Fuzzy Szpilrajn Theorem through Indicators
Keywords:
fuzzy relation, Szpilrajn theorem, similarityAbstract
In this paper there are studied some numerical indicators which measure the degree to which a fuzzy relation verifies some properties (reflexivity, transitivity, etc. ).The main result is a fuzzy generalization of the Szpilrajn theorem in terms of such numerical indicators and is applied to any fuzzy relation.References
R. Belohlávek, Fuzzy Relational Systems. Foundations and Principles, Kluwer, 2002. http://dx.doi.org/10.1007/978-1-4615-0633-1
U. Bodenhofer, Similarity-based Generalizations of Fuzzy Orderings Preserving the Classical Ax- ioms, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, Vol. 3, pp. 593-610, 2000. http://dx.doi.org/10.1142/S0218488500000411
U. Bodenhofer, F. Klawonn, A Formal Study of Linearity Axioms for Fuzzy Orderings, Fuzzy Sets and Systems, Vol. 145, pp. 323-354, 2004. http://dx.doi.org/10.1016/S0165-0114(03)00128-3
S. Gottwald, Fuzzy Sets and Fuzzy Logic, Vieweg, Braunschweig, 1993. http://dx.doi.org/10.1007/978-3-322-86812-1
P. Hájek, Methamathematics of Fuzzy Logic, Kluwer, 1998. http://dx.doi.org/10.1007/978-94-011-5300-3
U. Höhle, N. Blanchard, Partial Ordering in L-undeterminate sets, Information Sciences, Vol. 35, pp. 135-144, 1985. http://dx.doi.org/10.1016/0020-0255(85)90045-3
E. P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer, 2000. http://dx.doi.org/10.1007/978-94-015-9540-7
M. Richter, Revealed Preference Theory, Econometrica, Vol. 34, pp. 635-645, 1966. http://dx.doi.org/10.2307/1909773
I. J. Rudas, J. Fodor, Information Aggregation in Intelligent Systems using Generalized Operators, International Journal of Computers, Communications and Control, Vol. 1, pp. 47-57, 2006. http://dx.doi.org/10.15837/ijccc.2006.1.2272
E. Szpilrajn, Sur l'Extension de l'Ordre Partiel, Fundamenta Mathematicae, Vol. 16, pp. 386-389, 1930.
L. A. Zadeh, Similarity Relations and Fuzzy Orderings, Information Sciences, Vol. 3, pp. 177-200, 1971. http://dx.doi.org/10.1016/S0020-0255(71)80005-1
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