The null space of fuzzy inclusion measures

摘要: In this article, some formal relationships between the different axiomatic definitions of inclusion measure are analyzed. In particular, the links between the different proposals about the null-space (the collection of pairs associated with a null degree of inclusion) are studied. Taking as starting point the well-known axiomatics of Kitainik and Sinha-Dougherty, we observe that other alternative proposals about the null-space are incompatible with both the null-space and the decomposition axioms of these authors. We also conclude that both the axiomatics of Kitainik and those of Sinha-Dougherty contain certain redundancies. Reduced equivalent lists of axioms are proposed.