RT journal article
T1 Functional degrees of inclusion and similarity between L-fuzzy sets.
A1 Madrid Labrador, Nicolás Miguel
A1 Ojeda Aciego, Manuel
A2 Matemáticas
K1 Fuzzy sets
K1 Measure of inclusion
K1 Measure of Similarity
AB 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.
SN 0165-0114
YR 2020
FD 2020
LK http://hdl.handle.net/10498/38432
UL http://hdl.handle.net/10498/38432
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026