Certain Hybrid Rough Models with Type-2 Soft Information
Musavarah Sarwar and Muhammad Akram
The integration of rough sets with other algebraic structures is a key approach to study different types of uncertainties simultaneously with a single mathematical approach. The main focus of this research article is to integrate the notions of rough approximations, type-2 soft sets and fuzzy sets in different ways. By computing rough approximations of fuzzy sets and type-2 soft sets, we introduce the novel concepts of rough fuzzy soft set, rough type-2 soft set and rough fuzzy type-2 soft set. Applying type-2 soft approximations on fuzzy sets and rough sets simultaneously, we establish the novel notions of type-2 soft rough set, type-2 soft rough fuzzy set and fuzzy type-2 soft rough set. We study certain properties, operations and algebraic relations on these hybrid models. We establish formulae to compute type-2 soft approximations and rough approximations of fuzzy sets to reduce calculation complexity. We study the importance of roughness and fuzziness in type-2 soft knowledge with a decision making problem. We give a comparison analysis of the presented approach with existing to show its efficacy and out-performance.
Keywords: Rough type-2 soft set, rough fuzzy type-2 soft set, fuzzy type-2 soft rough set, decision making