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.
Highlights
The multi-criteria decision making (MCDM) techniques have been rigorously investigated by many researchers around the real world
We present a result to show that LDFSR
The indiscernibility relation is “the selection of best material handling equipment”. This relation can be observed by LDFSR, ð : Q → Ġ given as Table 11
Summary
The multi-criteria decision making (MCDM) techniques have been rigorously investigated by many researchers around the real world. Due to uncertain and vague information, the complexity of human’s decision making has grown broadly in the present era This pursuit gave rise to many resourceful techniques to deal with real-world problems. This is an individualistic generalization of crisp set theory and was first originated by Pawlak (1982) This hypothesis acts as a tool for investigating and implementing solutions for various decision making difficulties found in the fields of computer intelligence, image processing, data analysis, medical sciences, and many more. Some integrated MCDM methods studied by researchers are TOPSIS (technique for the order preference by similarity to ideal solution), VIKOR (vlse kriterijumska optimizacija kompromisno resenje), PROMETHEE (preference ranking organization method for enrichment evaluations), COPRAS (complex proportional assessment), MOORA (multi-objective optimization by ratio analysis), GRA (grey relational analysis), ANP (analytic network process), BWM (best worst method), and aggregation operators
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