| Title:
|
Constructing mixed uninorms on bounded lattices (English) |
| Author:
|
Tian, Xiaofeng |
| Author:
|
Xie, Aifang |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2025 |
| Pages:
|
577-591 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we present the definition of mixed uninorms and propose several methods for constructing two special classes of mixed uninorms on bounded lattices through t-subnorms and t-superconorms. These methods generalize $\mathbb{U}_{\min},$ $\mathbb{U}_{\max},$ $\mathbb{U}_{\min}^{1}$ and $\mathbb{U}_{\max}^{0}$ on bounded lattices that have been previously discussed in the literature. Some examples are given to construct mixed uninorms on bounded lattices. (English) |
| Keyword:
|
bounded lattices |
| Keyword:
|
uninorms |
| Keyword:
|
T-superconorm |
| Keyword:
|
T-subnorm |
| MSC:
|
03B52 |
| MSC:
|
06Dxx |
| DOI:
|
10.14736/kyb-2025-4-0577 |
| . |
| Date available:
|
2025-09-19T17:12:32Z |
| Last updated:
|
2025-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153076 |
| . |
| Reference:
|
[1] Asici, E., Mesiar, R.: On the construction of uninorms on bounded lattices..Fuzzy Sets Syst. 408 (2021), 65-85. |
| Reference:
|
[2] Birkhoff, G.: Lattice Theory. (Third edition.).Amer. Math. Soc., Rhode Island 1967. |
| Reference:
|
[3] Bodjanova, S., Kalina, M.: Construction of uninorms on bounded lattices..In: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, Subotica, 2014, pp. 61-66. |
| Reference:
|
[4] Baets, B. De, Mesiar, R.: Triangular norm on product lattice,.Fuzzy Sets Syst. 104 (1999), 61-75. |
| Reference:
|
[5] Coomann, G. De, Kerre, E.: Order norms on bounded partially ordered sets..J. Fuzzy Math. 2 (1994), 281-310. |
| Reference:
|
[6] Çaylı, G. D.: Alternative approaches for generating uninorms on bounded lattices..Inform. Sci. 488 (2019) 111-139. |
| Reference:
|
[7] Çaylı, G. D.: New methods to construct uninorms on bounded lattices..Int. J. Approx. Reason. 115 (2019), 254-264. |
| Reference:
|
[8] Çaylı, G. D.: On the structure of uninorms on bounded lattices..Fuzzy Sets Syst. 357 (2019), 2-26. |
| Reference:
|
[9] Çaylı, G. D.: Uninorms on bounded lattices with the underlying t-norms and t-conorms..Fuzzy Sets Syst. 395 (2020), 107-129. |
| Reference:
|
[10] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices..Inform. Sci. 367 (2016), 221-231. |
| Reference:
|
[11] Çaylı, G. D.: New construction approaches of uninorms on bounded lattices..Int. J. Gen. Syst. 50 (2021), 139-158. |
| Reference:
|
[12] Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets.Kluwer Acad. Publ., Boston 2000. |
| Reference:
|
[13] Dan, Y. X., Hu, B. Q., Qiao, J. S.: New constructions of uninorms on bounded lattices..Int. J. Approx. Reason. 110 (2019), 185-209. |
| Reference:
|
[14] Dan, Y. X., Hu, B. Q.: A new structure for uninorms on bounded lattices..Fuzzy Sets Syst. 386 (2020), 77-94. |
| Reference:
|
[15] Fodor, J. C., Yager, R. R., Rybalov, A.: Structure of uninorms..Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. Zbl 1232.03015, 10.1142/S0218488597000312 |
| Reference:
|
[16] Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E.: Aggregation Functions..Cambridge University Press, 2009. Zbl 1206.68299 |
| Reference:
|
[17] Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E.: Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes..Inf. Sci. 181 (2011), 23-43. |
| Reference:
|
[18] Hua, X. J., Ji, W.: Uninorms on bounded lattices constructed by t-norms and t-subconorms..Fuzzy Sets Syst. 427 (2022), 109-131. |
| Reference:
|
[19] Hua, X J., Zhang, H. P., Ouyang, Y.: Note on Construction of uninorms on bounded lattices..Kybernetika 57 (2021), 2, 372-382. |
| Reference:
|
[20] He, P., Wang, X. P.: Constructing uninorms on bounded lattices by using additive generators..Int. J. Approx. Reason. 136 (2021), 1-13. |
| Reference:
|
[21] Ji, W.: Constructions of uninorms on bounded lattices by means of t-subnorms and t-subconorms..Fuzzy Sets Syst. 403 (2021), 38-55. |
| Reference:
|
[22] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices..Fuzzy Sets Syst. 261 (2015), 33-43. MR 3291484, |
| Reference:
|
[23] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms..Springer Science Business Media, 2013. Zbl 1087.20041 |
| Reference:
|
[24] Ouyang, Y., Zhang, H. P.: Constructing uninorms via closure operators on a bounded lattice.Fuzzy Sets Syst. 395 (2020), 93-106. |
| Reference:
|
[25] Pedrycz, W., Hirota, K.: Uninorm-based logic neurons as adaptive and interpretable processing constructs..Soft Comput. 11 (2007), 41-52. |
| Reference:
|
[26] Schweizer, B., Sklar, A., al, et: Statistical metric spaces..Pacific J. Math. 10 (1960), 313-334. |
| Reference:
|
[27] Xiu, Z. Y., Zheng, X.: New construction methods of uninorms on bounded lattices via uninorms..Fuzzy Sets Syst. 465 (2023), 108-535. |
| Reference:
|
[28] Yager, R. R.: Aggregation operators and fuzzy systems modeling..Fuzzy Sets Syst. 67 (1994), 129-145. |
| Reference:
|
[29] Yager, R. R., Rybalov, A.: Uninorms aggregation operators..Fuzzy Sets Syst. 80 (1996), 111-120. |
| 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. |
| Reference:
|
[31] Yager, R. R.: Uninorms in fuzzy system modeling..Fuzzy Sets Syst. 122 (2001), 167-175. MR 1839955, |
| Reference:
|
[32] Zhao, B., Wu, T.: Some further results about uninorms on bounded lattices..Int. J. Approx. Reason. 130 (2021), 22-49. |
| . |
