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\(k\)-\(l_p\)-Lipschitz t-norms. (English) Zbl 1189.03058
Summary: \(k\)-\(l_p\)-Lipschitz t-norms are shown to be ordinal sums of \(k\)-\(l_p\)-Lipschitz Archimedean t-norms. Additive generators of \(k\)-\(l_p\)-Lipschitz t-norms are characterized by means of \(k\)-\(p\)-convexity. Several necessary and sufficient conditions for a function to be a \(k\)-\(p\)-convex additive generator are also given.

MSC:
03E72 Theory of fuzzy sets, etc.
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[1] Alsina, C.; Frank, M.J.; Schweizer, B., Problems on associative functions, Aequationes math., 66, 128-140, (2003) · Zbl 1077.39021
[2] T. Calvo, R. Mesiar, Stability of aggregation operators, in: Proc. EUSFLAT’2001, Leicester, 2001, pp. 475-478.
[3] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, Trends in logic, studia logica library, vol. 8, (2000), Kluwer Acad. Publishers Dordrecht · Zbl 0972.03002
[4] Mesiarová, A., A note on two open problems of alsina, Frank and schweizer, Aequationes math., 72, 1-2, 41-46, (2006) · Zbl 1101.39011
[5] Mesiarová, A., Lipschitz continuity of triangular norms, (), 309-321
[6] Moynihan, R., On τT semigroups of probability distribution functions II, Aequationes math., 17, 19-40, (1978) · Zbl 0386.22005
[7] Schweizer, B.; Sklar, A., Associative functions and abstract semigroups, Publ. math. debrecen, 10, 69-81, (1963) · Zbl 0119.14001
[8] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), North-Holland New York · Zbl 0546.60010
[9] Y.-H. Shju, Absolute continuity in the τT-operations, in: Ph.D. Thesis, Illinois Institute of Technology, Chicago, 1984.
[10] Yager, R.R., On global requirements for implication operators in fuzzy modus ponens, Fuzzy sets syst., 106, 3-10, (1999) · Zbl 0931.68117
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