Some results on the weak dominance relation between ordered weighted averaging operators and T-norms

Gang Li; Zhenbo Li; Jing Wang

Kybernetika (2024)

  • Issue: 3, page 379-393
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Li, Gang, Li, Zhenbo, and Wang, Jing. "Some results on the weak dominance relation between ordered weighted averaging operators and T-norms." Kybernetika (2024): 379-393. <http://eudml.org/doc/299284>.

@article{Li2024,
abstract = {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.},
author = {Li, Gang, Li, Zhenbo, Wang, Jing},
journal = {Kybernetika},
keywords = {domination; OWA operators; ordinal sum; t-norm},
language = {eng},
number = {3},
pages = {379-393},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Some results on the weak dominance relation between ordered weighted averaging operators and T-norms},
url = {http://eudml.org/doc/299284},
year = {2024},
}

TY - JOUR
AU - Li, Gang
AU - Li, Zhenbo
AU - Wang, Jing
TI - Some results on the weak dominance relation between ordered weighted averaging operators and T-norms
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
IS - 3
SP - 379
EP - 393
AB - 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.
LA - eng
KW - domination; OWA operators; ordinal sum; t-norm
UR - http://eudml.org/doc/299284
ER -

References

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  1. Alsina, C., Schweizer, B., Frank, M. J., Associative Functions: Triangular Norms and Copulas., World Scientific, 2006. MR2222258
  2. Alsina, C., Trillas, E., , Fuzzy Sets Syst. 50 (1992), 175-178. MR1185392DOI
  3. Běhounek, L., Bodenhofer, U., Cintula, P., Saminger-Platz, S., Sarkoci, P., , Fuzzy Sets Syst. 262 (2015), 78-101. MR3294358DOI
  4. Bentkowska, U., al., et, , Springer, Cham (2018). DOI
  5. Bejines, C., Ardanza-Trevijano, S., Chasco, M. J., Elorza, J., , Fuzzy Sets Syst. 446 (2022), 53-67. MR4473741DOI
  6. Bo, Q., Li, G., , Symmetry 14 (2022), 2354. DOI
  7. Beliakov, G., Bustince, H. S., Sanchez, T. C., 10.1007/978-3-319-24753-3_2, Stud. Fuzziness Soft Comput. 329, Springer, Berlin, Heidelberg 2016. MR3382259DOI10.1007/978-3-319-24753-3_2
  8. Bustince, H., Montero, J., Mesiar, R., , Fuzzy Sets Syst. 160 (2009), 766-777. Zbl1186.68459MR2493274DOI
  9. Calvo, T., , Fuzzy Sets Syst. 104 (1999), 85-96. MR1685812DOI
  10. Carbonell, M., Mas, M., Suñer, J., Torrens, J., 10.1142/S0218488596000202, Int. J. Uncertainty, Fuzziness Knowledge-Based Syst. 4 (1996), 351-368. MR1414353DOI10.1142/S0218488596000202
  11. Walle, B. V. De, Baets, B. De, Kerre, E., , Fuzzy Sets Syst. 97 (1998), 349-359. MR1639465DOI
  12. Walle, B. V. De, Baets, B. De, Kerre, E., , Fuzzy Sets Syst. 99 (1998), 303-310. MR1645693DOI
  13. Díaz, S., Montes, S., Baets, B. De, , IEEE Trans. Fuzzy Syst. 15 (2007), 275-286. DOI
  14. Drewniak, J., Rak, E., , Fuzzy Sets Syst. 161 (2010), 189-201. MR2566238DOI
  15. Drewniak, J., Rak, E., , Fuzzy Sets Syst. 191 (2012), 62-71. MR2874823DOI
  16. Durante, F., Ricci, R. G., 10.1016/j.ins.2009.04.001, Inform. Sci. 179 (2009), 2389-2694. MR2536413DOI10.1016/j.ins.2009.04.001
  17. Durante, F., Ricci, R. G., , Fuzzy Sets Syst. 335 (2018), 55-66. MR3765540DOI
  18. Fechner, W., Rak, E., Zedam, L., , Fuzzy Sets Syst. 332 (2018), 56-73. MR3732249DOI
  19. Fodor, J., Roubens, M., Fuzzy Preference Modelling and Multicriteria Decision Support., Kluwer Academic Publishers, Dordrecht 1994. Zbl0827.90002
  20. Grabisch, M., Marichal, J., Mesiar, R., Pap, E., Aggregation Functions., Cambridge University Press, Cambridge 2009. Zbl1206.68299MR2538324
  21. Klement, E. P., Mesiar, R., Pap, E., Triangular Norms., Kluwer Academic Publishers, Dordrecht 2000. Zbl1087.20041MR1790096
  22. Li, G., Zhang, L., Wang, J., Li, Z., , Fuzzy Sets Syst. 467 (2023), 108487. MR4598457DOI
  23. Mesiar, R., Saminger, S., , Soft Computing 8 (2004), 562-570. DOI
  24. Nagy, B., Basbous, R., Tajti, T., , Fuzzy Sets Syst. 376 (2019), 127-151. MR4011088DOI
  25. Nguyen, H. T., Walker, C. L., Walker, E. A., A first Course in Fuzzy Logic., Taylor and Francis, CRC Press, 2019. MR3887670
  26. Saminger, S., Mesiar, R., Bodenhofer, U., , Int. J. Uncert. Fuzziness Knowledge-Based Syst. 10 (2002), 11-35. Zbl1053.03514MR1962666DOI
  27. Saminger, S., Baets, B. De, Meyer, H. De, On the dominance relation between ordinal sums of conjunctors., Kybernetika 42 (2006), 337-350. MR2253393
  28. Saminger, S., , Fuzzy Sets Syst. 160 (2009), 2017-2031. MR2555018DOI
  29. Sarkoci, P., Domination in the families of Frank and Hamacher t-norms., Kybernetika 41 (2005), 349-360. MR2181423
  30. Sarkoci, P., , Aequat. Math. 75 (2008), 201-207. MR2424129DOI
  31. Schweizer, B., Sklar, A., Probabilistic Metric Spaces., North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York 1983. Zbl0546.60010MR0790314
  32. Su, Y., Riera, J. V., Ruiz-Aguilera, D., Torrens, J., , Fuzzy Sets Syst. 357 (2019), 27-46. MR3913057DOI
  33. Tardiff, R. M., , Aequat. Math. 20 (1980), 51-58. MR0569950DOI
  34. Yager, R. R., , IEEE Trans. Systems Man Cybernet. 18 (1988), 183-190. MR0931863DOI
  35. Yang, X. P., , Fuzzy Sets Syst. 397 (2020), 41-60. MR4135509DOI

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