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

Di Nola, Antonio, et al. "Fuzzy relation equation under a class of triangular norms: A survey and new results.." Stochastica 8.2 (1984): 99-145. <http://eudml.org/doc/38901>.

@article{DiNola1984,
abstract = {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.},
author = {Di Nola, Antonio, Pedrycz, Witold, Sessa, Salvatore, Pei Zhuang, Wang},
journal = {Stochastica},
keywords = {Conjuntos difusos; Probabilidad; Ecuaciones; Norma triangular; fuzzy number; possibility measure; generalized fuzzy relation equations; minimal fuzziness measure; approximate solutions; fuzzy equations; copying with fuzziness},
language = {eng},
number = {2},
pages = {99-145},
title = {Fuzzy relation equation under a class of triangular norms: A survey and new results.},
url = {http://eudml.org/doc/38901},
volume = {8},
year = {1984},
}

TY - JOUR
AU - Di Nola, Antonio
AU - Pedrycz, Witold
AU - Sessa, Salvatore
AU - Pei Zhuang, Wang
TI - Fuzzy relation equation under a class of triangular norms: A survey and new results.
JO - Stochastica
PY - 1984
VL - 8
IS - 2
SP - 99
EP - 145
AB - 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.
LA - eng
KW - Conjuntos difusos; Probabilidad; Ecuaciones; Norma triangular; fuzzy number; possibility measure; generalized fuzzy relation equations; minimal fuzziness measure; approximate solutions; fuzzy equations; copying with fuzziness
UR - http://eudml.org/doc/38901
ER -