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Some examples of weak uninorms. (English) Zbl 1470.03016

Summary: It is proved that, except for the uninorms and the nullnorms, there are no continuous weak uninorms who have no more than one nontrivial idempotent element. And some examples of discontinuous weak uninorms are shown. All of these examples are not \(n\)-uninorms, thus not uninorms or nullnorms.

MSC:

03B52 Fuzzy logic; logic of vagueness

References:

[1] Grabisch, M.; Marichal, J.-L.; Mesiar, R.; Pap, E., Aggregation functions: means, Information Sciences, 181, 1, 1-22 (2011) · Zbl 1206.68298 · doi:10.1016/j.ins.2010.08.043
[2] Grabisch, M.; Marichal, J.-L.; Mesiar, R.; Pap, E., Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes, Information Sciences, 181, 1, 23-43 (2011) · Zbl 1206.68299 · doi:10.1016/j.ins.2010.08.040
[3] Klement, E. P.; Mesiar, R.; Pap, E., Triangular Norms (2000), Dodrecht, The Netherlands: Kluwer Academic, Dodrecht, The Netherlands · Zbl 0972.03002
[4] Starczewski, J. T., Extended triangular norms, Information Sciences, 179, 6, 742-757 (2009) · Zbl 1165.03010 · doi:10.1016/j.ins.2008.11.009
[5] Yager, R. R., Aggregation operators and fuzzy systems modeling, Fuzzy Sets and Systems, 67, 2, 129-145 (1994) · Zbl 0845.93047 · doi:10.1016/0165-0114(94)90082-5
[6] Fodor, J. C.; Yager, R. R.; Rybalov, A., Structure of uninorms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 4, 411-427 (1997) · Zbl 1232.03015 · doi:10.1142/S0218488597000312
[7] Yager, R. R.; Rybalov, A., Uninorm aggregation operators, Fuzzy Sets and Systems, 80, 1, 111-120 (1996) · Zbl 0871.04007 · doi:10.1016/0165-0114(95)00133-6
[8] Calvo, T.; de Baets, B.; Fodor, J., The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets and Systems, 120, 3, 385-394 (2001) · Zbl 0977.03026 · doi:10.1016/S0165-0114(99)00125-6
[9] Mas, M.; Mayor, G.; Torrens, J., T-operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7, 1, 31-50 (1999) · Zbl 1087.03515 · doi:10.1142/S0218488599000039
[10] Akella, P., Structure of \(n\)-uninorms, Fuzzy Sets and Systems, 158, 15, 1631-1651 (2007) · Zbl 1122.03044 · doi:10.1016/j.fss.2007.02.015
[11] Akella, P., \(C\)-sets of \(n\)-uninorms, Fuzzy Sets and Systems, 160, 1, 1-21 (2009) · Zbl 1183.03046 · doi:10.1016/j.fss.2008.04.011
[12] Li, Y.-M.; Shi, Z.-K., Weak uninorm aggregation operators, Information Sciences, 124, 1-4, 317-323 (2000) · Zbl 0954.03058 · doi:10.1016/S0020-0255(99)00137-1
[13] Li, Y.-M.; Shi, Z.-K., Remarks on uninorm aggregation operators, Fuzzy Sets and Systems, 114, 3, 377-380 (2000) · Zbl 0962.03052 · doi:10.1016/S0165-0114(98)00247-4
[14] Wu, J.; Luo, M., Some properties of weak uninorms, Information Sciences, 181, 18, 3917-3924 (2011) · Zbl 1247.03038 · doi:10.1016/j.ins.2011.04.036
[15] Wu, J., Some properties of AMC operators · Zbl 1165.03010 · doi:10.1016/j.ins.2008.11.009
[16] Klement, E. P.; Mesiar, R.; Pap, E., Triangular norms as ordinal sums of semigroups in the sense of A. H. Clifford, Semigroup Forum, 65, 1, 71-82 (2002) · Zbl 1007.20054 · doi:10.1007/s002330010127
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