On similarity in fuzzy description logics

Eva Armengol, Pilar Dellunde, Àngel García-Cerdaña

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2016 Elsevier B.V. This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics. For this purpose we use concrete domains in the fuzzy description logic IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these objects.
Original languageEnglish
Pages (from-to)49-74
JournalFuzzy Sets and Systems
Volume292
DOIs
Publication statusPublished - 1 Jun 2016

Keywords

  • Attribute-value representation
  • Description logics
  • Fuzzy description logics
  • Similarity box
  • Similarity relation

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