A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli

Kybernetika (2023)

  • Volume: 59, Issue: 5, page 768-790
  • ISSN: 0023-5954

Abstract

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Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.

How to cite

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Çayli, Gül Deniz. "A characterization of uninorms on bounded lattices via closure and interior operators." Kybernetika 59.5 (2023): 768-790. <http://eudml.org/doc/299172>.

@article{Çayli2023,
abstract = {Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.},
author = {Çayli, Gül Deniz},
journal = {Kybernetika},
keywords = {bounded lattice; closure operator; uninorm; interior operator; T-norm; T-conorm},
language = {eng},
number = {5},
pages = {768-790},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A characterization of uninorms on bounded lattices via closure and interior operators},
url = {http://eudml.org/doc/299172},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Çayli, Gül Deniz
TI - A characterization of uninorms on bounded lattices via closure and interior operators
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 5
SP - 768
EP - 790
AB - Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.
LA - eng
KW - bounded lattice; closure operator; uninorm; interior operator; T-norm; T-conorm
UR - http://eudml.org/doc/299172
ER -

References

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  1. Aşıci, E., , Kybernetika 57 (2021), 352-371. MR4273580DOI
  2. Aşıcı, E., Mesiar, R., , Kybernetika 57 (2021), 989-1004. MR4376872DOI
  3. Beliakov, G., Pradera, A., Calvo, T., Aggregation Functions: A Guide for Practitioners., Springer, Berlin 2007. 
  4. Benítez, J. M., Castro, J. L., Requena, I., , IEEE Trans. Neural Netw. 8 (1997), 1156-1163. DOI
  5. Birkhoff, G., Lattice Theory., American Mathematical Society Colloquium Publishers, Providence 1967. Zbl0537.06001MR0227053
  6. Bodjanova, S., Kalina, M., , In: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, Subotica 2014. DOI
  7. Bodjanova, S., Kalina, M., , In: IWIFSGN 2017, EUSFLAT 2017, AISC, vol. 641 J. Kacprzyk et al. eds. Springer, Cham, 2018, pp. 224-234. DOI
  8. Bodjanova, S., Kalina, M., , In: AGOP 2019, AISC, vol. 981 R. Halaś et al. eds. Springer, Cham, 2019, pp. 183-194. DOI
  9. Çayli, G. D., 10.1016/j.ins.2019.03.007, Inf. Sci. 488 (2019), 111-139. MR3924420DOI10.1016/j.ins.2019.03.007
  10. Çayli, G. D., , Int. J. Approx. Reason. 115 (2019), 254-264. MR4018632DOI
  11. Çayli, G. D., , Appl. Math. Comput. 366 (2020), 124746. MR4011595DOI
  12. Çayli, G. D., , Fuzzy Sets Syst. 395 (2020), 107-129. MR4109064DOI
  13. Çayli, G. D., , Int. J. Uncertain. Fuzziness Knowl. Based Syst. 28 (2020), 807-835. MR4155937DOI
  14. Çayli, G. D., , Int. J. Gen. Syst. 50 (2021), 139-158. MR4222196DOI
  15. Çayli, G. D., Karaçal, F., Mesiar, R., , Int. J. Gen. Syst. 48 (2019), 235-259. MR3904571DOI
  16. Dan, Y., Hu, B. Q., Qiao, J., , Int. J. Approx. Reason. 110 (2019), 185-209. MR3947797DOI
  17. Dan, Y., Hu, B. Q., , Fuzzy Sets Syst. 386 (2020), 77-94. MR4073387DOI
  18. Baets, B. De, , European J. Oper. Res. 118 (1999), 631-642. Zbl1178.03070DOI
  19. Baets, B. De, Fodor, J., Ruiz-Aguilera, D., Torrens, J., , Int. J. Uncertain. Fuzziness Knowl. Based Syst. 17 (2009), 1-14. Zbl1178.03070MR2514519DOI
