Aggregation operators from the ancient NC and EM point of view

Ana Pradera; Enric Trillas

Kybernetika (2006)

  • Volume: 42, Issue: 3, page 243-260
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Pradera, Ana, and Trillas, Enric. "Aggregation operators from the ancient NC and EM point of view." Kybernetika 42.3 (2006): 243-260. <http://eudml.org/doc/33803>.

@article{Pradera2006,
abstract = {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.},
author = {Pradera, Ana, Trillas, Enric},
journal = {Kybernetika},
keywords = {Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations; non-contradiction principle; excluded-middle principle; aggregation operator; strong negation},
language = {eng},
number = {3},
pages = {243-260},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Aggregation operators from the ancient NC and EM point of view},
url = {http://eudml.org/doc/33803},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Pradera, Ana
AU - Trillas, Enric
TI - Aggregation operators from the ancient NC and EM point of view
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 3
SP - 243
EP - 260
AB - 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.
LA - eng
KW - Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations; non-contradiction principle; excluded-middle principle; aggregation operator; strong negation
UR - http://eudml.org/doc/33803
ER -

References

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  1. Bouchon-Meunier B., ed., Aggregation and Fusion of Imperfect Information, (Studies in Fuzziness and Soft Computing, Vol. 12.), Physica–Verlag, Heidelberg 1998 Zbl0886.00008MR1644801
  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 Zbl0977.03026MR1829256
  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 MR1936383
  4. Dubois D., Prade H., 10.1016/0020-0255(85)90027-1, Information Sciences 36 (1985), 85–121 (1985) Zbl0582.03040MR0813766DOI10.1016/0020-0255(85)90027-1
  5. Klement E. P., Mesiar, R., Pap E., Triangular Norms, (Trends in Logic, Vol. 8.) Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  6. Nelsen R. B., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics, Vol. 139.) Springer, New York 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
  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 Zbl1122.68128
  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 (1979) MR0562440
  10. Trillas E., Alsina, C., Pradera A., 10.1080/0308107021000042462, Internat. J. General Systems 31 (2002), 499–513 Zbl1019.03049MR1934706DOI10.1080/0308107021000042462
  11. Yager R. R., Rybalov A., 10.1016/0165-0114(95)00133-6, Fuzzy Sets and Systems 80 (1996), 111–120 (1996) Zbl0871.04007MR1389951DOI10.1016/0165-0114(95)00133-6

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