\((\top,\bot,N)\) fuzzy logic (Q2775909)

The paper discusses some elementary concepts and properties of \((\top,\perp,N)\)-fuzzy logics, where \(\top\) is a triangular norm (evaluation of conjunction), \(\bot\) is a triangular conorm (evaluation of disjunction), and \(N\) is a strong negation (evaluation of negation). The discussed logics work with \([0,1]\)-valued truth functions. Relationship between Boolean truth (falsity) of disjunctive and conjunctive normal forms and fuzzy truth (falsity) of these forms is discussed, too.NEWLINENEWLINENEWLINEThe paper uses unusual notations and does not give full information about the fuzzy logical connectives evaluations applied here, and thus brings problems to unskilled readers. On the other hand, the majority of the presented results can be found or derived from known results (unfortunately not quoted here), and thus for skilled readers there are only few new results. Especially, recent monographs [\textit{P. Hájek}, Metamathematics of fuzzy logic, Dordrecht: Kluwer (1998; Zbl 0937.03030); \textit{V. Novák}, \textit{I. Perfilieva} and \textit{J. Mockor}, Mathematical principles of fuzzy logic, Dordrecht: Kluwer (1999; Zbl 0940.03028)] are missing among the references.