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Functional degrees of inclusion and similarity between L-fuzzy sets. Madrid-Labrador, Nicolás Miguel Ojeda-Aciego, Manuel Conjuntos difusos https://openpolicyfinder.jisc.ac.uk/id/publication/11428 Inclusion is one of the most basic relations between sets. In this paper, we show how to represent the degree of inclusion between two L-fuzzy sets via a function. Specifically, such a function determines the minimal modifications needed in an L-fuzzy set to be included (in Zadeh's sense) into another. To reach such a goal, firstly we present the notion of f-inclusion, which defines a family of crisp binary relations between L-fuzzy sets that are used as indexes of inclusion and, subsequently, we define the φ-degree of inclusion as the most suitable f-inclusion under certain criterion. In addition, we also present three φ-degrees of similarity definable from the φ-degree of inclusion. We show that the φ-degree of inclusion and the φ-degrees of similarities satisfy versions of many common axioms usually required for measures of inclusion and similarity in the literature. 2025-10-15T09:47:17Z 2025-10-15T09:47:17Z 2020-07-20 journal article Nicolás Madrid, Manuel Ojeda-Aciego: Functional degrees of inclusion and similarity between L-fuzzy sets. Fuzzy Sets Syst. 390: 1-22 (2020) https://hdl.handle.net/10630/40243 10.1016/j.fss.2019.03.018 eng open access Elsevier