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Keywords:
bounded lattice; uni-nullnorm; null-uninorm; uninorm; T-norm
bounded lattice; uni-nullnorm; null-uninorm; uninorm; T-norm
Summary:
In this paper, we present the representation for uni-nullnorms with disjunctive underlying uninorms on bounded lattices. It is shown that our method can cover the representation of nullnorms on bounded lattices and some of existing construction methods for uni-nullnorms on bounded lattices. Illustrative examples are presented simultaneously. In addition, the representation of null-uninorms with conjunctive underlying uninorms on bounded lattices is obtained dually.
References:
[1] Akella, P.: Structure of n-uninorms. Fuzzy Sets Syst. 158 (2007), 1631-1651. DOI | MR 2341328
[2] Bedregal, B. C., Santos, H. S., Callejas-Bedregal, R.: T-norms on bounded lattices: t-norm morphisms and operators. In: IEEE International Conference on Fuzzy Systems, 2006. MR 2406220
[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.
[4] Calvo, T., Baets, B. De, Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets Syst. 120 (2001), 385-394. DOI | MR 1829256 | Zbl 0977.03026
[5] Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Inf. Sci. 36 (1985), 85-121. DOI | MR 0813766 | Zbl 0582.03040
[6] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Construction methods for uni-nullnorms and null-uninorms on bounded lattice. Kybernetika 55 (2019), 994-1015. DOI | MR 4077141
[7] Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge 2009. MR 2538324 | Zbl 1206.68299
[8] Karaçal, F., Ince, M. A., Mesiar, R.: Nullnorms on bounded lattices. Inf. Sci. 325 (2015), 227-236. DOI | MR 3392300
[9] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43. DOI | MR 3291484
[10] Menger, K.: Statistical metrics. Proc. Natl. Acad. Sci. USA 28 (1942), 535-537. DOI | MR 0007576 | Zbl 0063.03886
[11] Sun, F., Qu, X. B., Huang, X. J.: Characterizations of residual implications derived from uni-nullnorms. Comput. Appl. Math. 39 (2020), 1-18. DOI | MR 4078434
[12] Sun, F., Wang, X. P., Qu, X. B.: Uni-nullnorms and null-uninorms. J. Intell. Fuzzy Syst. 32 (2017), 1969-1981. DOI
[13] Sun, F., Wang, X. P., Qu, X. B.: Characterizations of uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms. Fuzzy Sets Syst. 334 (2018), 24-35. DOI | MR 3742230
[14] Sun, X. R., Liu, H. W.: Representation of nullnorms on bounded lattices. Inf. Sci. 539 (2020), 269-276. DOI | MR 4117402
[15] Wang, G., Qin, F., Li, W. H.: Distributivity and conditional distributivity for uni-nullnorms. Fuzzy Sets Syst. 372 (2019), 34-49. DOI | MR 3961834
[16] Wang, Y. M., Zhan, H., Liu, H. W.: Uni-nullnorms on bounded lattices. Fuzzy Sets Syst. 386 (2020), 132-144. DOI | MR 4073382
[17] Wang, Y. M., Zhao, Y. Y., Liu, H. W.: Methods for obtaining uni-nullnorms and null-uninorms on bounded lattices. Fuzzy Sets Syst. 441 (2022), 279-285. DOI | MR 4434851
[18] Wu, X., Liang, S., Luo, Y., Çaylı, G. D.: Construction methods for the smallest and largest uni-nullnorms on bounded lattices. Fuzzy Sets Syst. 427 (2022), 132-148. DOI | MR 4343693
[19] Yager, R. R.: Aggregation operators and fuzzy systems modelling. Fuzzy Sets Syst. 67 (1994), 129-145. DOI | MR 1302575
[20] Yager, R. R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120. DOI | MR 1389951 | Zbl 0871.04007
[21] Yager, R. R.: Defending against strategic manipulation in uninorm-based multi-agent decision making. Eur. J. Oper. Res. 141 (2002), 217-232. DOI | MR 1925395 | Zbl 0998.90046
[22] Zhang, H. P., Ouyang, Y., Baets, B. De: Constructions of uni-nullnorms and null-uninorms on a bounded lattice. Fuzzy Sets Syst. 403 (2021), 78-87. DOI | MR 4174509
[23] Zhang, H. P., Ouyang, Y., Wang, Z., Baets, B. De: A complete representation theorem for nullnorms on bounded lattices with ample illustrations. Fuzzy Sets Syst. 439 (2022), 157-169. DOI | MR 4418953
[24] Zhang, T. H., Qin, F., Li, W. H.: On the distributivity equations between uni-nullnorms and overlap (grouping) functions. Fuzzy Sets Syst. 403 (2021), 56-77. DOI | MR 4174508
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