×

The structure of continuous uni-norms. (English) Zbl 0989.03058

Summary: The concept of uni-norm aggregation operators (uni-norms) was introduced by Yager and Rybalov to unify and generalize the t-norms and t-conorms. Considering that uni-norms continuous on \([0,1]^2\) must be t-norms or t-conorms, we concentrate our attention on uni-norms continuous in \((0,1)^2\) in this paper. We mainly investigate their properties, representation and structure.

MSC:

03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] B. DeBoets, Uninorms: the known classes, Third Internat. FLINS Workshop on Fuzzy Logic and Intelligent Technologic, 1998.; B. DeBoets, Uninorms: the known classes, Third Internat. FLINS Workshop on Fuzzy Logic and Intelligent Technologic, 1998.
[2] Dombi, J., A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operator, Fuzzy Sets and Systems, 8, 149-163 (1982) · Zbl 0494.04005
[3] Dubios, D.; Prade, H., A review of fuzzy set aggregation connectives, Inform. Sci., 3, 85-121 (1995) · Zbl 0582.03040
[4] Fodor, J.; Yager, R. R.; Rybalov, A., Structure of uninorms, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 5, 411-427 (1997) · Zbl 1232.03015
[5] Klement, E. P.; Mesiar, R.; Pap, E., On the relationship of associative compensatory operators to triangular norms and conorms, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 4, 129-144 (1996) · Zbl 1232.03041
[6] Klement, E. P.; Mesiar, R.; Pap, E., A characterization of the ordering of continuous t-norm, Fuzzy Sets and Systems, 86, 189-195 (1997) · Zbl 0914.04006
[7] Ling, C. H., Representation of associative functions, Publ. Math. Debrecen, 12, 189-212 (1965) · Zbl 0137.26401
[8] Mesiar, R.; Pap, E., Different interpretations of triangular norms and related operations, Fuzzy Sets and Systems, 96, 183-189 (1998) · Zbl 0927.03045
[9] Mostert, P. S.; Shields, A. L., On the structure of semigroups on a compact manifold with boundary, Ann. Math., 65, 117-143 (1957) · Zbl 0096.01203
[10] Yager, R. R.; Rybolov, A., Uninorm aggregation operators, Fuzzy Sets and Systems, 80, 111-120 (1996) · Zbl 0871.04007
[11] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[12] Zimmermann, H. J., Fuzzy Set and Its Applications (1991), Kluwer: Kluwer Dordrecht · Zbl 0719.04002
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.