Additive generators of discrete semi-uninorms

Ya-Ming Wang; Hang Zhan; Yuan-Yuan Zhao

Kybernetika (2024)

  • Volume: 60, Issue: 6, page 740-753
  • ISSN: 0023-5954

Abstract

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This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in 𝒰 min and 𝒰 max that are generated by additive generators.

How to cite

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Wang, Ya-Ming, Zhan, Hang, and Zhao, Yuan-Yuan. "Additive generators of discrete semi-uninorms." Kybernetika 60.6 (2024): 740-753. <http://eudml.org/doc/299893>.

@article{Wang2024,
abstract = {This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in $\mathcal \{U\}_\{\min \}$ and $\mathcal \{U\}_\{\max \}$ that are generated by additive generators.},
author = {Wang, Ya-Ming, Zhan, Hang, Zhao, Yuan-Yuan},
journal = {Kybernetika},
keywords = {aggregation operations; semi-uninorms; additive generators; semi-t-norms; semi-t-conorms; finite chains},
language = {eng},
number = {6},
pages = {740-753},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Additive generators of discrete semi-uninorms},
url = {http://eudml.org/doc/299893},
volume = {60},
year = {2024},
}

TY - JOUR
AU - Wang, Ya-Ming
AU - Zhan, Hang
AU - Zhao, Yuan-Yuan
TI - Additive generators of discrete semi-uninorms
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 6
SP - 740
EP - 753
AB - This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in $\mathcal {U}_{\min }$ and $\mathcal {U}_{\max }$ that are generated by additive generators.
LA - eng
KW - aggregation operations; semi-uninorms; additive generators; semi-t-norms; semi-t-conorms; finite chains
UR - http://eudml.org/doc/299893
ER -

References

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  1. Beliakov, G., Pradera, A., Calvo, T., Aggregation functions: A guide for practitioners., Stud. Fuzziness Soft Comput. 221 (2007), Springer, Berlin, Heidelberg. 
  2. Calvo, T., Mayor, G., Mesiar, R., 10.1007/978-3-7908-1787-4, Stud. Fuzziness Soft Comput. 97 (2002), Springer, Berlin, Heidelberg. MR1936384DOI10.1007/978-3-7908-1787-4
  3. Baets, B. De, Mesiar, R., , Fuzzy Sets Syst. 104 (1999), 61-75. Zbl0935.03060MR1685810DOI
  4. Baets, B. De, Mesiar, R., , Trends in Logic (S. Rodabaugh and E.-P. Klement, eds.), 20 (2003), pp. 389-400. MR2046749DOI
  5. Baets, B. De, Fodor, J., Ruiz-Aguilera, D., Torrens, J., , Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 17 (2009), 1-14. Zbl1178.03070MR2514519DOI
  6. Durante, F., Klement, E. P., Mesiar, R., Sempi, C., , Mediterr. J. Math. 4 (2007), 343-356. MR2349892DOI
  7. Fodor, J., , IEEE Trans. Fuzzy Syst. 8 (2000), 791-795. DOI
  8. Fodor, J., Keresztfalvi, T., , Int. J. Approx. Reason. 12 (1995), 69-84. MR1315634DOI
  9. Fodor, J., Yager, R. R., Rybalov, A., , Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. Zbl1232.03015MR1471619DOI
  10. Han, L., Liu, H. W., On the distributivity of logical operators on a finite chain., School Math., Shandong University 2014, pp. 42-47. MR3234920
  11. Kolesarova, A., Mesiar, R., Mordelova, J., Sempi, C., , IEEE Trans. Fuzzy Syst. 14 (2006), 698-705. DOI
  12. Li, G., Liu, H. W., Fodor, J., , Int. J. Intell. Syst. 30 (2015), 421-440. DOI
  13. Liu, H. W., , Fuzzy Sets Syst. 191 (2012), 72-82. MR2874824DOI
  14. Munar, M., Massanet, S., Ruiz-Aguilera, D., , Fuzzy Sets Syst. 462 (2023), 108469. MR4584400DOI
  15. Mas, M., Mayor, G., Torrens, J., , Int. J. Intell. Syst. 14 (1999), 909-922. MR1691482DOI
  16. Mas, M., Monserrat, M., Torrens, J., , IEEE Trans. Fuzzy Syst. 11 (2003), 647-651. DOI
  17. Mas, M., Monserrat, M., Torrens, J., , Fuzzy Sets Syst. 146 (2004), 3-17. Zbl1045.03029MR2074199DOI
  18. Mas, M., Monserrat, M., Torrens, J., , Fuzzy Sets Syst. 167 (2011), 82-91. MR2765249DOI
  19. Mayor, G., Monreal, J., , IEEE Trans. Fuzzy Syst. 15 (2007), 1046-1052. DOI
  20. Mayor, G., Monreal, J., , Fuzzy Sets Syst. 264 (2015), 110-120. MR3303667DOI
  21. Mayor, G., Torrens, J., Triangular Norms on Discrete Settings, in Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms., Elsevier, Amsterdam. 2005, pp. 189-230. MR2165236
  22. Mayor, G., Suñer, J., Torrens, J., , IEEE Trans. Fuzzy Syst. 13 (2005), 468-477. DOI
  23. Pradera, A., Beliakov, G., Bustince, H., , Inform. Sci. 329 (2016), 357-380. DOI
  24. Ruiz-Aguilera, D., Torrens, J., , Fuzzy Sets Syst. 268 (2015), 44-58. MR3320246DOI
  25. Sander, W., , In: Aggregation Operators (T. Calvo, G. Mayor, R. Mesiar, eds.), Physica-Verlag, Heidelberg 2002, pp. 124-158. MR1936386DOI

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