Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
uninorm; representable uninorm; aggregation functions; negation; contradictory information
uninorm; representable uninorm; aggregation functions; negation; contradictory information
Summary:
Uninorms, as binary operations on the unit interval, have been widely applied in information aggregation. The class of almost equitable uninorms appears when the contradictory information is aggregated. It is proved that among various uninorms of which either underlying t-norm or t-conorm is continuous, only the representable uninorms belong to the class of almost equitable uninorms. As a byproduct, a characterization for the class of representable uninorms is obtained.
References:
[1] Bustince, H., Montero, J., Mesiar, R.: Migrativity of aggregation functions. Fuzzy Sets Syst. 160 (2009), 766-777. DOI 10.1016/j.fss.2008.09.018 | MR 2493274 | Zbl 1186.68459
[2] Baets, B. De: Idempotent uninorms. Eur. J. Oper. Res. 118 (1998), 631-642. DOI 10.1016/s0377-2217(98)00325-7 | Zbl 1178.03070
[3] Baets, B. De, Fodor, J.: Residual operators of uninorms. Soft Comput. 3 (1999), 89-100. DOI 10.1007/s005000050057
[4] Baets, B.De, Fodor, J.: Van Melle's combining function in MYCIN is a representable uninorm: An alternative proof. Fuzzy Sets Syst. 104 (1999), 133-136. DOI 10.1016/s0165-0114(98)00265-6 | MR 1685816 | Zbl 0928.03060
[5] Baets, B. De, Kwasnikowska, N., Kerre, E.: Fuzzy morphology based on uninorms. In: Seventh IFSA World Congress, Prague 1997, pp. 215-220.
[6] Hliněná, D., Kalina, M., Král', P.: A class of implications related to Yager's $f-$implications. Information Sciences 260 (2014), 171-184. DOI 10.1016/j.ins.2013.09.045 | MR 3146461
[7] Drygaś, P.: Discussion of the structure of uninorms. Kybernetika 41 (2005), 213-226. MR 2138769 | Zbl 1249.03093
[8] Drygaś, P.: On the structure of continuous uninorms. Kybernetika 43 (2007), 183-196. MR 2343394 | Zbl 1132.03349
[9] 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
[10] Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of uninorms locally internal in $A(e)$ with continuous underlying operators. Fuzzy Sets Syst. (submitted).
[11] Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht 1994. DOI 10.1007/978-94-017-1648-2 | Zbl 0827.90002
[12] Fodor, J., Yager, R. R., Rybalov, A.: Structure of uninorms. Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst. 5 (1997), 411-427. DOI 10.1142/s0218488597000312 | MR 1471619 | Zbl 1232.03015
[13] Fodor, J., Baets, B. De: A single-point characterization of representable uninorms. Fuzzy Sets Syst. 202 (2012), 89-99. DOI 10.1016/j.fss.2011.12.001 | MR 2934788 | Zbl 1268.03027
[14] Gabbay, D. M., Metcalfe, G.: Fuzzy logics based on $[0,1)$-continuous uninorms. Arch. Math. Log. 46 (2007), 425-449. DOI 10.1007/s00153-007-0047-1 | MR 2321585 | Zbl 1128.03015
[15] Li, G., Liu, H.-W.: Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t-conorm. Fuzzy Sets and Systems (2015). DOI 10.1016/j.fss.2015.01.019
[16] Li, G., Liu, H.-W., Fodor, J.: Single-point characterization of uninorms with nilpotent underlying t-norm and t-conorm. Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst. 22 (2014), 591-604. DOI 10.1142/s0218488514500299 | MR 3252143
[17] Hu, S., Li, Z.: The structure of continuous uninorms. Fuzzy Sets Syst. 124 (2001), 43-52. DOI 10.1016/s0165-0114(00)00044-0 | MR 1859776
[18] Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: Migrative uninorms and nullnorms over t-norms and t-conorms. Fuzzy Sets and Syst. 261 (2015), 20-32. DOI 10.1016/j.fss.2014.05.012 | MR 3291483
[19] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. DOI 10.1007/978-94-015-9540-7 | MR 1790096 | Zbl 1087.20041
[20] Petrík, M., Mesiar, R.: On the structure of special classes of uninorms. Fuzzy Sets Syst. 240 (2014), 22-38. DOI 10.1016/j.fss.2013.09.013 | MR 3167510 | Zbl 1315.03099
[21] Pradera, A.: Uninorms and non-contradiction. In: Lecture Notes in Computer Sciences, vol. 5285, (V. Torra and Y. Narukawa, eds.), Springer 2008, pp. 50-61. DOI 10.1007/978-3-540-88269-5_6 | Zbl 1178.68590
[22] Pradera, A., Trillas, E.: Aggregation, non-contradiction and excluded-middle. Mathware Soft Comput. XIII (2006), 189-201. MR 2321602 | Zbl 1122.68128
[23] Pradera, A., Trillas, E.: Aggregation operators from the ancient NC and EM point of view. Kybernetika 42 (2006), 243-260. MR 2253387 | Zbl 1249.03101
[24] Pradera, A., Beliakov, G., Bustince, H.: Aggregation functions and contradictory information. Fuzzy Sets Syst. 191 (2012), 41-61. DOI 10.1016/j.fss.2011.10.007 | MR 2874822 | Zbl 1238.68162
[25] Qin, F., Zhao, B.: The distributive equations for idempotent uninorms and nullnorms. Fuzzy Sets Syst. 155 (2005), 446-458. DOI 10.1016/j.fss.2005.04.010 | MR 2181001 | Zbl 1077.03514
[26] Ruiz, D., Torrens, J.: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm. IEEE Trans. Fuzzy Syst. 14 (2006), 180-190. DOI 10.1109/tfuzz.2005.864087
[27] Ruiz-Aguilera, D., Torrens, J., Baets, B. De, Fodor, J. C.: Some remarks on the characterization of idempotent uninorms. In: IPMU 2010, LNAI 6178 (E. Hüllermeier, R. Kruse and F. Hoffmann, eds.), Springer-Verlag, Berlin - Heidelberg 2010, pp. 425-434. DOI 10.1007/978-3-642-14049-5_44
[28] Ruiz-Aguilera, D., Torrens, J.: S- and R-implications from uninorms continuous in $]0,1[^{2}$ and their distributivity over uninorms. Fuzzy Sets Syst. 160 (2009), 832-852. DOI 10.1016/j.fss.2008.05.015 | MR 2493278 | Zbl 1184.03014
[29] Xie, A., Liu, H.: On the distributivity of uninorms over nullnorms. Fuzzy Sets Syst. 211 (2013), 62-72. DOI 10.1016/j.fss.2012.05.008 | MR 2991797 | Zbl 1279.03047
[30] Yager, R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120. DOI 10.1016/0165-0114(95)00133-6 | MR 1389951 | Zbl 0871.04007
[31] Yager, R., Rybalov, A.: Bipolar aggregation using the Uninorms. Fuzzy Optim. Decis. Making 10 (2011), 59-70. DOI 10.1007/s10700-010-9096-8 | MR 2799503 | Zbl 1304.91068
[32] Yager, R.: Uninorms in fuzzy systems modeling. Fuzzy Sets Syst. 122 (2001), 167-175. DOI 10.1016/s0165-0114(00)00027-0 | MR 1839955 | Zbl 0978.93007
Search
Partner of
