An essay on name and extension of rule-given properties

  • Enric Trillas
  • Susana Cubillo
  • A. R. De Soto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 945)


In the crisp case, any non-empty set A of a universe X is a preordering's class under the material conditional →A. Then, the elements of A are to be considered as those of X satisfying the property of being the ”followers” of any a ε A; we could see A as a ”segment of the structure (X, →).

Based on this idea, it is studied the frequent case in which a vague or crisp predicate P is known through both a set of rules (representable by a fuzzy or crisp preorder) and by a crisp prototype. The paper shows how, on this hypothesis, the extension of P or the membership function of the (fuzzy or crisp, respectively) set labelled P is obtained.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Enric Trillas
    • 1
  • Susana Cubillo
    • 2
  • A. R. De Soto
    • 3
  1. 1.Dept. Inteligencia ArtificialU.P.M.MadridSpain
  2. 2.Dept. Matemática AplicadaU.P.M.MadridSpain
  3. 3.Dept. Dirección y Economía de la EmpresaU.L.E.LeónSpain

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