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Keywords:
domination; OWA operators; ordinal sum; t-norm
domination; OWA operators; ordinal sum; t-norm
Summary:
Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More attention is paid to the weak dominance relation between ordered weighted averaging operators and Łukasiewicz t-norm. Furthermore, the relationships between weak dominance and some functional inequalities of aggregation operators are discussed.
References:
[1] Alsina, C., Schweizer, B., Frank, M. J.: Associative Functions: Triangular Norms and Copulas. World Scientific, 2006. MR 2222258
[2] Alsina, C., Trillas, E.: On almost distributive Łukasiewicz triplets. Fuzzy Sets Syst. 50 (1992), 175-178. DOI | MR 1185392
[3] Běhounek, L., Bodenhofer, U., Cintula, P., Saminger-Platz, S., Sarkoci, P.: Graded dominance and related graded properties of fuzzy conncectives. Fuzzy Sets Syst. 262 (2015), 78-101. DOI | MR 3294358
[4] Bentkowska, U., al., et: Dominance of Binary Operations on Posets. Springer, Cham (2018). DOI
[5] Bejines, C., Ardanza-Trevijano, S., Chasco, M. J., Elorza, J.: Aggregation of indistinguishability operators. Fuzzy Sets Syst. 446 (2022), 53-67. DOI | MR 4473741
[6] Bo, Q., Li, G.: The submodular inequality of aggregation operators. Symmetry 14 (2022), 2354. DOI
[7] Beliakov, G., Bustince, H. S., Sanchez, T. C.: A practical guide to averaging functions. Stud. Fuzziness Soft Comput. 329, Springer, Berlin, Heidelberg 2016. DOI 10.1007/978-3-319-24753-3_2 | MR 3382259
[8] Bustince, H., Montero, J., Mesiar, R.: Migrativity of aggregation functions. Fuzzy Sets Syst. 160 (2009), 766-777. DOI | MR 2493274 | Zbl 1186.68459
[9] Calvo, T.: On some solutions of the distributivity equation. Fuzzy Sets Syst. 104 (1999), 85-96. DOI | MR 1685812
[10] Carbonell, M., Mas, M., Suñer, J., Torrens, J.: On distributivity and modularity in De Morgan triplets. Int. J. Uncertainty, Fuzziness Knowledge-Based Syst. 4 (1996), 351-368. DOI 10.1142/S0218488596000202 | MR 1414353
[11] Walle, B. V. De, Baets, B. De, Kerre, E.: A plea for the use of Łukasiewicz triplets in the definition of fuzzy preference structures. (I). General argumentation. Fuzzy Sets Syst. 97 (1998), 349-359. DOI | MR 1639465
[12] Walle, B. V. De, Baets, B. De, Kerre, E.: A plea for the use of Łukasiewicz triplets in the definition of fuzzy preference structures. (II). The identity case. Fuzzy Sets Syst. 99 (1998), 303-310. DOI | MR 1645693
[13] Díaz, S., Montes, S., Baets, B. De: Transitivity bounds in additive fuzzy preference structures. IEEE Trans. Fuzzy Syst. 15 (2007), 275-286. DOI
[14] Drewniak, J., Rak, E.: Subdistributivity and superdistributivity of binary operations. Fuzzy Sets Syst. 161 (2010), 189-201. DOI | MR 2566238
[15] Drewniak, J., Rak, E.: Distributivity inequalities of monotonic operations. Fuzzy Sets Syst. 191 (2012), 62-71. DOI | MR 2874823
[16] Durante, F., Ricci, R. G.: Supermigrative semi-copulas and triangular norms. Inform. Sci. 179 (2009), 2389-2694. DOI 10.1016/j.ins.2009.04.001 | MR 2536413
[17] Durante, F., Ricci, R. G.: Supermigrativity of aggregation functions. Fuzzy Sets Syst. 335 (2018), 55-66. DOI | MR 3765540
[18] Fechner, W., Rak, E., Zedam, L.: The modularity law in some classes of aggregation operators. Fuzzy Sets Syst. 332 (2018), 56-73. DOI | MR 3732249
[19] Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht 1994. Zbl 0827.90002
[20] Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge 2009. MR 2538324 | Zbl 1206.68299
[21] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. MR 1790096 | Zbl 1087.20041
[22] Li, G., Zhang, L., Wang, J., Li, Z.: Some results on the weak dominance between t-norms and t-conorms. Fuzzy Sets Syst. 467 (2023), 108487. DOI | MR 4598457
[23] Mesiar, R., Saminger, S.: Domination of ordered weighted averaging operators over t-norms. Soft Computing 8 (2004), 562-570. DOI
[24] Nagy, B., Basbous, R., Tajti, T.: Lazy evaluations in Łukasiewicz type fuzzy logic. Fuzzy Sets Syst. 376 (2019), 127-151. DOI | MR 4011088
[25] Nguyen, H. T., Walker, C. L., Walker, E. A.: A first Course in Fuzzy Logic. Taylor and Francis, CRC Press, 2019. MR 3887670
[26] Saminger, S., Mesiar, R., Bodenhofer, U.: Domination of aggregation operators and preservation of transitivity. Int. J. Uncert. Fuzziness Knowledge-Based Syst. 10 (2002), 11-35. DOI | MR 1962666 | Zbl 1053.03514
[27] Saminger, S., Baets, B. De, Meyer, H. De: On the dominance relation between ordinal sums of conjunctors. Kybernetika 42 (2006), 337-350. MR 2253393
[28] Saminger, S.: The dominance relation in some families of continuous Archimedean t-norms and copulas. Fuzzy Sets Syst. 160 (2009), 2017-2031. DOI | MR 2555018
[29] Sarkoci, P.: Domination in the families of Frank and Hamacher t-norms. Kybernetika 41 (2005), 349-360. MR 2181423
[30] Sarkoci, P.: Dominance is not transitive on continuous triangular norms. Aequat. Math. 75 (2008), 201-207. DOI | MR 2424129
[31] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York 1983. MR 0790314 | Zbl 0546.60010
[32] Su, Y., Riera, J. V., Ruiz-Aguilera, D., Torrens, J.: The modularity condition for uninorms revisted. Fuzzy Sets Syst. 357 (2019), 27-46. DOI | MR 3913057
[33] Tardiff, R. M.: On a functional inequality arising in the construction of the product of several metric spaces. Aequat. Math. 20 (1980), 51-58. DOI | MR 0569950
[34] Yager, R. R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems Man Cybernet. 18 (1988), 183-190. DOI | MR 0931863
[35] Yang, X. P.: Resolution of bipolar fuzzy relation equations with max-Łukasiewicz composition. Fuzzy Sets Syst. 397 (2020), 41-60. DOI | MR 4135509
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