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Residual implications and co-implications from idempotent uninorms
Kybernetika, Tome 40 (2004) no. 1, pp. 21-38 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03B52, 06F05, 94D05
Keywords: t-norm; T-conorm; idempotent uninorm; aggregation; implication function 
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Ruiz, Daniel; Torrens, Joan. Residual implications and co-implications from idempotent uninorms. Kybernetika, Tome 40 (2004) no. 1, pp. 21-38. http://geodesic.mathdoc.fr/item/KYB_2004_40_1_a2/

[1] Bustince H., Burillo, P., Soria F.: Automorphisms, negations and implication operators. Fuzzy Sets and Systems 134 (2003), 209–229 | DOI | MR

[2] Czogala E., Drewniak J.: Associative monotonic operations in fuzzy set theory. Fuzzy Sets and Systems 12 (1984), 249–269 | DOI | MR | Zbl

[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

[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 | Zbl

[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] 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 | MR | Zbl

[12] Fodor J. C.: Contrapositive symmetry on fuzzy implications. Fuzzy Sets and Systems 69 (1995), 141–156 | DOI | MR

[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 | Zbl

[15] Martín J., Mayor, G., Torrens J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137 (2003), 27–42 | MR | Zbl

[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 | MR | Zbl

[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 | MR | Zbl

[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

[21] Yager R. R., Rybalov A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111–120 | DOI | MR | Zbl