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A note to a construction of t-norms based on pseudo-inverses of monotone functions. (English) Zbl 0953.26009
Summary: Many constructions of t-norms are known in the literature. This paper discusses a construction of t-norms by the pseudo-inverse of a non-decreasing function. The necessity and the sufficiency of some conditions of this construction are analyzed. Some easily verifiable sufficient conditions of this construction are given.

26E50 Fuzzy real analysis
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] B. Demant, Deformationnen von t-Normen, ihre Symmetrien and Symmetriebrechungen, preprint. · Zbl 0817.04003
[2] Jenei, S., Fibred triangular norms, Fuzzy sets and systems, 103, 67-82, (1999) · Zbl 0946.26017
[3] E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, to appear. · Zbl 0972.03002
[4] Klement, E.P.; Mesiar, R.; Pap, E., Constructions of t-norms via pseudo-inverses, Enriched lattice structures for many valued and fuzzy logics, Linz, 16-18, (1997)
[5] Menger, K., Statistical metrics, (), 535-537 · Zbl 0063.03886
[6] Mesiar, R., On some constructions of new triangular norms, Mathware and soft computing, 2, 39-45, (1995) · Zbl 0837.47056
[7] Schweizer, B.; Sklar, A., Espaces Métriques aléatoires, Comptes rendus acad. sci. Paris, 247, 2092-2094, (1958) · Zbl 0085.12503
[8] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), North-Holland New York · Zbl 0546.60010
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