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See detailA Polynomial Time Subsumption Algorithm for Nominal Safe $ELO_{\bot}$ under Rational Closure
Casini, Giovanni UL; Straccia, Umberto; Meyer, Thomas

in Information Sciences (in press)

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal ... [more ▼]

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe $ELO_{\bot}$, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe $ELO_{\bot}$ under RC that relies entirely on a series of classical, monotonic $EL_{\bot}$ subsumption tests. Therefore, any existing classical monotonic $EL_{\bot}$ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability. [less ▲]

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See detailGeneralized qualitative Sugeno integrals
Dubois, Didier; Prade, Henri; Rico, Agnès et al

in Information Sciences (2017), 415-416

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of ... [more ▼]

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of Sugeno integrals on totally ordered bounded chains, by extending the operation that combines the value of the capacity on each subset of criteria and the value of the utility function over elements of the subset. We show that the generalized concept of Sugeno integral splits into two functionals, one based on a general multiple-valued conjunction (we call integral) and one based on a general multiple-valued implication (we call cointegral). These fuzzy conjunction and implication connectives are related via a so-called semiduality property, involving an involutive negation. Sugeno integrals correspond to the case when the fuzzy conjunction is the minimum and the fuzzy implication is Kleene-Dienes implication, in which case integrals and cointegrals coincide. In this paper, we consider a very general class of fuzzy conjunction operations on a finite setting, that reduce to Boolean conjunctions on extreme values of the bounded chain, and are non-decreasing in each place, and the corresponding general class of implications (their semiduals). The merit of these new aggregation operators is to go beyond pure lattice polynomials, thus enhancing the expressive power of qualitative aggregation functions, especially as to the way an importance weight can affect a local rating of an object to be chosen. [less ▲]

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See detailk-Metric antidimension: A privacy measure for social graphs
Trujillo Rasua, Rolando UL; Yero, Ismael G.

in Information Sciences (2016), 328

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See detailk-Metric Antidimension: a Privacy Measure for Social Graphs
Trujillo Rasua, Rolando UL; Yero, Ismael G.

in Information Sciences (2015), 328

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See detailMicroaggregation-and permutation-based anonymization of movement data
Domingo-Ferrer, Josep; Trujillo Rasua, Rolando UL

in Information Sciences (2012), 208

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See detailMicroaggregation-and Permutation-Based Anonymization of Mobility Data
Domingo-Ferrer, Josep; Trujillo Rasua, Rolando UL

in Information Sciences (2012), 208

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See detailAggregation functions: Means
Grabisch, Michel; Marichal, Jean-Luc UL; Mesiar, Radko et al

in Information Sciences (2011), 181(1), 1-22

This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic ... [more ▼]

This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic classification on aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with multiple arities (extended means). [less ▲]

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See detailAggregation functions: Construction methods, conjunctive, disjunctive and mixed classes
Grabisch, Michel; Marichal, Jean-Luc UL; Mesiar, Radko et al

in Information Sciences (2011), 181(1), 23-43

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions ... [more ▼]

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions and on special classes of aggregation functions, covering the well-known conjunctive, disjunctive, and mixed aggregation functions. Some fields of applications are included. [less ▲]

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See detailAn axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Kojadinovic, Ivan; Marichal, Jean-Luc UL; Roubens, Marc

in Information Sciences (2005), 172(1-2), 131-153

To extend the classical Shannon entropy to non-additive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this ... [more ▼]

To extend the classical Shannon entropy to non-additive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this new concept on the basis of three axioms: the symmetry property, a boundary condition for which the entropy reduces to the Shannon entropy, and a generalized version of the well-known recursivity property. We also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy-like measure. Lastly, we provide an interpretation of it in the framework of aggregation by the discrete Choquet integral. [less ▲]

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