Novel Characterizations of Rough Soft Sets: Equivalent Soft Sets in Pawlak Approximation Space with Applications

Abstract

Rough soft sets include both a partition set of alternatives and the parameters that classify the alternatives. Therefore, the decision-making models proposed on the rough soft set structure should be able to select the appropriate partition set and the appropriate alternative. In this paper, a novel concept of equivalent soft sets in an approximation space is introduced, and various characterizations of rough soft sets are given. Parametric and alternative equivalence numbers of a soft set in a Pawlak approximation space are assigned, and using these, three functions, namely, the set determinant parametric function, the alternative determinant parametric function, and the common determinant parametric function, are defined, and then a group decision-making method, SetAltDM on rough soft sets, is presented. The effectiveness of SetAltDM is supported by many comparative examples. Two novel similarity measures, PR and weighted-PR similarity methods, are proposed, and a similarity-based decision-making method with a real-life application about benchmarking is given.