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Construction of 2-uninorms on bounded lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 15، دوره 19، شماره 1، فروردین و اردیبهشت 2022، صفحه 189-200 اصل مقاله (227.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6560 | ||
| نویسندگان | ||
| A. Xie* 1؛ Z. Yi2 | ||
| 1Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi, 330031, China | ||
| 2College of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, 330031, China | ||
| چکیده | ||
| Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U_1 and U_2, defined on sublattices [0,d] and [d,1], respectively, this paper presents two methods for constructing binary operators on L which extend both U_1 and U_2. We show that our first construction is a 2-uninorm on L if and only if U_2 is conjunctive and our second construction is a 2-uninorm on L if and only if U_1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0,d]^2 and [d,1]^2 are respectively U_1 and U_2. | ||
| کلیدواژه‌ها | ||
| Bounded lattices؛ 2-uninorms؛ uninorms؛ nullnorms | ||
| مراجع | ||
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[1] P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
[2] B. Bedregal, G. Beliakov, H. Bustince, J. Fernández, A. Pradera, R. Reiser, (S,N)-implications on bounded lattices, Advances in Fuzzy Implication Functions, Springer Heidelberg New York Dordrecht London, 101-124.
[3] G. Birkhoff, Lattice theory, American Mathematical Society Colloquium Publishers, Providence, RI, 1967.
[4] S. Bodjanova, M. Kalina, Construction of uninorms on bounded lattices, in: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, Subotica, Serbia, September 11-13, 2014.
[5] T. Calvo, B. De Baets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets and Systems, 120 (2001), 385-394.
[6] G. D. Çaylı, On the structure of uninorms on bounded lattices, Fuzzy Sets and Systems, 357 (2019), 2-26.
[7] G. D. Çaylı, Uninorms on bounded lattices with the underlying t-norms and t-conorms, Fuzzy Sets and Systems, 395 (2020), 107-129.
[8] G. D. Çaylı, Nullnorms on bounded lattices derived from t-norms and t-conorms, Information Sciences, 512 (2020), 1134-1154.
[9] G. D. Çaylı, P. Drygaś, Some properties of idempotent uninorms on a special class of bounded lattices, Information Sciences, 422 (2018), 352-363.
[10] G. D. Çaylı, F. Karaçal, Construction of uninorms on bounded lattices, Kybernetika, 53 (2017), 394-417.
[11] G. D. Çaylı, F. Karaçal, Idempotent nullnorms on bounded lattices, Information Sciences, 425 (2018), 154-163.
[12] G. D. Çaylı, F. Karaçal, R. Mesiar, On a new class of uninorms on bounded lattices, Information Sciences, 367-368 (2016), 221-231.
[13] P. V. de Campos Souza, E. Lughofer, An advanced interpretable fuzzy neural network model based on uni-nullneuron constructed from n-uninorms, Fuzzy Sets and Systems, Doi:10.1016/j.fss.2020.11.019.
[14] Y. X. Dan, B. Q. Hu, J. S. Qiao, New constructions of uninorms on bounded lattices, International Journal of Approximate Reasoning, 110 (2019), 185-209.
[15] B. De Bates, Idempotent uninorms, European Journal of Operational Research, 118 (1998), 631-642.
[16] B. De Baets, J. Fodor, Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof, Fuzzy Sets and Systems, 104 (1999), 133-136.
[17] B. De Baets, R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems, 104 (1999), 61-75.
[18] P. Drygaś, Discussion of the stucrture of uninorms, Kybernetika, 41 (2005), 213-226.
[19] P. Drygaś, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 291 (2016), 82-97.
[20] R. Duda, P. Hart, N. Nilsson, Subjective Bayesian methods for rule-based inference systems, In Proceedings National Computer Conference and Exposition (AFIPS), 45 (1976), 1075-1082.
[21] U. Ërtuğrul, A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice, New Trends in Mathematical Sciences, 5(2) (2017), 1-9.
[22] U. Ërtuğrul, Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms, Fuzzy Sets and Systems, 334 (2018), 94-109.
[23] J. Fodor, R. R. Yager, A. Rybalov, Structure of uninorms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5 (1997), 411-427.
[24] M. A. İnce, F. Karaçal, R. Mesiar, Medians and nullnorms on bounded lattices, Fuzzy Sets and Systems, 289 (2016), 74-81.
[25] F. Karaçal, M. A. İnce, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
[26] F. Karaçal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
[27] E. P. Klement, R. Mesiar, E. Pap, Triangular norms. Dordrecht, The Netherlands: Kluwer, 2000.
[28] G. J. Klir, B. Yuan, Fuzzy sets and fuzzy logic: Theory and applications, Prentice Hall PTR, Upper Saddle River, New Jersey, 1995.
[29] Y. M. Li, Z. K. Shi, Weak uninorm aggregation operators, Fuzzy Sets and Systems, 124 (2000), 317-323.
[30] M. Mas, G. Mayor, J. Torrens, T-operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7(1) (1999), 31-50.
[31] A. Mesiarová-Zemánková, Characterization of uninorms with continuous underlying t-norm and t-conorm by their set of discontinuity points, IEEE Transactions on Fuzzy Systems, 26(2) (2018), 705-714.
[32] A. Mesiarová-Zemánková, Characterization of idempotent n-uninorms, Fuzzy Sets and Systems, doi:10.1016/j.fss. 2020.12.019.
[33] A. Mesiarová-Zemánková, Characterizing functions of n-uninorms with continuous underlying functions, IEEE Transactions on Fuzzy Systems, Doi:10.1109/TFUZZ.2021.3057231.
[34] Y. Ouyang, H. P. Zhang, Constructing uninorms via closure operators on a bounded lattice, Fuzzy Sets and Systems, 395 (2020), 93-106.
[35] F. Sun, X. P. Wang, X. B. Qu, Uni-nullnorms and null-uninorms, Journal of Intelligent and Fuzzy Systems, 32 (2017), 1969-1981.
[36] A. K. Tsadiras, K. G. Margaritis, The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons, Fuzzy Sets and Systems, 93 (1998), 263-274.
[37] Y. M. Wang, H. Zhan, W. H. Liu, Uni-nullnorms on bounded lattices, Fuzzy Sets and Systems, 386 (2020), 132-144.
[38] Y. M. Wang, W. W. Zong, H. Zhan, W. H. Liu, On migrative 2-uninorms and nullnorms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 27(2) (2019), 303-328.
[39] X. Wu, S. Liang, Y. Luo, G. D. Çaylı, Construction methods for the smallest and largest uni-nullnorms on bounded lattices, Fuzzy Sets and Systems, Doi: 10.1016/j.fss.2021.02.010.
[40] A. F. Xie, S. J. Li, On constructing the strongest and weakest uninorms on bounded lattices, Fuzzy Sets and Systems, 386 (2020), 95-104.
[41] R. R. Yager, Uninorms in fuzzy systems modeling, Fuzzy Sets and Systems, 122 (2001), 167-175.
[42] R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 180 (1996), 111-120.
[43] H. P. Zhang, Y. Ouyang, B. De Baets, Constructions of uni-nullnorms and null-uninorms on a bounded lattice, Fuzzy Sets and Systems, 403 (2021), 78-87.
[44] T. H. Zhang, F. Qin, On distributive laws between 2-uninorms and overlap (grouping) functions, International Journal of Approximate Reasoning, 119 (2020), 353-372.
[45] H. J. Zhou, X. Liu, Characterizations of (U2, N)-implications generated by 2-uninorms and fuzzy negations from the point of view of material implication, Fuzzy Sets and Systems, 378 (2020), 79-102.
[46] W. 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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