Previous |  Up |  Next


Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations
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.
[1] Bouchon-Meunier B., ed.: Aggregation and Fusion of Imperfect Information. (Studies in Fuzziness and Soft Computing, Vol. 12.), Physica–Verlag, Heidelberg 1998 MR 1644801 | Zbl 0886.00008
[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 1829256 | Zbl 0977.03026
[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 1936383
[4] Dubois D., Prade H.: A review of fuzzy set aggregation connectives. Information Sciences 36 (1985), 85–121 DOI 10.1016/0020-0255(85)90027-1 | MR 0813766 | Zbl 0582.03040
[5] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. (Trends in Logic, Vol. 8.) Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[6] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics, Vol. 139.) Springer, New York 1999 DOI 10.1007/978-1-4757-3076-0 | MR 1653203 | Zbl 1152.62030
[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 1122.68128
[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 0562440
[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 10.1080/0308107021000042462 | MR 1934706 | Zbl 1019.03049
[11] 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
Partner of
EuDML logo