Itziar García-Honrado
University of León
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Featured researches published by Itziar García-Honrado.
Information Sciences | 2010
Enric Trillas; Itziar García-Honrado; Ana Pradera
In a preordered set, or preset, consequence operators in the sense of Tarski, defined on families of subsets, are introduced. From them, the corresponding sets of conjectures, hypotheses, speculations and refutations are considered, studying the relationships between these sets and those previously defined on ortholattices. All the concepts introduced are illustrated with three particular consequence operators, whose behavior is studied in detail. The results obtained are applied to the case of fuzzy sets endowed with the usual pointwise ordering.
soft computing | 2012
Itziar García-Honrado; Enric Trillas
Guessing from a piece of information is what humans do in their reasoning processes, that is why reasoning and obtaining conjectures can be considered almost equivalent. These reasoning processes are nothing else than posing new questions which possible answers are non contradictory with the available information. This is the idea that allows to introduce different mathematical models by means of different conjecture operators, built up depending on how the concept of non-contradiction is understood. A relevant contribution of this chapter is that there can be conjecture operators not coming from Tarski’s operators of consequences, in this way untying the concept of conjecture from a previously given deductive system. The concept of a conjecture proves to include those of logical consequences, hypotheses and speculations.
information processing and management of uncertainty | 2010
Enric Trillas; Takehiko Nakama; Itziar García-Honrado
Various forms of probability and probabilistic concepts have been discussed in fuzzy logic since its very inception, but their mathematical foundations have yet to be fully established. In this paper, we investigate theoretical issues concerning (1) probability measures as membership functions, (2) probability measures for fuzzy sets, and (3) fuzzy-valued probabilities.
soft computing | 2012
Takehiko Nakama; Enric Trillas; Itziar García-Honrado
Various forms of probability and probabilistic concepts have been discussed in fuzzy logic since its very inception, but their mathematical foundations have yet to be fully established. In this paper, we investigate theoretical issues concerning probability functions as membership functions, probability measures for fuzzy sets, and fuzzy-valued probabilities.
north american fuzzy information processing society | 2010
C. Alsina; Enric Trillas; Itziar García-Honrado
This paper deals with a problem in fuzzy logic that can be traced back to classical logic: the reduction of one conditional to another. In particular, the reduction of R-implications to S-implications and to Q-operators is considered, although the more complex case is the reduction of a Q-operator to an S-implication, equivalent to find the complete solution of a functional equation involving strong negations, continuous t-conorms, and continuous t-norms. Necessary and sufficient conditions for the validity of such equation are presented in several cases, but other cases remain open and deserve to be studied.
Archive | 2013
Enric Trillas; Itziar García-Honrado
This paper just contains some reflections on the well known classical ’Sorites Paradox’, under which it appears that some imprecise linguistic terms cannot have a crisp extension, that there is no any subset containing the elements in the universe verifying the term. Such reflections are conducted from a typically layperson’s point of view that heaps are not definable by means of the number of grains of sand they have, but mainly by its three-dimensional shape. Representing imprecise terms P by means of fuzzy sets, or contextual membership functions, it is shown that the Black’s separation point is sometimes uniquely determinable, and that it always exists a crisp subset whose elements are ’more’ P than either not P, or an opposite of P. Additionally, some considerations on the case of heaps once compared with the shape of either a pyramid, or a circular cone, are done.
conference of european society for fuzzy logic and technology | 2011
Itziar García-Honrado; Enric Trillas
This paper takes into account the Wittgenstein’s idea of family resemblance as a particular crisp relation between some fuzzy sets, that is, between some representations of predicates use from its use. It is shown that all uses of the same predicate actually do have some kind of family resemblance, that some pairs of predicates cannot, and how the predicates migration between different universes of discourse can be related with family resemblance. A possibility of sketching all that through Galois Connections is also considered.
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems | 2013
Itziar García-Honrado; Enric Trillas; Claudi Alsina
This short paper is devoted to study the law (μ → σ) · λ ≤ μ → σ·λ, with fuzzy sets μ, σ, and λ, in the case the conditional → is functionally expressible by a numerical function J, and the intersection · is functionally expressible by a continuous t-norm T. That is, it deals with the functional inequality T(J(a,b),c) ≤ J(a,T(b,c)) in the unknowns T and J.
international symposium on multiple-valued logic | 2011
Itziar García-Honrado; Enric Trillas
This short paper just contains some reflections on the symmetric difference operator translating into an algebraic framework the connective exclusive disjunction, the linguistic either/or. In particular, it tries to find an upper bound for the fuzzy operators generalizing the classical symmetric difference, that is, those to deal with imprecise statements. This search is made throughout the preservation of the inferential schemes of disjunctive syllogism in fuzzy logic. The paper tries to stress the inferential interest of the symmetric difference.
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems | 2016
Angela Blanco-Fernández; Patricia Díaz-Díaz; Itziar García-Honrado; Ana Belén Ramos-Guajardo; Luis José Rodríguez-Muñiz
Spanish primary and secondary school curricula comprise several contents, learning outcomes and assessment criteria directly related with probability and approximate calculus. Some of them refer to situations modeled by the students, which entail not only uncertainty but also imprecision. For this reason, different techniques including fuzzy logic and fuzzy sets theory could be applied when dealing with this kind of situations in the classroom. Several teaching situations handling imprecise concepts in primary and secondary schools are suggested from a theoretical point of view. These more exible ways of reasoning could be combined with the traditional probability approach, allowing to tackle more general problems and not only those involving exact calculations or specific numerical assignments. Moreover, this type of approaches will provide the students with tools to manage imprecision as a mathematical tool in their personal life.