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Keywords:
uni-nullnorm; bounded lattices; uni-nullnorms; null-norms; uninorms; nullnorms; t-norms
uni-nullnorm; bounded lattices; uni-nullnorms; null-norms; uninorms; nullnorms; t-norms
Summary:
In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice $L$ are given and a contruction method is presented.
References:
[1] P., Akella,: Structure of n-uninorms. Fuzzy Sets Systems 158 (2007), 1631-1651. DOI 10.1016/j.fss.2007.02.015 | MR 2341328
[2] G., Birkhoff,: Lattice Theory. Third edition. Providence, 1967. DOI 10.1090/coll/025 | MR 0227053
[3] S., Bodjanova,, M., Kalina,: Construction of uninorms on bounded lattices. IEEE 12th International Symposium on Intelligent Systems and Informatics (SISY) Book Series: International Symposium on Intelligent Systems and Informatics, 2014, pp. 61-66. DOI 10.1109/sisy.2014.6923558
[4] T., Calvo,, De, Baets, B., J., Fodor,: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets Systems 120 (2001), 385-394. DOI 10.1016/s0165-0114(99)00125-6 | MR 1829256
[5] D., Çaylı, G., Ü., Ertuğrul,, T., Köroğlu,, F., Karaçal,: Notes on locally internal uninorm on bounded lattice. Kybernetika 53 (2017), 5, 911-921. DOI 10.14736/kyb-2017-5-0911 | MR 3750111
[6] D., Çaylı, G., F., Karaçal,: Construction of uninorms on bounded lattices. Kybernetika 53 (2017), 3, 394-417. DOI 10.14736/kyb-2017-3-0394 | MR 3684677
[7] Ü., Ertuğrul,: Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms. Fuzzy Sets Systems 334 (2018), 94-109. DOI 10.1016/j.fss.2017.07.020 | MR 3742235
[8] Ü., Ertuğrul,, N., Kesicioğlu, M., F., Karaçal,: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327. DOI 10.1016/j.ins.2015.10.019
[9] J., Fodor,, R., Yager, R., A., Rybalov,: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 4, 411-427. DOI 10.1142/s0218488597000312 | MR 1471619 | Zbl 1232.03015
[10] M., Grabisch,, J.-L., Marichal,, R., Mesiar,, E., Pap,: Aggregation Functions. Cambridge University Press, 2009. DOI 10.1017/cbo9781139644150 | MR 2538324 | Zbl 1206.68299
[11] F., Karaçal,, Ü., Ertuğrul,, R., Mesiar,: Characterization of uninorms on bounded lattices. Fuzzy Sets Systems 308 (2017), 54-71. DOI 10.1016/j.fss.2016.05.014 | MR 3579154
[12] F., Karaçal,, A., İnce, M., R., Mesiar,: Nullnorms on bounded lattices. Inf. Sci. 325 (2015), 227-236. DOI 10.1016/j.ins.2015.06.052 | MR 3392300
[13] F., Karaçal,, R., Mesiar,: Uninorms on bounded lattices. Fuzzy Sets Systems 261 (2015), 33-43. DOI 10.1016/j.fss.2014.05.001 | MR 3291484
[14] N., Kesicioğlu, M.: Some notes on the partial orders induced by a uninorm and a nullnorm in a bounded lattice. Fuzzy Sets Systems 346 (2018), 55-71. DOI 10.1016/j.fss.2017.08.010 | MR 3812757
[15] N., Kesicioğlu, M., Ü., Ertuğrul,, F., Karaçal,: Some notes on U-partial order. Kybernetika 55 (2019), 3, 518-530. DOI 10.14736/kyb-2019-3-0518 | MR 4015996
[16] P., Klement, E., R., Mesiar,, E., Pap,: On Locally Internal Monotonic Operations. Kluwer Academic Publishers, Dordrecht 2000.
[17] M., Mas,, G., Mayor,, J., Torrens,: t-operators. Int. J. Uncertain. Fuzziness Knowl.-Based Systems 7 (1999), 31-50. DOI 10.1142/s0218488599000039 | MR 1691482 | Zbl 1005.03047
[18] M., Mas,, G., Mayor,, J., Torrens,: The distributivity condition for uninorms and t-operators. Fuzzy Sets Systems 128 (2002), 209-225. DOI 10.1016/S0165-0114(01)00123-3 | MR 1908427 | Zbl 1005.03047
[19] F., Sun,, P., Wang, X., B., Qu, X.: Uni-nullnorms and null-uninorms. J. Intell. Fuzzy Systems 32 (2017), 1969-1981. DOI 10.3233/JIFS-161495
[20] F., Sun,, P., Wang, X., B., Qu, X.: Characterizations of uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms. Fuzzy Sets Systems 334 (2018), 24-35. DOI 10.1016/j.fss.2017.03.001 | MR 3742230
[21] Y.-M., Wang,, W.-H., Liu,: On the distributivity equation for uni-nullnorms. Kybernetika 55 (2019), 1, 24-43. DOI 10.14736/kyb-2019-1-0024 | MR 3935413
[22] G., Wang,, F., Qin,, W.-H., Liu,: Distributivity and conditional distributivity for uni-nullnorms. Fuzzy Sets Systems 372 (2018), 34-49. DOI 10.1016/j.fss.2018.08.008 | MR 3961834
[23] Y.-M., Wang,, H., Zhan,, H.-W., Liu,: Uni-nullnorms on bounded lattices. Fuzzy Sets Systems (2019). MR 4073382
[24] R., Yager, R., A., Rybalov,: Uninorm aggregation operators. Fuzzy Sets Systems 80 (1996), 1, 111-120. DOI 10.1016/0165-0114(95)00133-6 | MR 1389951 | Zbl 0871.04007
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