A new approach to construct uninorms via uninorms on bounded lattices

Zhen-Yu Xiu; Xu Zheng

Kybernetika (2024)

  • Issue: 2, page 125-149
  • ISSN: 0023-5954

Abstract

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In this paper, on a bounded lattice L , we give a new approach to construct uninorms via a given uninorm U * on the subinterval [ 0 , a ] (or [ b , 1 ] ) of L under additional constraint conditions on L and U * . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.

How to cite

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Xiu, Zhen-Yu, and Zheng, Xu. "A new approach to construct uninorms via uninorms on bounded lattices." Kybernetika (2024): 125-149. <http://eudml.org/doc/299444>.

@article{Xiu2024,
abstract = {In this paper, on a bounded lattice $L$, we give a new approach to construct uninorms via a given uninorm $U^\{*\}$ on the subinterval $[0,a]$ (or $[b,1]$) of $L$ under additional constraint conditions on $L$ and $U^\{*\}$. This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.},
author = {Xiu, Zhen-Yu, Zheng, Xu},
journal = {Kybernetika},
keywords = {bounded lattices; $t$-norms; $t$-conorms; uninorms},
language = {eng},
number = {2},
pages = {125-149},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A new approach to construct uninorms via uninorms on bounded lattices},
url = {http://eudml.org/doc/299444},
year = {2024},
}

TY - JOUR
AU - Xiu, Zhen-Yu
AU - Zheng, Xu
TI - A new approach to construct uninorms via uninorms on bounded lattices
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
IS - 2
SP - 125
EP - 149
AB - In this paper, on a bounded lattice $L$, we give a new approach to construct uninorms via a given uninorm $U^{*}$ on the subinterval $[0,a]$ (or $[b,1]$) of $L$ under additional constraint conditions on $L$ and $U^{*}$. This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.
LA - eng
KW - bounded lattices; $t$-norms; $t$-conorms; uninorms
UR - http://eudml.org/doc/299444
ER -

