Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Manuscript in preparation. Home/Search Document Not in Database Summary Related Articles |
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Diagonals of Continuous Triangular Norms - Mesiar, Navara (1999) Self-citation (Mesiar) (Correct)
....continuous t norms. In each case, the class of all t norms with a given diagonal is constructively characterized. Note that the only diagonal of a continuous t norm having a unique underlying t norm is the identity, ffi(x) x; in this case, the corresponding t norm is the minimum t norm TM [4, 7]. We shall often use the following representation theorem for continuous Archimedean t norms (see, e.g. 4, 5, 7] Theorem 1.4 : Let T be a continuous Archimedean t norm. There is an additive generator of T , i.e. a continuous strictly decreasing function f : 0; 1] 0; 1] such that 8x; y ....
.... Note that the only diagonal of a continuous t norm having a unique underlying t norm is the identity, ffi(x) x; in this case, the corresponding t norm is the minimum t norm TM [4, 7] We shall often use the following representation theorem for continuous Archimedean t norms (see, e.g. [4, 5, 7]) Theorem 1.4 : Let T be a continuous Archimedean t norm. There is an additive generator of T , i.e. a continuous strictly decreasing function f : 0; 1] 0; 1] such that 8x; y 2 [0; 1] T (x; y) f Gamma1 (min(f(0) f(x) f(y) Notice that the condition T (x; 1) x implies that ....
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Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Manuscript in preparation.
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