Roughness and entropy measures of a soft set

TL;DR

This paper introduces new roughness and entropy measures for soft sets, analyzing their properties and comparing them to classical rough set theory within the soft computing framework.

Contribution

It develops novel roughness and entropy measures for soft sets, preserving foundational principles and expanding theoretical understanding in soft computing.

Findings

Proposed roughness measures are defined within two conceptual frameworks.

Systematic analysis of properties using theoretical and computational methods.

Comparison with classical rough set theory highlights unique contributions.

Abstract

Soft set theory is an important and emerging area within soft computing, owing to its attribute-oriented mathematical framework and its wide applicability in diverse domains, including science and social sciences. The theoretical constraints associated with the selection of subsets of the sets of attributes in soft set theory have further motivated the development of hybrid and extended theoretical models. In this paper, we introduce two distinct roughness measures and six entropy measures for soft sets and systematically investigate their properties using both theoretical analysis and computational techniques. The proposed roughness measures are defined within two distinct conceptual frameworks. Throughout the development of these measures and the corresponding results, the foundational principles of soft set theory, as established by Molodtsov, are strictly preserved. Furthermore, the proposed framework is shown to be novel with respect to roughness characterization, and a comparative analysis with classical rough set theory is presented to highlight the theoretical distinctions and contributions of this work.