Similarity, entropy and subsethood measures based on cardinality of soft hybrid sets

TL;DR

This paper introduces cardinality-based measures for soft hybrid sets, including similarity, entropy, and subsethood, and explores their relationships and applications in uncertain data analysis.

Contribution

It defines the concept of cardinality for various soft hybrid sets and develops related measures, providing new tools for uncertainty modeling.

Findings

Defined cardinality for soft, fuzzy, and hybrid sets

Developed entropy, similarity, and subsethood measures based on cardinality

Presented an application for representing soft hybrid spaces

Abstract

The real world is inherently uncertain, imprecise and vague. Soft set theory was firstly introduced by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainties, not clearly defined objects. A soft set consists of two parts which are parameter set and approximate value set. So while talking about any property on a soft set, it is notable to consider that each parts should be evaluated separately. In this paper, by taking into account this case, we firstly define the concept of cardinality of soft hybrid sets which are soft set, fuzzy soft set, fuzzy parameterized soft set and fuzzy parameterized fuzzy soft set. Then we discuss the entropy, similarity and subsethood measures based on cardinality in a soft hybrid set, and investigate the relationships among these concepts as well as related examples. Finally, we present an application which is a representation method based on cardinality of a soft hybrid space.