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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 ...
Multidistances and inequality measures on abstract sets: an axiomatic approach
(Elsevier, 2021)
Artículo / Artikulua,
Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among ...
Topologies for semicontinuous Richter–Peleg multi-utilities
(Springer, 2020)
info:eu-repo/semantics/article,
The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite ...
Why using topological and analytical methods in aggregation of fuzzy preferences?
(2020)
info:eu-repo/semantics/conferenceObject,
The Arrow’s Impossibility Theorem states that there is no function fusing individual preferences into a social one satisfying certain properties of 'common sense'. On the contrary, in some of the fuzzy extensions of the ...
Unexpected thresholds from independence of irrelevant alternatives in fuzzy arrow theorems
(2019)
info:eu-repo/semantics/conferenceObject,
It is well known Arrow Theorem and its impact into Social Choice. It states that under an apparently mild set of conditions no rule fusing individual preferences into a social one is possible. In order to solve this ...
Fuzzy Arrovian theorems when preferences are strongly-connected
(University of Sistan and Baluchestan, 2022)
Artículo / Artikulua,
In this paper we study the aggregation of fuzzy preferences on non-necessarily finite societies. We characterize in terms of possibility and impossibility a family of models of strongly-connected preferences in which the ...
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 ...
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, ...