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Conditional distributivity of continuous triangular norms over 2-uninorms | ||
Iranian Journal of Fuzzy Systems | ||
دوره 20، شماره 2، خرداد و تیر 2023، صفحه 69-82 اصل مقاله (199.9 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7557 | ||
نویسندگان | ||
S. P. Liu؛ F. Qin* | ||
School of Mathematics and Statistics, Jiangxi Normal University, 330022 Nanchang, PR China | ||
چکیده | ||
Conditional distributivity of aggregation functions, which has received wide attention from the researchers, is vital for many different fields, for example, integration theory, utility theory and so on. This article is mainly devoted to dealing with the conditional distributivity of continuous t-norms over 2-uninorms. As the first step for investigating the conditional distributivity of 2-uninorms, we give the complete characterization of all pairs $(T,\mathcal{H})$ {fulfilling} this property. Compared to the case of distributivity of continuous t-norms over 2-uniorms, which leads to the 2-uninorm must be idempotent, the results obtained in this paper demonstrate that conditional distributivity and distributivity on this topic, are not equivalent. | ||
کلیدواژهها | ||
Conditional distributivity؛ 2-uninorms؛ uninorms؛ continuous triangular norms | ||
مراجع | ||
[1] P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
[2] G. Beliakov, A Pradera, T. Calvo, Aggregation functions: A guide for practitioners, Springer, Berlin, Heidelberg, 2007.
[3] T. Calvo, G. Mayor, R. Mesiar, Aggregation operators: New trends and applications, Springer, Berlin, Heidelberg, 2002.
[4] J. Drewniak, P. Dryga´s, E. Rak, Distribitivity equations for uninorms and nullnorms, Fuzzy Sets and Systems, 159 (2008), 1646-1657.
[5] P. Dryga´s, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 291 (2016), 82-97.
[6] D. Dubois, L. Godo, H. Prade, A. Zapico, Making decision in a qualitative setting: From decision under uncertainty to case-based decision, in: A. G. Cohn, L. Schurbet, S. C. Shapiro (Eds.), Proceedings of the 6th International Conference Principles of Knowledge Representation and Reasoning, KR98, San Francisco, CA, (1998), 594-605. [7] D. Dubois, E. Pap, H. Prade, Hybrid probabilistic-possibilistic mixtures and utility functions, in: Preferences and Decisions under Incomplete Knowledge. Studies in Fuzziness and Soft Computing, 51, Springer-Verlag, (2000), 51-73. [8] D. Dubois, E. Pap, H. Prade, Pseudo-additive measures and the independence of events, in: Technologies for Constructing Intelligent Systems 1, in: Stud. Fuzziness Soft Comput., 89, Springer-Verlag, (2001), 179-191. [9] M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap, Aggregation functions, Cambridge University Press, New York, 2009.
[10] D. Joˇci´c, I. Stajner-Papuga, ˇ Restricted distributuvity for aggregation operators with absorbing element, Fuzzy Sets and Systems, 224 (2013), 23-35. [11] D. Joˇci´c, I. Stajner-Papuga, ˇ Distributivity and conditional distributivity for T-uninorms, Information Sciences, 424 (2018), 91-103. [12] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.
[13] G. Li, H. W. Liu, Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t-conorm, Fuzzy Sets and Systems, 287 (2016), 154-171. [14] W. H. Li, F. Qin, Conditinoal distributivity equation for uninorms with continuous underlying operators, IEEE Transactions on Fuzzy Systems, 28(8) (2020), 1664-1678. [15] W. H. Li, F. Qin, New results on the migrativity properties for overlap(grouping) functions and uninorms, Iranian Journal of Fuzzy Systems, 18 (2021), 111-128. [16] M. Mas, G. Mayor, J. Torrens, The distribitivity equations for uninorms and t-operators, Fuzzy Sets and Systems, 128 (2002), 209-225. [17] M. Mas, G. Mayor, J. Torrens, Corrigendum to ”the distribitive equations for uninorms and t-operators”, [Fuzzy Sets and Systems, 128 (2002), 209-225], Fuzzy Sets and Systems, 153 (2005), 297-299. [18] A. Mesiarov´a-Zem´ankov´a, The n-uninorms with continuous underlying t-norms and t-conorms, International Journal of General Systems, 50(1) (2020), 92-116.
[19] A. Mesiarov´a-Zem´ankov´a, Characterizing functions of n-uninorms with continuous underlying functions, IEEE Transactions on Fuzzy Systems, 30(5) (2021), 1239-1247. [20] A. Mesiarov´a-Zem´ankov´a, Characterization of n-uninorms with continuous underlying functions via z-ordinal sum construction, International Journal of Approximate Reasoning, 133 (2021), 60-79. [21] A. Mesiarov´a-Zem´ankov´a, Characterization of idempotent n-uninorms, Fuzzy Sets and Systems, 427 (2022), 1-22.
[22] F. Qin, B. Zhao, The distributive equations for idempotent uninorms and nullnorms, Fuzzy Sets and Systems, 155 (2005), 446-458.
[23] D. Ruiz-Aguilera, J. Torrens, Distributivity and conditional distributivity of a uninorm and a continuous t-conorm, IEEE Transactions on Fuzzy Systems, 14(2) (2006), 180-190. [24] X. R. Sun, H. W. Liu, The left (right) distributivity of semi-t-operators over 2-uninorms, Iranian Journal of Fuzzy Systems, 17 (2020), 103-116. [25] F. Sun, X. P. Wang, X. B. Qu, Uni-nullnorms and null-uninorms, Journal of Intelligent and Fuzzy Systems, 32 (2017), 1969-1981. [26] G. Wang, F. Qin, W. H. Li, Distributivity and conditional distributivity for uni-nullnorms, Fuzzy Sets and Systems, 372 (2019), 34-49. [27] A. Xie, H. Liu, On the distribitivity of uninorms over nullnorms, Fuzzy Sets and Systems, 211 (2013), 62-72.
[28] R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
[29] F. X. Zhang, E. Rak, J. Bazan, On the distributivity of continuous triangular norms and triangular conorms with respect to 2-uninorm, Fuzzy Sets and Systems, 395 (2020), 168-177. [30] W. Zong, Y. Su, H. W. Liu, B. De Baets, On the structure of 2-uninorms, Information Sciences, 467 (2018), 506-527. | ||
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