Previous |  Up |  Next

Article

Keywords:
bounded lattice; uninorm; idempotent uninorm; locally internal
Summary:
In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.
References:
[1] Aşıcı, E., Karaçal, F.: Incomparability with respect to the triangular order. Kybernetika 52 (2016), 15-27. DOI 10.14736/kyb-2016-1-0015 | MR 3482608
[2] Birkhoff, G.: Lattice Theory. American Mathematical Society Colloquium Publ., Providence 1967. DOI 10.1090/coll/025 | MR 0227053 | Zbl 0537.06001
[3] Baets, B. De: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631-642. DOI 10.1016/s0377-2217(98)00325-7 | Zbl 1178.03070
[4] Baets, B. De, Fodor, J.: A single-point characterization of representable uninorms. Fuzzy Sets Syst. 202 (2012), 89-99. DOI 10.1016/j.fss.2011.12.001 | MR 2934788
[5] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices. Inform. Sci. 367-368 (2016), 221-231. DOI 10.1016/j.ins.2016.05.036 | MR 3684677
[6] Çaylı, G. D., Drygaś, P.: Some properties of idempotent uninorms on bounded lattices. Inform. Sci. 422 (2018), 352-363. DOI 10.1016/j.ins.2017.09.018 | MR 3709474
[7] Drewniak, J., Drygaś, P.: On a class of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10 (2002), 5-10. DOI 10.1142/s021848850200179x | MR 1962665
[8] Drygaś, P.: On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums. Fuzzy Sets Syst. 161 (2010), 149-157. DOI 10.1016/j.fss.2009.09.017 | MR 2566236 | Zbl 1191.03039
[9] Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of uninorms locally internal in $A(e)$ with continuous underlying operators. Fuzzy Sets Syst. 287 (2016), 137-153. DOI 10.1016/j.fss.2009.09.017 | MR 3447023
[10] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327. DOI 10.1016/j.ins.2015.10.019
[11] Fodor, J., Yager, R. R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. DOI 10.1142/s0218488597000312 | MR 1471619 | Zbl 1232.03015
[12] Kesicioğlu, M. N., Mesiar, R.: Ordering based on implications. Fuzzy Sets Syst. 276 (2014), 377-386. DOI 10.1016/j.ins.2013.12.047 | MR 3206505
[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] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43. DOI 10.1016/j.fss.2014.05.001 | MR 3291484
[15] Karaçal, F., Ertuğrul, Ü., Mesiar, R.: Characterization of uninorms on bounded lattices. Fuzzy Sets Syst. 308 (2017), 54-71. DOI 10.1016/j.fss.2016.05.014 | MR 3579154
[16] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Dordrecht, Kluwer Acad. Publ., 2000. DOI 10.1007/978-94-015-9540-7 | MR 1790096 | Zbl 1087.20041
[17] Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets Syst. 137 (2003), 27-42. DOI 10.1016/s0165-0114(02)00430-x | MR 1992696 | Zbl 1022.03038
[18] Mesiarová-Zemánková, A.: Multi-polar t-conorms and uninorms. Inform. Sci. 301 (2015), 227-240. DOI 10.1016/j.ins.2014.12.060 | MR 3311790
[19] Yager, R. R.: Uninorms in fuzzy system modeling. Fuzzy Sets Syst. 122 (2001), 167-175. DOI 10.1016/s0165-0114(00)00027-0 | MR 1839955
[20] Yager, R. R.: Defending against strategic manipulation in uninorm-based multi-agent decision making. European J. Oper. Res. 141 (2002), 217-232. DOI 10.1016/s0377-2217(01)00267-3 | MR 1925395 | Zbl 0998.90046
[21] Yager, R. R., Rybalov, A.: Uninorms aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120. DOI 10.1016/0165-0114(95)00133-6 | MR 1389951
Partner of
EuDML logo