×

zbMATH — the first resource for mathematics

When \(QM\)-operators are implication functions and conditional fuzzy relations. (English) Zbl 0953.03031
Summary: Some fuzzy reasoning systems base inference processes on fuzzy implication functions. Although there has been a great deal of work done on characterizing \(R\)- and \(S\)-implications, little is known about \(QM\)-implications in spite of their long history since they came to fuzzy logic by analogy with the quantum mechanic logic. This paper tackles the study of some characteristics of this type of operator. It focuses on the \(QM\)-implication operator both as an implication function and also as a \(T\)-conditional function, giving useful tools to characterize them.

MSC:
03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] On the characterization of S and R implications. Proceedings of the VI I.F.S.A. World Congress, São Paulo (Brazil). 1995; 1:317-319.
[2] Bandler, Fuzzy Sets Syst 4 pp 13– (1979)
[3] Bandler, Int J Man-Machine Stud 12 pp 89– (1980)
[4] Dubois, Int J Cybernet Syst 15 pp 293– (1984)
[5] Fuzzy sets and fuzzy logic. Wiesbaden: Vieweg-Verlag; 1993.
[6] Smets, Int J Approx Reason 1/4 pp 327– (1987)
[7] Trillas, Stochastica III pp 47– (1979)
[8] Trillas, Math Soft Comput 3 pp 105– (1996)
[9] Nota sobre el concepto de implicación borrosa. Actas ESTYLF’98 (in Spanish). 1998; p 238-243.
[10] A few remarks on some T-conditional functions. Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, Barcelona. 1997; 1:153-156.
[11] A glance on implication and T-conditional functions. In: editors. Discovering the world with fuzzy logic. to appear.
[12] On mode and implication in approximate reasoning. In: editors. Approximate reasoning in expert systems. North-Holland: Elsevier Science Publishers B.V.; 1985.
[13] Yager, Int J Man-Machine Stud 13 pp 323– (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.