  20. Drewniak, J., Drygaś, P., , Int. J. Uncertain. Fuzziness Knowl. Based Syst. 10 (2002), 5-10. MR1962665DOI
  21. Drossos, C. A., , Fuzzy Sets Syst. 104 (1999), 53-59. MR1685809DOI
  22. Drossos, C. A., Navara, M., Generalized t-conorms and closure operators., In: Proc. EUFIT '96, Aachen, 1996, pp. 22-26. 
  23. Drygaś, P., On the structure of continuous uninorms., Kybernetika 43 (2007), 183-196. Zbl1132.03349MR2343394
  24. Drygaś, P., Rak, E., , Fuzzy Sets Syst. 291 (2016), 82-97. MR3463655DOI
  25. Dubois, D., Prade, H., Fundamentals of Fuzzy Sets., Kluwer Academic Publisher, Boston 2000. MR1890229
  26. Dubois, D., Prade, H., , Inf. Sci. 36 (1985), 85-121. Zbl0582.03040MR0813766DOI
  27. Engelking, R., General Topology., Heldermann Verlag, Berlin 1989. Zbl1281.54001MR1039321
  28. Ertuğrul, Ü., Kesicioğlu, M., Karaçal, F., , Kybernetika 55 (2019), 994-1015. MR4077141DOI
  29. Everett, C. J., , Trans. Am. Math. Soc. 55 (1944), 514-525. MR0010556DOI
  30. Fodor, J., Yager, R. R., Rybalov, A., , Int. J. Uncertain. Fuzziness Knowl. Based Syst. 5 (1997), 411-427. Zbl1232.03015MR1471619DOI
  31. González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D., , IEEE Trans. Fuzzy Syst. 23 (2015), 872-884. DOI
  32. He, P., Wang, X. P., , Int. J. Approx. Reason. 136 (2021), 1-13. MR4270087DOI
  33. Homenda, W., Jastrzebska, A., Pedrycz, W., , Appl. Math. Comput. 290 (2016), 392-411. MR3523438DOI
  34. Hua, X. J., Ji, W., , Fuzzy Sets Syst. 427 (2022), 109-131. MR4343692DOI
  35. Karaçal, F., Ertuğrul, Ü., Kesicioğlu, M., , Kybernetika 55 (2019), 976-993. MR4077140DOI
  36. Karaçal, F., Mesiar, R., , Fuzzy Sets Syst. 261 (2015), 33-43. MR3291484DOI
  37. Klement, E. P., Mesiar, R., Pap, E., Triangular Norms., Kluwer Academic Publishers, Dordrecht 2000. Zbl1087.20041MR1790096
  38. Klement, E. P., Mesiar, R., Pap, E., , Fuzzy Sets Syst. 143 (2004), 5-26. MR2060270DOI
  39. Klement, E. P., Mesiar, R., Pap, E., , Fuzzy Sets Syst. 145 (2004), 411-438. MR2075838DOI
  40. Medina, J., , Fuzzy Sets Syst. 202 (2012), 75-88. MR2934787DOI
  41. Menger, K., 10.1073/pnas.28.12.535, PNAS 8 (1942), 535-537. Zbl0063.03886MR0007576DOI10.1073/pnas.28.12.535
  42. Metcalfe, G., Montagna, F., , J. Symb. Log. 72 (2007), 834-864. MR2354903DOI
  43. Ouyang, Y., Zhang, H. P., , Fuzzy Sets Syst. 395 (2020), 93-106. MR4109063DOI
  44. Sun, X. R., Liu, H. W., , Fuzzy Sets Syst. 427 (2022), 96-108. MR4343691DOI
  45. Saminger, S., , Fuzzy Sets Syts. 157 (2006), 1403-1416. Zbl1099.06004MR2226983DOI
  46. Schweizer, B., Sklar, A., Probabilistic Metric Spaces., Elsevier North-Holland, New York 1983. Zbl0546.60010MR0790314
  47. Schweizer, B., Sklar, A., Associative functions and statistical triangular inequalities., Publ. Math. 8 (1961), 169-186. MR0132939
  48. Takács, M., Uninorm-based models for FLC systems., J. Intell. Fuzzy Syst. 19 (2008), 65-73. 
  49. Yager, R. R., , Fuzzy Sets Syst. 67 (1994), 129-145. MR1302575DOI
  50. Yager, R. R., Rybalov, A., , Fuzzy Sets Syst. 80 (1996), 111-120. Zbl0871.04007MR1389951DOI
  51. Yager, R. R., , Fuzzy Sets Syst. 122 (2001), 167-175. MR1839955DOI
  52. Yager, R. R., Defending against strategic manipulation in uninorm-based multi-agent decision making., Fuzzy Sets Syst. 140 (2003), 331-339. Zbl0998.90046MR1925395
  53. Zhao, B., Wu, T., , Int. J. Approx. Reason. 130 (2021), 22-49. MR4188974DOI

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