When \(QM\)-operators are implication functions and conditional fuzzy relations.

*(English)*Zbl 0953.03031Summary: 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 |

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\textit{E. Trillas} et al., Int. J. Intell. Syst. 15, No. 7, 647--655 (2000; Zbl 0953.03031)

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