Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis

Abstract

Rough set (RS) and fuzzy set (FS) theories were developed to account for ambiguity in the data processing. The most persuasive and modernist abstraction of an FS is the linear Diophantine FS (LD-FS). This paper introduces a resilient hybrid linear Diophantine fuzzy RS model (LDF-RS) on paired universes based on a linear Diophantine fuzzy relation (LDF-R). This is a typical method of fuzzy RS (F-RS) and bipolar FRS (BF-RS) on two universes that are more appropriate and customizable. By using an LDF-level cut relation, the notions of lower approximation (L-A) and upper approximation (U-A) are defined. While this is going on, certain fundamental structural aspects of LD-FAs are thoroughly investigated, with some instances to back them up. This cutting-edge LDF-RS technique is crucial from both a theoretical and practical perspective in the field of medical assessment.

Another approach to linear Diophantine fuzzy rough sets on two universes and its application towards decision-making problems

“…• Recently, Ayub et al [13,14] introduced the notion of roughness in LD-FSs on two different universes, where crisp lower and upper approximations were defined by using an arbitrary LD-FR and the ( )…”

“…In LD-FSs, the ranking of objects is easy according to the approach of Riaz and Hashmi [48] technique. Since then, there have been various exciting models and techniques for ranking among objects in the framework of LD-FSs (see [12][13][14][15][16][17][18]). But, the situation is not straightforward in the case of LDF-RSs.…”

“…But, the situation is not straightforward in the case of LDF-RSs. However, Ayub et al [13,14] proposed various techniques for ranking in the case of LDF-RSs. But, these techniques are independent of the proposed technique of this study.…”

“…Almagrabi et al [12] offered a new approach to a q-linear Diophantine fuzzy emergency decision support system for COVID-19. Ayubet al [13,14] linear Diophantine Fuzzy RSs. Further, Ayub et al [15] initiated the idea of LD-FRs and their algebraic properties with applications in DM problems.…”

Multi-Attribute Decision-Making for T-Spherical Fuzzy Information Utilizing Schweizer-Sklar Prioritized Aggregation Operators for Recycled Water

“…We will expand our decision-making algorithm in future work to accommodate various extensions of fuzzy sets, including favorite associations, data-driven agreement models, and significant decisionmaking issues [53][54][55][56][57][58]. Additionally, we will discuss their applicability to many fields like artificial intelligence, machine learning, game theory, etc.…”