2026-05-28T09:25:05Zhttps://riuma.uma.es/rest/oai/requestoai:riuma.uma.es:10630/402432026-02-03T11:26:56Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga
author
Madrid-Labrador, Nicolás Miguel
author
Ojeda-Aciego, Manuel
2025-10-15T09:47:17Z
2025-10-15T09:47:17Z
2020-07-20
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
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.
eng
Conjuntos difusos
Functional degrees of inclusion and similarity between L-fuzzy sets.
journal article
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URL
https://riuma.uma.es/bitstreams/606cb86e-d112-408a-bea9-d88862a2a8d7/download
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cf3dee274f1728cfee52734a438f3fad
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application/pdf
R2-f-inclusion.pdf