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

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.