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Keywords:
uninorm; bounded lattice; partial order; equivalence; T-norm
uninorm; bounded lattice; partial order; equivalence; T-norm
Summary:
In this paper, an equivalence on the class of uninorms on a bounded lattice is discussed. Some relationships between the equivalence classes of uninorms and the equivalence classes of their underlying t-norms and t-conorms are presented. Also, a characterization for the sets admitting some incomparability w.r.t. the U-partial order is given.
References:
[1] Aşıcı, E., Karaçal, F.: On the T-partial order and properties. Inform. Sci. 267 (2014), 323-333. DOI 10.1016/j.ins.2014.01.032 | MR 3177320
[2] Baczyński, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing, vol. 231, Springer, Berlin, Heidelberg, 2008. MR 2428086 | Zbl 1293.03012
[3] Birkhoff, G.: Lattice Theory. Third edition. Providence, 1967. DOI 10.1090/coll/025 | MR 0227053
[4] Calvo, T., Mayor, G., Mesiar, R.: Aggregation operators. New Trends and Applications. Studies in Fuzziness and Soft Computing, Physica-Verlag HD, Heidelberg, 2002. DOI 10.1007/978-3-7908-1787-4 | MR 1936384
[5] Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of a class of uninorms with continuous underlying operators. Fuzzy Sets and Systems 287 (2016), 137-153. DOI 10.1016/j.fss.2015.07.015 | MR 3447023
[6] Ertuğrul, U., Kesicioğlu, M. N., Karaçal, F-: Ordering based on uninorms. Inform. Sci. 330 (2016) 315-327. DOI 10.1016/j.ins.2015.10.019
[7] Fodor, J., Yager, R., Rybalov, A.: Structure of uninorm. Int. J. Uncertain. Fuzziness Knowledge-Based Systems 5 (1997), 411-427. DOI 10.1142/s0218488597000312 | MR 1471619
[8] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, 2009. MR 2538324 | Zbl 1206.68299
[9] Hliněná, D., Kalina, M., Král, P.: Pre-orders and orders generated by conjunctive uninorms. In: Inf. Proc. Manage. of Uncert. Knowledge-Based Syst. Communications in Computer and Inf. Sci. 444 (2014), pp. 307-316. MR 3616458
[10] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets and Systems 261 (2015), 33-43. DOI 10.1016/j.fss.2014.05.001 | MR 3291484
[11] Karaçal, F., Kesicioğlu, M. N.: A T-partial order obtained from t-norms. Kybernetika 47 (2011), 300-314. MR 2828579 | Zbl 1245.03086
[12] Kesicioğlu, M. N.: Some notes on the partial orders induced by a uninorm and a nullnorm in a bounded lattice. Fuzzy Sets and Systems 346 (2018), 59-71. DOI 10.1016/j.fss.2014.10.006 | MR 3812757
[13] Kesicioğlu, M. N., Ertuğrul, Ü., Karaçal, F.: An equivalence relation based on the U-partial order. Inform. Sci. 411 (2017), 39-51. DOI 10.1016/j.ins.2017.05.020 | MR 3659313
[14] Kesicioğlu, M. N., Karaçal, F., Mesiar, R.: Order-equivalent triangular norms. Fuzzy Sets and Systems 268 (2015), 59-71. DOI 10.1016/j.fss.2014.10.006 | MR 3320247
[15] Kesicioğlu, M. N., Mesiar, R.: Ordering based on implications. Inform. Sci. 276 (2014), 377-386. DOI 10.1016/j.ins.2013.12.047 | MR 3206505
[16] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. MR 1790096 | Zbl 1087.20041
[17] Lu, J., Wang, K., Zhao, B.: Equivalence relations induced by the U-partial order. Fuzzy Sets and Systems 334 (2018), 73-82. DOI 10.1016/j.fss.2017.07.013 | MR 3742233
[18] Mas, M., Mayor, G., Torrens, J.: The modularity condition for uninorms nd t-operators. Fuzzy Sets and Systems 126 (2002), 207-218. DOI 10.1016/s0165-0114(01)00055-0 | MR 1884687
[19] Mas, M., Massanet, S., Ruiz-Aguilera, D., Torrens, J.: A survey on the existing classes of uninorms. J. Intell. Fuzzy Syst. 29 (2015), 1021-1037. DOI 10.3233/ifs-151728 | MR 3414365
[20] Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets and Systems 157 (2006), 1403-1416. DOI 10.1016/j.fss.2005.12.021 | MR 2226983 | Zbl 1099.06004
[21] Yager, R. R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111-120. DOI 10.1016/0165-0114(95)00133-6 | MR 1389951 | Zbl 0871.04007
[22] Yager, R. R.: Aggregation operators and fuzzy systems modelling. Fuzzy Sets and Systems 67 (1994), 129-145. DOI 10.1016/0165-0114(94)90082-5 | MR 1302575
[23] Yager, R. R.: Uninorms in fuzzy system modelling. Fuzzy Sets and Systems 122 (2001), 167-175. DOI 10.1016/s0165-0114(00)00027-0 | MR 1839955
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