Conjunction and disjunction on \(([0,1],\leq)\). (English) Zbl 0844.03010
Summary: In multivalued logic, to functionally obtain the truth value of “\(p\) and \(q\)”, \(t\)-norms are used, but there are many situations in real life in which other functions are also used. This paper contains two definitions of conjunction including large families of possible conjunction functions.
Furthermore, a new definition of local conjunction is given and, symmetrically, some definitions of disjunction and of local disjunction. In particular, quasiarithmetic and weighted means are studied.
Furthermore, a new definition of local conjunction is given and, symmetrically, some definitions of disjunction and of local disjunction. In particular, quasiarithmetic and weighted means are studied.
MSC:
| 03B50 | Many-valued logic |
Keywords:
\(t\)-conorms; quasiarithmetic means; aggregation functions; \(t\)-norms; conjunction; disjunction; weighted meansReferences:
| [1] | Aczél, J., (Lectures on Functional Equations and their Applications (1966), Academic Press: Academic Press New York) · Zbl 0139.09301 |
| [2] | Alsina, C.; Trillas, E.; Valverde, L., On some logical connectives for fuzzy sets theory, J. Math. Anal. Appl., 93, 1, 15-26 (1983) · Zbl 0522.03012 |
| [3] | Birkhoff, G., Lattice Theory, (Amer. Math. Soc. Colloquium Publ., Vol. 25 (1948), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0126.03801 |
| [4] | Mayor, G.; Torrens, J., Algebras filtrantes: algunos centros de interés, (Actas Primer Congreso Español sobre Tecnologías y Lógica Fuzzy. Actas Primer Congreso Español sobre Tecnologías y Lógica Fuzzy, Granada (1991)), 41-45, (in Spanish) |
| [5] | Mayor, G.; Trillas, E., On the representation of some aggregation functions (1985), ISMVL: ISMVL Virginia |
| [6] | Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), Elsevier: Elsevier New York · Zbl 0546.60010 |
| [7] | Trillas, E., Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica, III, 1, 47-59 (1979) · Zbl 0419.03035 |
| [8] | Trillas, E.; Alsina, C.; Cubillo, S.; Jacas, J., On “And” in [0,1], (Proc. IPMU, 92 (1992)), 329-332 |
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