Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment

Abstract

The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In this paper, the notions of linear Diophantine fuzzy soft rough sets (LDFSRSs) and soft rough linear Diophantine fuzzy sets (SRLDFSs) are proposed as new hybrid models of soft sets, rough sets, and LDFS. The suggested models of LDFSRSs and SRLDFSs are more flexible to discuss fuzziness and roughness in terms of upper and lower approximation operators. Certain operations on LDFSRSs and SRLDFSs have been established to discuss robust multi-criteria decision making (MCDM) for the selection of sustainable material handling equipment. For these objectives, some algorithms are developed for the ranking of feasible alternatives and deriving an optimal decision. Meanwhile, the ideas of the upper reduct, lower reduct, and core set are defined as key factors in the proposed MCDM technique. An application of MCDM is illustrated by a numerical example, and the final ranking in the selection of sustainable material handling equipment is computed by the proposed algorithms. Finally, a comparison analysis is given to justify the feasibility, reliability, and superiority of the proposed models.

Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making

“…In the future, we will encompass the investigated ideas in the environment of complex q-rung orthopair fuzzy sets [32][33][34][35][36], spherical and T-spherical fuzzy sets [37], complex T-spherical fuzzy sets [38], and complex neutrosophic sets [39,40], etc. We will use [41][42][43] to enhance the excellence of the scrutinized approaches. Furthermore, we may also apply the proposed aggregation operators to two-sided matching decision-making problems or consider the consensus reaching process with complex intuitionistic fuzzy soft sets in group decision making by referring to two-sided matching decision making with multigranular hesitant fuzzy linguistic term sets and incomplete criteria weight information [44][45][46].…”

Cubic M-polar Fuzzy Hybrid Aggregation Operators with Dombi’s T-norm and T-conorm with Application

“…Riaz and Hashmi [35] developed the notion of cubic m-polar fuzzy sets and established cubic m-polar fuzzy averaging aggregation operators for agribusiness MAGDM. Recently, Riaz and Hashmi [36][37][38] introduced some new extensions of fuzzy sets named as linear Diophantine fuzzy set (LDFS), soft rough linear Diophantine fuzzy set, and spherical linear Diophantine sets. Kamaci [39] introduced algebraic structure to LDFS with an interesting application to coding theory, which is based on LDFS codes.…”

Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

“…A LDFS is a strong model to relax the limitations of MD and NMD due to existence of reference/control parameters. Riaz et al [52] extended LDFS to the idea of soft rough LDFS sets with application to sustainable material handling equipment. Riaz et al [53] introduced spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM.…”