Couso, InésBustince Sola, HumbertoFernández Fernández, Francisco JavierSánchez, Luciano2020-01-132020-12-042019I. Couso, H. Bustince, J. Fernandez and L. Sanchez, 'The null space of fuzzy inclusion measures,' in IEEE Transactions on Fuzzy Systems.1063-670610.1109/TFUZZ.2019.2957248https://academica-e.unavarra.es/handle/2454/36053Some formal relationships between the different axiomatic definitions of inclusion measure are analysed. 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 that of Sinha-Dougherty contain certain redundancies. Reduced equivalent lists of axioms are proposed.8 p.application/pdfeng© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other workSubsethood measureFuzzy inclusionSinha-Dougherty axiomsKitainik axioms keywordsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia