| Title:
|
New methods to construct uninorms by extending uninorms with closure operators and t-superconorms (English) |
| Author:
|
Qi, Jun |
| Author:
|
Xiu, Zhen-Yu |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
6 |
| Year:
|
2025 |
| Pages:
|
855-871 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we provide new methods to construct uninorms by extending given uninorms on a subinterval of a bounded lattice with closure operators (resp. interior operators) and t-superconorms (resp. t-subnorms). Meanwhile, these methods for uninorms generalize some known methods for uninorms in the literature. An example is also provided to show our method. (English) |
| Keyword:
|
bounded lattices |
| Keyword:
|
closure operators |
| Keyword:
|
t-superconorms |
| Keyword:
|
uninorms |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| MSC:
|
06B20 |
| DOI:
|
10.14736/kyb-2025-6-0855 |
| . |
| Date available:
|
2026-01-07T16:40:23Z |
| Last updated:
|
2026-01-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153267 |
| . |
| Reference:
|
[1] Aşcı, E., Mesiar, R.: On the construction of uninorms on bounded lattices..Fuzzy Sets Systems 408 (2021), 65-85. |
| Reference:
|
[2] Birkhoff, G.: Lattice Theory..Amer. Math. Soc., Rhode Island, 1967. Zbl 0537.06001 |
| Reference:
|
[3] Bodjanova, S., Kalina, M.: Construction of uninorms on bounded lattices..In: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, September 11-13, Subotica, Serbia, 2014, 61-66. |
| Reference:
|
[4] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices..Inform. Sci. 367 (2016), 221-231. |
| Reference:
|
[5] Çaylı, G. D., Ertuğrul, Ü., Karaçal, F.: Some further construction methods for uninorms on bounded lattices..Int. J. General Systems 52 (2023), 4, 414-442. |
| Reference:
|
[6] Çaylı, G. D.: New construction approaches of uninorms on bounded lattices..Int. J. General Systems 50 (2021), 139-158. |
| Reference:
|
[7] Çaylı, G. D.: An alternative construction of uninorms on bounded lattices..Int. J. General Systems 52 (2023), 5, 574-596. |
| Reference:
|
[8] Çaylı, G. D.: Constructing uninorms on bounded lattices through closure and interior operators..Int. J. Uncertainty Fuzziness Knowledge-Based Systems 32 (2024), 1, 109-129. |
| Reference:
|
[9] Everett, C. J.: Closure operators and Galois theory in lattices..Trans. Amer. Math. Soc. 55 (1944), 514-525. |
| Reference:
|
[10] Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E.: Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes..Inform. Sci. 181 (2011), 23-43. |
| Reference:
|
[11] Hájek, P.: Combining Functions for Certainty Degrees in Consulting Systems..Int. J. Man-Machine Studies 22 (1985), 1, 59-76. |
| Reference:
|
[12] Hájek, P., Havránek, T., Jiroušek, R.: Uncertain Information Processing in Expert Systems..CRC Press, Boca Raton 1992. |
| Reference:
|
[13] Hua, X. J., Zhang, H. P., Ouyang, Y.: Note on "Construction of uninorms on bounded lattices"..Kybernetika 57 (2021), 2, 372-382. |
| Reference:
|
[14] He, P., Wang, X. P.: Constructing uninorms on bounded lattices by using additive generators..Int. J. Approx. Reason. 136 (2021), 1-13. |
| Reference:
|
[15] Hua, X. J., Ji, W.: Uninorms on bounded lattices constructed by t-norms and t-subconorms..Fuzzy Sets Systems 427 (2022), 109-131. |
| Reference:
|
[16] Ji, W.: Constructions of uninorms on bounded lattices by means of t-subnorms and t-subconorms..Fuzzy Sets Systems 403 (2021), 38-55. |
| Reference:
|
[17] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices..Fuzzy Sets Systems 261 (2015), 33-43. |
| Reference:
|
[18] Karaçal, F., Ertuğrul, Ü., Mesiar, R.: Characterization of uninorms on bounded lattices..Fuzzy Sets Systems 308 (2017), 54-71. |
| Reference:
|
[19] Klement, E. P., Mesiar, R., Pap, E.: A Universal Integral As Common Frame for Choquet and Sugeno Integral..IEEE Trans. Fuzzy Systems 18 (2010), 178-187. |
| Reference:
|
[20] Menger, K.: Statistical metrics..In: Proc. National Academy of Sciences of the United States of America 8 (1942), 535-537. Zbl 0063.03886, |
| Reference:
|
[21] Metcalfe, G., Montagna, F.: Substructural Fuzzy Logics..J. Symbolic Logic 72 (2007), 3, 834-864. |
| Reference:
|
[22] Ouyang, Y., Zhang, H. P.: Constructing uninorms via closure operators on a bounded lattice..Fuzzy Sets Systems 395 (2020), 93-106. |
| Reference:
|
[23] Palmeira, E. S., Bedregal, B. C.: Extension of fuzzy logic operators defined on bounded lattices via retractions..Comput. Math. Appl. 63 (2012), 1026-1038. |
| Reference:
|
[24] Saminger, S.: On ordinal sums of triangular norms on bounded lattices..Fuzzy Sets Systems 157 (2006), 1403-1416. Zbl 1099.06004, |
| Reference:
|
[25] Takács, M.: Uninorm-Based Models for FLC Systems..J. Intell. Fuzzy Systems 19 (2008), 1, 65-73. |
| Reference:
|
[26] Xiu, Z. Y., Zheng, X.: New construction methods of uninorms on bounded lattices via uninorms..Fuzzy Sets Systems 465 (2023), 108535. |
| Reference:
|
[27] Xiu, Z. Y., Zheng, X.: A new approach to construct uninorms via uninorms on bounded lattices..Kybernetika 60 (2024), 2, 125-149. |
| Reference:
|
[28] Yager, R. R., Rybalov, A.: Uninorm aggregation operators..Fuzzy Sets Systems 80 (1996), 111-120. Zbl 0871.04007, |
| Reference:
|
[29] Zhao, B., Wu, T.: Some further results about uninorms on bounded lattices..Int. J. Approx. Reasoning 130 (2021), 22-49. |
| Reference:
|
[30] Zhang, H. P., Wu, M., Wang, Z., Ouyang, Y., Baets, B. De: A characterization of the classes Umin and Umax of uninorms on a bounded lattice..Fuzzy Sets Systems 423 (2021), 107-121. |
| . |
