On the representation of fuzzy rules

In fuzzy logic, connectives have a meaning that, can frequently be known through the use of these connectives in a given context. This implies that there is not a universal-class for each type of connective, and because of that several continuous t-norms, continuous t-conorms and strong negations, are employed to represent, respectively, the and, the or, and the not. The same happens with the case of the connective If/then for which there is a multiplicity of models called T-conditionals or implications. To reinforce that there is not a universal-class for this connective, four very simple classical laws translated into fuzzy logic are studied.

[1]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[2]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[3]  Tommaso Flaminio,et al.  T-norm-based logics with an independent involutive negation , 2006, Fuzzy Sets Syst..

[4]  E. Trillas.  Sobre funciones de negación en la teoría de conjuntos difusos. , 1979 .

[5]  Joan Torrens,et al.  S-implications and R-implications on a finite chain , 2004, Kybernetika.

[6]  G. Mayor,et al.  Triangular norms on discrete settings , 2005 .

[7]  Thomas Whalen.  Interpolating between fuzzy rules using improper S-implications , 2007, Int. J. Approx. Reason..

[8]  Joan Torrens,et al.  QL-implications versus D-implications , 2006, Kybernetika.

[9]  S. Gottwald.  A Treatise on Many-Valued Logics , 2001 .

[10]  Joan Torrens,et al.  On two types of discrete implications , 2005, Int. J. Approx. Reason..

[11]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[12]  E. Trillas,et al.  On MPT-implication functions for Fuzzy Logic , 2004 .

[13]  R. Mesiar,et al.  Logical, algebraic, analytic, and probabilistic aspects of triangular norms , 2005 .

[14]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[15]  Lluis Godo,et al.  Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[16]  Gary M. Hardegree.  Material implication in orthomodular (and Boolean) lattices , 1981, Notre Dame J. Formal Log..

[17]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[18]  Joan Torrens,et al.  A Survey on Fuzzy Implication Functions , 2007, IEEE Transactions on Fuzzy Systems.