References

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  1. Aşıcı, E., Mesiar, R., , Fuzzy Sets Syst. 408 (2021), 65-85. MR4210984DOI
  2. Birkhoff, G., Lattice theory. (Third Edition.), Amer. Math. Soc., Rhode Island 1967. MR0227053
  3. Baczyński, M., Jayaram, B., Fuzzy Implications., Springer, Berlin 2008. Zbl1293.03012
  4. Bodjanova, S., Kalina, M., Construction of uninorms on bounded lattices., In: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, Subotica. 
  5. Çaylı, G. D., Karaçal, F., Mesiar, R., , Inf. Sci. 367 (2016), 221-231. MR3684677DOI
  6. Çaylı, G. D., Karaçal, F., , Kybernetika 53 (2017), 3, 394-417. MR3684677DOI
  7. al., G. D. Çaylı et, , Kybernetika 53 (2017), 5, 911-921. MR3750111DOI
  8. Çaylı, G. D., , Fuzzy Sets Syst. 332 (2018), 129-143. MR3732255DOI
  9. Çaylı, G.D., , Fuzzy Sets Syst. 357 (2019), 2-26. MR3913056DOI
  10. Çaylı, G. D., , Inf. Sci. 488 (2019), 111-139. MR3924420DOI
  11. Çaylı, G. D., , Int. J. Approx. Reason. 115 (2019), 254-264. MR4018632DOI
  12. Çaylı, G. D., , Kybernetika 55 (2019), 2, 273-294. MR4014587DOI
  13. Çaylı, G. D., , Fuzzy Sets Syst. 395 (2020), 107-129. MR4109064DOI
  14. Çaylı, G. D., , Int. J. Gen. Syst. 50 (2021), 139-158. MR4222196DOI
  15. Çaylı, G. D., , Int. J. Gen. Syst. 47 (2018), 772-793. MR3867053DOI
  16. Çaylı, G. D., Ertuğrul, Ü., Karaçal, F., , Int. J. Gen. Syst. 52 (2023), 4, 414-442. MR4589126DOI
  17. Baets, B. De, Fodor, J., , Fuzzy Sets Syst. 104 (1999), 133-136. Zbl0928.03060MR1685816DOI
  18. Baets, B. De, Mesiar, R., , Fuzzy Sets Syst. 104 (1999), 61-75. Zbl0935.03060MR1685810DOI
  19. Dan, Y. X., Hu, B. Q., Qiao, J. S., , Int. J. Approx. Reason. 110 (2019), 185-209. MR3947797DOI
  20. Dan, Y. X., Hu, B. Q., , Fuzzy Sets Syst. 386 (2020), 77-94. MR4073387DOI
  21. Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F., , Int. J. Gen. Syst. 48 (2019), 7, 775-791. MR4001869DOI
  22. Ertuğrul, Ü., Yeşilyurt, M., , Inf. Sci. 517 (2020), 198-216. MR4050654DOI
  23. Ertuğrul, Ü., Karaçal, F., Mesiar, R., , Int. J. Intell. Syst. 30 (2015), 807-817. DOI
  24. al., M. Grabisch et, Aggregation Functions., Cambridge University Press, 2009. 
  25. al., M. Grabisch et, , Inf. Sci. 181 (2011), 23-43. MR2737458DOI
  26. Höhle, U., Commutative, residuated l-monoids., In: Non-Classical Logics and Their Applications to Fuzzy Subsets: A Handbook on the Mathematical Foundations of Fuzzy Set Theory (U. Höhle and E. P. Klement, eds.), Kluwer, Dordrecht 1995. MR1345641
  27. Hua, X. J., Zhang, H. P., Ouyang, Y., , Kybernetika 57 (2021), 2, 372-382. MR4273581DOI
  28. He, P., Wang, X. P., , Int. J. Approx. Reason. 136 (2021), 1-13. MR4270087DOI
  29. Hua, X. J., Ji, W., , Fuzzy Sets Syst. 427 (2022), 109-131. MR4343692DOI
  30. Jenei, S., Baets, B. De, , Fuzzy Sets Syst. 139 (2003), 699-707. MR2015162DOI
  31. Ji, W., , Fuzzy Sets Syst. 403 (2021), 38-55. MR4174507DOI
  32. Karaçal, F., Mesiar, R., , Fuzzy Sets Syst. 261 (2015), 33-43. MR3291484DOI
  33. Karaçal, F., Ertuğrul, Ü., Mesiar, R., , Fuzzy Sets Syst. 308 (2017), 54-71. MR3579154DOI
  34. Karaçal, F., Ertuğrul, Ü., Kesicioğlu, M., , Kybernetika 55 (2019), 6, 976-993. MR4077140DOI
  35. Karaçal, F., Kesicioğlu, M., Ertuğrul, Ü., , Int. J. Gen. Syst. 49 (2020), 3, 277-301. MR4085740DOI
  36. Liang, X., Pedrycz, W., , Fuzzy Sets Syst. 160 (2009), 3475-3502. MR2563300DOI
  37. Menger, K., 10.1073/pnas.28.12.535, Proc. Natl. Acad. Sci. USA 8 (1942), 535-537. Zbl0063.03886MR0007576DOI10.1073/pnas.28.12.535
  38. Medina, J., , Fuzzy Sets Syst. 202 (2012), 75-88. MR2934787DOI
  39. Ouyang, Y., Zhang, H. P., , Fuzzy Sets Syst. 395 (2020), 93-106. MR4109063DOI
  40. Pedrycz, W., Hirota, K., , Soft Comput. 11 (2007), 1, 41-52. DOI
  41. Schweizer, B., Sklar, A., , Pacific J. Math. 10 (1960), 313-334. Zbl0136.39301MR0115153DOI
  42. Schweizer, B., Sklar, A., Probabilistic Metric Spaces., North-Holland, New York 1983. Zbl0546.60010MR0790314
  43. Schweizer, B., Sklar, A., Associative functions and statistical triangular inequalities., Publ. Math. 8 (1961), 169-186. MR0132939
  44. Saminger, S., , Fuzzy Sets Syst. 157 (2006), 1403-1416. Zbl1099.06004MR2226983DOI
  45. Saminger, S., Klement, E., Mesiar, R., , Indag. Math. 19 (2008), 1, 135-150. MR2466398DOI
  46. Wang, Z., , Inf. Sci. 177 (2007), 887-896. MR2287146DOI
  47. Xie, A. F., Li, S. J., , Fuzzy Sets Syst. 386 (2020), 95-104. MR4073391DOI
  48. Xiu, Z. Y., Zheng, X., , Fuzzy Sets Syst. 465 (2023), 108535. MR4594058DOI
  49. Xiu, Z. Y., Jiang, Y. X., , J. Intell. Fuzzy Syst. 45 (2023), 2, 2019-2030. MR4388021DOI
  50. Yager, R. R., Rybalov, A., , Fuzzy Sets Syst. 80 (1996), 111-120. Zbl0871.04007MR1389951DOI
  51. Zhao, B., Wu, T., 10.1016/j.ijar.2020.12.008, Int. J. Approx. Reason. 130 (2021), 22-49. MR4188974DOI10.1016/j.ijar.2020.12.008
  52. al., H. P. Zhang et, , Fuzzy Sets Syst. 423 (2021), 107-121. MR4310515DOI
  53. Zimmermann, H. J., Fuzzy Set Theory and Its Applications. (Fourth Edition.), Kluwer, Aachen 2001. MR1882395

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