Abstract
The full information about the values of a t-norm is given by the preimages of one-point sets {β} with β ∈ [0, 1] under the t-norm T or, equivalently, by the sets of solutions of the equations T(x, y) = β. For continuous t-norms these preimages are completely described in Section 7.1. For arbitrary t-norms, a complete characterization of the preimages of {0} is given. Also, for continuous t-norms T, the unique solvability of the equation T (a, x) = b with (a, b) ∈ [0,1[2 and b ≤ a is investigated.
A key reason for the growth in the importance of discrete mathematics is that information is stored and manipulated by computing machines in a discrete fashion.
Kenneth H. Rosen
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© 2000 Springer Science+Business Media Dordrecht
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Klement, E.P., Mesiar, R., Pap, E. (2000). Values and discretization of t-norms. In: Triangular Norms. Trends in Logic, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9540-7_7
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DOI: https://doi.org/10.1007/978-94-015-9540-7_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5507-1
Online ISBN: 978-94-015-9540-7
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