Presentación | Participantes | Bibliografía (DML-E) | Bibliografía adicional | Enlaces de interés | Otros proyectos DML | Ayuda  
INICIO | 28 de noviembre de 2023

On the fundamentals of fuzzy sets.

Título inglés On the fundamentals of fuzzy sets.
Título español Sobre los fundamentos de los conjuntos difusos.
Autor/es Lowen, Robert
Organización Univ. Antwerp, Amberes, Bélgica
Revista 0210-7821
Publicación 1984, 8 (2): 157-169, 13 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés A considerable amount of research has been done on the notions of pseudo complement, intersection and union of fuzzy sets [1], [4], [11]. Most of this work consists of generalizations or alternatives of the basic concepts introduced by L. A. Zadeh in his famous paper [13]: generalization of the unit interval to arbitrary complete and completely distributive lattices or to Boolean algebras [2]; alternatives to union and intersection using the concept of t-norms [3], [10]; alternative complements in the unit interval in [4], [11], a.s.o. Although it is usually accepted that I := [0,1] is a natural generalization of {0,1} and that a --> 1 - a is a natural generalization of the Boolean complement on {0,1}, we do however not find canonical and mathematical justification for this fact, which nevertheless lies at the heart of the definition of fuzzy sets. It is the purpose of this note to present a canonical way of obtaining I and L. A. Zadeh's pseudocomplement.
Moreover, if we consistently use this canonical machine we shall see that also other set-concepts can, and maybe should have been extended to fuzzy sets. Further we also give a possible generalization involving a choice of arbitrary t-norms.
Clasificación UNESCO 110208 ; 120102
Palabras clave español Conjuntos difusos ; Estudio teórico
Código MathReviews MR0783403
Código Z-Math Zbl 0577.04001
Icono pdf Acceso al artículo completo
Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)