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Weak Fuzzy S-Subsethood Measures: Overlap Index

Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.