Definition and construction of fuzzy DI-subsethood measures

In this paper we study a method of construction of the fuzzy subsethood measures of V.R. Young [V.R. Young, Fuzzy subsethood, Fuzzy Sets and Systems 77 (1996) 371–384] and the fuzzy subsethood measures of J. Fan, X. Xie, and J. Pei [J. Fan, X. Xie, J. Pei, Subsethood measures: new definitions, Fuzzy Sets and Systems 106 (1999) 201–209]. We establish the conditions under which our constructions satisfy the axioms of Sinha and Dougherty’s inclusion measures and we present different methods for obtaining fuzzy entropies from said measures. Next we present a particular case of Young’s subsethood measures, DI-subsethood measures. For these we also analyze their construction and the conditions under which they satisfy different axioms.