Representations and constructions of similarity-based fuzzy orderings. (English) Zbl 1052.91032

Summary: This contribution advocates the dissemination of similarity-based fuzzy orderings – a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings, equivalence relations, and orderings are taken into account. In contrast to earlier papers on the topic, this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept.


91B08 Individual preferences
Full Text: DOI


[1] Bandler, W.; Kohout, L., Fuzzy power sets and fuzzy implication operators, Fuzzy sets and systems, 4, 183-190, (1980) · Zbl 0433.03013
[2] U. Bodenhofer, The construction of ordering-based modifiers, in: G. Brewka, R. Der, S. Gottwald, A. Schierwagen (Eds.), Fuzzy-Neuro Systems ’99, Leipziger Universitätsverlag, 1999, pp. 55-62.
[3] U. Bodenhofer, A Similarity-Based Generalization of Fuzzy Orderings, Schriftenreihe der Johannes-Kepler-Universität Linz, Vol. C26, Universitätsverlag Rudolf Trauner, 1999. · Zbl 0949.03049
[4] Bodenhofer, U., A similarity-based generalization of fuzzy orderings preserving the classical axioms, Internat. J. uncertain. fuzziness knowledge-based systems, 8, 5, 593-610, (2000) · Zbl 1113.03333
[5] De Baets, B.; Mesiar, R., Pseudo-metrics and T-equivalences, J. fuzzy math., 5, 2, 471-481, (1997) · Zbl 0883.04007
[6] De Baets, B.; Mesiar, R., T-partitions, Fuzzy sets and systems, 97, 211-223, (1998) · Zbl 0930.03070
[7] M. De Cock, U. Bodenhofer, E.E. Kerre, Modelling linguistic expressions using fuzzy relations, in: Proc. 6th Internat. Conf. on Soft Computing (IIZUKA2000), Iizuka, October 2000, pp. 353-360.
[8] Fodor, J.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0827.90002
[9] Gottwald, S., Fuzzy sets and fuzzy logic, (1993), Vieweg Braunschweig
[10] S. Gottwald, A treatise on many-valued logics, in: Studies in Logic and Computation, Research Studies Press, Baldock, 2001. · Zbl 1048.03002
[11] P. Hájek, Metamathematics of Fuzzy Logic, Trends in Logic, Vol. 4, Kluwer Academic Publishers, Dordrecht, 1998.
[12] Höhle, U.; Blanchard, N., Partial ordering in L-underdeterminate sets, Inform. sci., 35, 133-144, (1985) · Zbl 0576.06004
[13] Klawonn, F.; Gebhardt, J.; Kruse, R., Fuzzy control on the basis of equality relations—with an example from idle speed control, IEEE trans. fuzzy systems, 3, 336-356, (1995)
[14] Klawonn, F.; Kruse, R., Equality relations as a basis for fuzzy control, Fuzzy sets and systems, 54, 2, 147-156, (1993) · Zbl 0785.93059
[15] E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Trends in Logic, Vol. 8, Kluwer Academic Publishers, Dordrecht, 2000. · Zbl 0972.03002
[16] Kruse, R.; Gebhardt, J.; Klawonn, F., Foundations of fuzzy systems, (1994), Wiley New York · Zbl 0843.68109
[17] Ling, C.H., Representation of associative functions, Publ. math. debrecen, 12, 189-212, (1965) · Zbl 0137.26401
[18] B. Moser, A new approach for representing control surfaces by fuzzy rule bases, Ph.D. Thesis, Johannes Kepler Universität Linz, October 1995.
[19] Ovchinnikov, S.V., Similarity relations, fuzzy partitions, and fuzzy orderings, Fuzzy sets and systems, 40, 1, 107-126, (1991) · Zbl 0725.04003
[20] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), North-Holland Amsterdam · Zbl 0546.60010
[21] Valverde, L., On the structure of F-indistinguishability operators, Fuzzy sets and systems, 17, 3, 313-328, (1985) · Zbl 0609.04002
[22] Wang, X.; De Baets, B.; Kerre, E.E., A comparative study of similarity measures, Fuzzy sets and systems, 73, 259-268, (1995) · Zbl 0852.04011
[23] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[24] Zadeh, L.A., Similarity relations and fuzzy orderings, Inform. sci., 3, 177-200, (1971) · Zbl 0218.02058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.