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On left and right uninorms on a finite chain. (English) Zbl 1045.03029
Summary: The main concern of this paper is to introduce and characterize the class of operators on a finite chain \(L\) having the same properties as pseudosmooth uninorms but without commutativity. Moreover, in this case we only require the existence of a one-side neutral element. These operators are characterized as combinations of AND and OR operators of directed algebras (smooth t-norms and smooth t-conorms) and the case of pseudosmooth uninorms is retrieved for the commutative case.

MSC:
03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
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[1] De Baets, B.; Mesiar, R., Triangular norms on product lattices, Fuzzy sets and systems, 104, 61-75, (1999) · Zbl 0935.03060
[2] Fodor, J.C., Smooth associative operations on finite ordinal scales, IEEE trans. fuzzy systems, 8, 791-795, (2000)
[3] Fodor, J.C.; Yager, R.R.; Rybalov, A., Structure of uninorms, Internat. J. uncertainty, fuzziness knowledge-based systems, 5, 4, 411-427, (1997) · Zbl 1232.03015
[4] L. Godo, C. Sierra, A new approach to connective generation in the framework of expert systems using fuzzy logic, Proc. XVIIIth ISMVL, Palma, 1988, pp. 157-162.
[5] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0972.03002
[6] Marichal, J.L., On the associativity functional equation, Fuzzy sets and systems, 114, 381-389, (2000) · Zbl 0962.39012
[7] Mas, M.; Mayor, G.; Torrens, J., T-operators, Internat. J. uncertainty, fuzziness knowledge-based systems, 7, 1, 31-50, (1999) · Zbl 1087.03515
[8] Mas, M.; Mayor, G.; Torrens, J., T-operators and uninorms on a finite totally ordered set, special issuethe mathematics of fuzzy sets, Internat. J. intell. systems, 14, 9, 909-922, (1999) · Zbl 0948.68173
[9] Mas, M.; Monserrat, M.; Torrens, J., On left and right uninorms, Internat. J. uncertainty, fuzziness knowledge-based systems, 9, 4, 491-507, (2001) · Zbl 1113.03341
[10] Mayor, G.; Torrens, J., On a class of operators for expert systems, Internat. J. intell. systems, 8, 7, 771-778, (1993) · Zbl 0785.68087
[11] Sander, W., Associative aggregation operators, (), 124-158 · Zbl 1025.03054
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