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The real world is inherently uncertain, imprecise and vague. Soft set theorywas firstly introduced by Molodtsov in 1999 as a general mathematical tool fordealing with uncertainties, not clearly defined objects. A soft set consists oftwo parts which are parameter set and approximate value set. So while talkingabout any property on a soft set, it is notable to consider that each partsshould be evaluated separately. In this paper, by taking into account thiscase, we firstly define the concept of cardinality of soft hybrid sets whichare soft set, fuzzy soft set, fuzzy parameterized soft set and fuzzyparameterized fuzzy soft set. Then we discuss the entropy, similarity andsubsethood measures based on cardinality in a soft hybrid set, and investigatethe relationships among these concepts as well as related examples. Finally, wepresent an application which is a representation method based on cardinality ofa soft hybrid space.

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