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Soft Computing

, Volume 1, Issue 4, pp 162–165 | Cite as

Characterizing non-monotonic fuzzy relations

  • S. Cubillo
  • E. Trillas
Original paper

Abstract

 This paper is on &-T-monotonic Fuzzy Relations and on the particular case of &-Monotonic Fuzzy Relations (in the crisp case &-Weakly-monotonic and &-Strongly-monotonic Relations, respectively). It goes a little further of the previous work the authors did on this kind of Fuzzy and Crisp Relations by proving a Characterization Theorem of &-T-monotonicity for Reflexive Fuzzy Relations that contains all the former results. This theorem is not only particularized to the crisp case but it is shown that then only crisp Logical States are needed. Of course, also Non-&-T-monotonic Fuzzy Relations and Non-Weak-&-monotonic crisp Relations became characterized.

Keywords Monotonic and non-monotonic fuzzy and crisp Relations Logical T-States Logical Fuzzy States and Logical States. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • S. Cubillo
    • 1
  • E. Trillas
    • 2
  1. 1.Dpt. Matemática Aplicada Universidad Politécnica de Madrid. Facultad Informática Campus de Montegancedo. Boadilla del Monte. 28660 Madrid. e-mail: scubillo@fi.upm.es
  2. 2.Dpt. Inteligencia Artificial. Universidad Politécnica de Madrid. Campus de Montegancedo. Boadilla del Monte. 28660 Madrid. e-mail: etrillas@fi.upm.es

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