Resumen de Fuzzy relation equation under a class of triangular norms: A survey and new results.

Antonio Di Nola, Witold Pedrycz , Salvatore Sessa

• By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions.

  We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to a triangular norm and conorm.

  Moreover we discuss the problem of characterization of the approximate solutions of fuzzy equations.

  Finally, the role of the equations considered here in creation of a formal framework for copying with fuzziness is illustrated by various examples in some well known schemes in applications of fuzzy set theory.