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Keywords:
t-norm; T-conorm; idempotent uninorm; aggregation; implication function
Summary:
This paper is devoted to the study of implication (and co-implication) functions defined from idempotent uninorms. The expression of these implications, a list of their properties, as well as some particular cases are studied. It is also characterized when these implications satisfy some additional properties specially interesting in the framework of implication functions, like contrapositive symmetry and the exchange principle.
References:
[1] Bustince H., Burillo, P., Soria F.: Automorphisms, negations and implication operators. Fuzzy Sets and Systems 134 (2003), 209–229 DOI 10.1016/S0165-0114(02)00214-2 | MR 1969102
[2] Czogala E., Drewniak J.: Associative monotonic operations in fuzzy set theory. Fuzzy Sets and Systems 12 (1984), 249–269 DOI 10.1016/0165-0114(84)90072-1 | MR 0740097 | Zbl 0555.94027
[3] Baets B. De: An order-theoretic approach to solving sup-T equations. In: Fuzzy Set Theory and Advanced Mathematical Applications (D. Ruan, ed.), Kluwer, Dordrecht 1995, pp. 67–87 Zbl 0874.04005
[4] Baets B. De: Uninorms: the known classes. In: Proc. Third International FLINS Workshop on Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry. World Scientific, Antwerp 1998
[5] Baets B. De: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631–642 DOI 10.1016/S0377-2217(98)00325-7 | Zbl 0933.03071
[6] Baets B. De: Generalized idempotence in fuzzy mathematical morphology. In: Fuzzy Techniques in Image Processing (E. E. Kerre and M. Nachtegael, eds.), Heidelberg 2000, pp. 58–75
[7] Baets B. De, Fodor J. C.: On the structure of uninorms and their residual implicators. In: Proc. 18th Linz Seminar on Fuzzy Set Theory, Linz, Austria 1997, pp. 81–87
[8] Baets B. De, Fodor J. C.: Residual operators of representable uninorms. In: Proc. Fifth European Congress on Intelligent Techniques and Soft Computing, Volume 1 (H.-J. Zimmermann, ed.), ELITE, Aachen 1997, pp. 52–56
[9] Baets B. De, Fodor J. C.: Residual operators of uninorms. Soft Computing 3 (1999), 89–100 DOI 10.1007/s005000050057
[10] Baets B. De, Kwasnikowska, N., Kerre E.: Fuzzy Morphology based on uninorms. In: Proc. Seventh IFSA World Congress, Prague 1997, pp. 215–220
[11] Fodor J. C., Yager R. R., Rybalov A.: Structure of Uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 5 (1997), 411–427 DOI 10.1142/S0218488597000312 | MR 1471619 | Zbl 1232.03015
[12] Fodor J. C.: Contrapositive symmetry on fuzzy implications. Fuzzy Sets and Systems 69 (1995), 141–156 DOI 10.1016/0165-0114(94)00210-X | MR 1317882
[13] González M., Ruiz, D., Torrens J.: Algebraic properties of fuzzy morphological operators based on uninorms. In: Artificial Intelligence Research and Development (I. Aguiló, L. Valverde, and M. T. Escrig, eds.), IOS Press, Amsterdam 2003, pp. 27–38
[14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, London 2000 MR 1790096 | Zbl 1087.20041
[15] Martín J., Mayor, G., Torrens J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137 (2003), 27–42 MR 1992696 | Zbl 1022.03038
[16] Mas M., Monserrat, M., Torrens J.: On left and right uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 9 (2002), 491–507 DOI 10.1142/S0218488501000909 | MR 1852342 | Zbl 1045.03029
[17] Nachtegael M., Kerre E. E.: Classical and fuzzy approaches towards mathematical morphology. In: Fuzzy Techniques in Image Processing (E. E. Kerre and M. Nachtegael, eds.), Heidelberg 2000, pp. 3–57
[18] Ruiz D., Torrens J.: Condición de modularidad para uninormas idempotentes. In: Proc. 11th Estylf, Leon, Spain 2002, pp. 177–182
[19] Ruiz D., Torrens J.: Distributive idempotent uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 11 (2003), 413–428 DOI 10.1142/S0218488503002168 | MR 2007849 | Zbl 1074.03026
[20] Ruiz D., Torrens J.: Residual implications and co–implications from idempotent uninorms. In: Proc. Summer School on Aggregation Operators 2003 (AGOP’2003), Alcalá de Henares, Spain 2003, pp. 149–154 MR 2068596
[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
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