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New family of triangular norms via contrapositive symmetrization of residuated implications. (English) Zbl 0941.03059
The paper deals with triangular norms connected with strong negation. Their properties are investigated and presented. The main results regard the description of the nilpotent minimum of triangular norms, which is described as a limit of nilpotent triangular norms where the nilpotent minimum is an extremal case. The problems solved in the paper are strongly related to the contrapositive symmetry of residuated implications.
Reviewer: M.Mareš (Praha)

03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] Fodor, J.C., Contrapositive symmetry of fuzzy implications, Fuzzy sets and systems, 69, 141-156, (1995) · Zbl 0845.03007
[2] Fodor, J.C.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (1994), Kluwer Academic Publisher Dordrecht · Zbl 0827.90002
[3] U. H\( ohle̋\), Commutative, residuated l-monoids, preprint.
[4] Jenei, S., Fibred triangular norms, Fuzzy sets and systems, 103, 67-82, (1999) · Zbl 0946.26017
[5] Jenei, S.; Fodor, J.C., On continuous triangular norms, Fuzzy sets and systems, 100, 273-282, (1998) · Zbl 0938.03084
[6] Ling, C.-H., Representation of associative functions, Publ. math. debrecen, 12, 189-212, (1965) · Zbl 0137.26401
[7] Ovchinnikov, S.; Roubens, M., On strict preference relations, Fuzzy sets and systems, 43, 319-326, (1991) · Zbl 0747.90006
[8] Trillas, E., Sobre funciones de negación en la teorı́ a de conjuntos difusos, Stochastica, III, 47-60, (1979)
[9] Weber, S., A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms, Fuzzy sets and systems, 11, 115-134, (1983) · Zbl 0543.03013
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