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Tied Adjointness Algebra-based Fuzzy Rough Sets and Their Applications in Decision Making
Rajesh Kedarnath Navandar, Jambi Ratna Raja Kumar, Sandeep P. Abhang, Pranoti Prashant Mane, Kalyani Kadam, Yogita D. Bhise, Suman Kumar Swarnkar, Antonios Kalampakas, Faisal Z. Duraihem, Sovan Samanta and Prasenjit Mandal
Morsi et al. [23] initiated the concept of tied adjointness algebra (TAA) and gave the idea of many valued rough sets (MVRSs) based on two independently chosen complete lattices and a t-norm. In the present study, we extend this concept by proposing constructive approaches of one and two pairs of (Φ,Ψ)-fuzzy rough approximation ((Φ,Ψ)-FRA) operators based on TAA, where (Φ,≤Φ), (Ψ,≤Ψ) are two poset. First, we introduce one pair of (Φ,Ψ)-FRA operators based on TAA and fuzzy relation, which are generalizations of MVRSs.With the basis of FRs, the basic properties of (Φ,Ψ)-FRA operators, and topological properties by the Galois connection and subsethood measure are also discussed. Then, we introduce two pairs of (Φ,Ψ)-FRA operators based on TAA and fuzzy relation, which is a generalization of one pair of (Φ,Ψ)-FRA operators. The basic properties of two pairs of (Φ,Ψ)-FRA operators are also discussed based on various types of fuzzy relations. The links between two types of approximation operators are carried out. Finally, based on (Φ,Ψ)-FRA operators a novel approach to the multicriteria decision-making (MCDM) method with the help of the PROMETHEE technique is proposed. An example is also provided to demonstrate the practicality and efficiency of our suggested approach in addressing real-world issues. Upon evaluating the ranking outcomes from both established methodologies and our newly introduced approach, it’s evident that the most favorable choice remains unchanged. This indicates a harmonious alignment between our suggested decision-making process and the conventional methods.
Keywords: Fuzzy rough approximation operators, fuzzy relation, topology, tied adjointness algebra