Previous |  Up |  Next


Title: Aggregation operators from the ancient NC and EM point of view (English)
Author: Pradera, Ana
Author: Trillas, Enric
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 42
Issue: 3
Year: 2006
Pages: 243-260
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Non-Contradiction and Excluded-Middle principles
Keyword: aggregation operators
Keyword: strong negations
MSC: 03B52
MSC: 03E72
idZBL: Zbl 1249.03101
idMR: MR2253387
Date available: 2009-09-24T20:15:37Z
Last updated: 2015-03-28
Stable URL:
Reference: [1] Bouchon-Meunier B., ed.: Aggregation and Fusion of Imperfect Information.(Studies in Fuzziness and Soft Computing, Vol. 12.), Physica–Verlag, Heidelberg 1998 Zbl 0886.00008, MR 1644801
Reference: [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 Zbl 0977.03026, MR 1829256
Reference: [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
Reference: [4] Dubois D., Prade H.: A review of fuzzy set aggregation connectives.Information Sciences 36 (1985), 85–121 Zbl 0582.03040, MR 0813766, 10.1016/0020-0255(85)90027-1
Reference: [5] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.(Trends in Logic, Vol. 8.) Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096
Reference: [6] Nelsen R. B.: An Introduction to Copulas.(Lecture Notes in Statistics, Vol. 139.) Springer, New York 1999 Zbl 1152.62030, MR 1653203, 10.1007/978-1-4757-3076-0
Reference: [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
Reference: [8] Pradera A., Trillas E.: Aggregation, Non-Contradiction and Excluded-Middle.Submitted for publication Zbl 1122.68128
Reference: [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
Reference: [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 Zbl 1019.03049, MR 1934706, 10.1080/0308107021000042462
Reference: [11] Yager R. R., Rybalov A.: Uninorm aggregation operators.Fuzzy Sets and Systems 80 (1996), 111–120 Zbl 0871.04007, MR 1389951, 10.1016/0165-0114(95)00133-6


Files Size Format View
Kybernetika_42-2006-3_1.pdf 697.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo