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Assigning numerical scores to linguistic expressions
(MDPI, 2017)
Artículo / Artikulua,
In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to ...
Binary relations coming from solutions of functional equations: orderings and fuzzy subsets
(World Scientific Publishing Company, 2017)
Artículo / Artikulua,
We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We ...
Weightable quasi-metrics related to fuzzy sets
(Hacettepe University (Turquía), 2018)
info:eu-repo/semantics/article,
We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership ...
Geometrical aggregation of finite fuzzy sets
(Elsevier, 2018)
info:eu-repo/semantics/article,
A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical ...
Decomposition and arrow-like aggregation of fuzzy preferences
(MDPI, 2020)
info:eu-repo/semantics/article,
We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this ...
An axiomatic approach to finite means
(Elsevier, 2018)
info:eu-repo/semantics/article,
In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring ...
A survey on the mathematical foundations of axiomatic entropy: representability and orderings
(MDPI, 2018)
info:eu-repo/semantics/article,
Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, ...