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Structural analysis of indistinguishability operators and related concepts
Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
Universitat Politècnica de Catalunya. Departament d'Estructures a l'Arquitectura; Universitat Politècnica de Catalunya. FIA - Modelització Matemàtica Funcional i Aplicacions
Given an indistinguishability operator E, it is possible to obtain the set of extensional fuzzy subsets HEHE and the respective operators of upper and lower approximations by extensional sets ¿E¿E and ¿E¿E. Reciprocally, given any of these objects, the initial indistinguishability operator E can be retrieved. It is well known that these concepts are in bijection. In this paper, we will prove that the relation underlying them is a lattice isomorphism. We will also consider further operators such as natural means and finally show the robustness of the results with respect to isomorphisms of t-norms.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
Fuzzy logic
Set theory
Artificial intelligence
Software engineering
Lògica difusa

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