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

• Autores: Antonio Di Nola, Witold Pedrycz, Salvatore Sessa
• Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 8, Nº. 2, 1984, págs. 99-145
• Idioma: inglés
• Títulos paralelos:
  • Ecuación relacional difusa bajo una clase de normas triangulares: Revisión y nuevos resultados.
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• Resumen

  • 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.