202 research outputs found
Lower Approximations by Fuzzy Consequence Operators
Peer ReviewedPostprint (author's final draft
Aggregation operators and lipschitzian conditions
Lipschitzian aggregation operators with respect to the natural T - indistin-
guishability operator Et and their powers, and with respect to the residuation ! T
with respect to a t-norm T and its powers are studied. A t-norm T is proved to be E
T -Lipschitzian and -Lipschitzian, and is
interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm
T with additive generator t , the quasi-
arithmetic mean generated by t
is proved to be the most stable aggregation
operator with respect to TPeer Reviewe
Fifty years of similarity relations: a survey of foundations and applications
On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft
On a conjecture concerning positive semi-definiteness
In [7] a conjecture relating the positive definiteness of a similarity with its transitivity with respect to the Lukasiewicz t-norm is made. In its current form, the conjecture is not true but from a modified version interesting consequences can be derived.Peer ReviewedPostprint (author's final draft
Aggregating T-equivalence relations
This contribution deals with the problem of aggregating Tequivalence relations, in the sense that we are looking for functions that preserve reflexivity, symmetry, and transitivity with respect to a given t-norm T. We obtain a complete description of those functions in terms of that we call T-triangular triplets. Any extra condition on the t-norm is assumed.Postprint (published version
ET-Lipschitzian aggregation operators
Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.Peer ReviewedPostprint (published version
T-Indistinguishability Operators with respect to Ordinal Sums.
Peer ReviewedPostprint (author’s final draft
Acciones de grupos borrosas
Este trabajo generaliza (fuzzifica) las acciones de un grupo sobre un conjunto para tratar situaciones donde hay imprecisiĂłn e incertidumbre. Las acciones borrosas pueden tratar la granularidad de un conjunto o incluso generarla definiendo una relaciĂłn de equivalencia borrosa en Ă©l.Peer ReviewedPostprint (author's final draft
Characterization of unidimensional averaged similarities
A T-indistinguishability operator (or fuzzy similarity relation) E is called unidimensional when it may be obtained from one single fuzzy subset (or fuzzy criterion). In this paper, we study when a T-indistinguishability operator that has been obtained as an average of many unidimensional ones is unidimensional too. In this case, the single fuzzy subset used to generate E is explicitly obtained as the quasi-arithmetic mean of all the fuzzy criteria primarily involved in the construction of E.Peer ReviewedPostprint (author's final draft
Generation and Characterization of Fuzzy T-preorders
This article studies T-preorders that can be generated in a natural way by a single fuzzy subset. These T-preorders are called one-dimensional and are of great importance, because every T-preorder can be generated by combining one-dimensional T-preorders.; In this article, the relation between fuzzy subsets generating the same T-preorder is given, and one-dimensional T-preorders are characterized in two different ways: They generate linear crisp orderings on X and they satisfy a Sincov-like functional equation. This last characterization is used to approximate a given T-preorder by a one-dimensional one by relating the issue to Saaty matrices used in the Analytical Hierarchical Process. Finally, strong complete T-preorders, important in decision-making problems, are also characterized.Peer ReviewedPostprint (author’s final draft
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