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Aggregation operators from the ancient NC and EM point of view
Kybernetika, Tome 42 (2006) no. 3, pp. 243-260 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper deals with the satisfaction of the well-known Non-Contradiction (NC) and Excluded-Middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a non-standard way, based on self-contradiction (as in Ancient Logic) instead of falsity (as in Modern Logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying the laws w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.
This paper deals with the satisfaction of the well-known Non-Contradiction (NC) and Excluded-Middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a non-standard way, based on self-contradiction (as in Ancient Logic) instead of falsity (as in Modern Logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying the laws w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.
Classification : 03B52, 03E72
Keywords: Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations 
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Pradera, Ana; Trillas, Enric. Aggregation operators from the ancient NC and EM point of view. Kybernetika, Tome 42 (2006) no. 3, pp. 243-260. http://geodesic.mathdoc.fr/item/KYB_2006_42_3_a0/

[1] Bouchon-Meunier B., ed.: Aggregation and Fusion of Imperfect Information. (Studies in Fuzziness and Soft Computing, Vol. 12.), Physica–Verlag, Heidelberg 1998 | MR | Zbl

[2] Calvo T., Baets, B. De, Fodor J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems 120 (2001), 385–394 | MR | Zbl

[3] Calvo T., Mayor, G., Mesiar R., eds: Aggregation Operators: New Trends and Applications. (Studies in Fuzziness and Soft Computing, Vol. 97.) Physica–Verlag, Heidelberg 2002 | MR

[4] Dubois D., Prade H.: A review of fuzzy set aggregation connectives. Information Sciences 36 (1985), 85–121 | DOI | MR | Zbl

[5] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. (Trends in Logic, Vol. 8.) Kluwer Academic Publishers, Dordrecht 2000 | MR | Zbl

[6] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics, Vol. 139.) Springer, New York 1999 | DOI | MR | Zbl

[7] Pradera A., Trillas E.: Aggregation and Non-Contradiction. In: Proc. 4th Conference of the European Society for Fuzzy Logic and Technology and 11th Rencontres Francophones sur la Logique Floue et ses applications, Barcelona 2005, pp. 165–170

[8] Pradera A., Trillas E.: Aggregation, Non-Contradiction and Excluded-Middle. Submitted for publication | Zbl

[9] Trillas E.: Sobre funciones de negación en la teoría de los subconjuntos difusos. Stochastica III-1 (1979) 47–59 (in Spanish). Reprinted (English version) in: Advances of Fuzzy Logic (S. Barro et al., eds.), Universidad de Santiago de Compostela 1998, pp. 31–43 | MR

[10] Trillas E., Alsina, C., Pradera A.: Searching for the roots of Non-Contradiction and Excluded-Middle. Internat. J. General Systems 31 (2002), 499–513 | DOI | MR | Zbl

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