the generalized fuzzy soft set [13], the interval-valued fuzzy soft set [14], the soft rough set [15], the vague soft set [16], the trapezoidal fuzzy soft set [17], the neutrosophic soft set [18], the intuitionistic neutrosophic soft set [19], the multi-fuzzy soft set [20] and the hesitant fuzzy soft set [21] are introduced. Agarwal defines the generalized intuitionistic fuzzy soft set (GIFSS) [22] which has some problems pointed out by Feng [23] and redefined GIFSS.In Reference [24], Coung defines the picture fuzzy set which is an extension of the fuzzy soft set and intuitionistic fuzzy set. In Reference [25], Sing defines the correlation coefficients of PFS and their applications in clustering anal...

Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects

“…Khan et al [12] define the generalized picture fuzzy soft set and applied them to decision-making problems. For study more about decision making, we refer to [13][14][15][16][17][18][19].Yager [20,21] defines the Pythagorean fuzzy sets P yF S, which is the successful extension of intuitionistic fuzzy sets, by putting a new condition on positive membership ξ and negative membership functions ν, i.e., 0 ≤ ξ 2 + ν 2 ≤ 1. This new condition expand the domain of membership functions like if we have ξ = 0.7 and ν = 0.5, then we cannot deal it with intuitionistic fuzzy set because 0.7 + 0.5 ≥ 1 but 0.7 2 + 0.5 2 = 0.49 + 0.25 = 0.74 ≤ 1 and hence P yF S applied successfully.…”

“…Khan et al [12] define the generalized picture fuzzy soft set and applied them to decision-making problems. For study more about decision making, we refer to [13][14][15][16][17][18][19].…”

Knowledge measure for the q‐rung orthopair fuzzy sets

“…The enterprise resource planning systems selection problem was solved by Hamy mean operators for by Wang et al 26 The multiplicative consistency of preference relation of was analyzed by Zhang et al 27 The multiparametric similarity measure and combinative distance‐based assessment were used to evaluate classroom teaching quality 28 . The distance, similarity, entropy, and inclusion measures for were defined by Peng et al 29 The similarity measures of based on cosine function were expounded by Wang et al 30 For more literature on decision making, refer to References [31–41].…”

The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM

“…Thereafter, many DM procedures based on the soft sets were constructed and their applications in various fields were given. For more details, we refer to read the papers given in (Çagman and Enginoglu 2010b;Athira et al 2019;Arora 2018, 2019;Khan et al 2019;Feng et al 2012;Herawan and Deris 2010;Perveen et al 2019;Selvachandran et al 2018b;Maji et al 2002). In Çagman and Enginoglu (2010a); the authors have defined the soft matrix which is a matrix representation of the soft set and its based approach to solve the DM problems.…”