Issue:Self-contradiction degrees in intuitionistic fuzzy sets

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http://ifigenia.org/wiki/issue:eusflat-2005-455-460

Title of paper: Self-contradiction degrees in intuitionistic fuzzy sets Author(s): Elena Castiñeira Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte ecastineira@fi.upm.es Susana Cubillo Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte Carmen Torres Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte Victoria Zarzosa Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte Presented at: Joint 4th Conference of the European Society for Fuzzy Logic and Technology and the 11th Rencontres Francophones sur la Logique Floue et ses Applications, Barcelona, Spain, September 7-9, 2005. Published in: Conference proceedings, pages 455-460 Download:  PDF (284  Kb, File info) Abstract: This paper is an attempt to model to what extent an intuitionistic fuzzy set is self-contradictory, both in the case of self-contradiction regarding a strong intuitionistic negation, and without depending on a specific negation. For this purpose, firstly, a geometrical study on self-contradiction regarding a negation is considered; afterwards some functions to measure degrees of self-contradictory depending on a negation are defined. Finally, the degree of self-contradiction independently of any negation is dealt with other functions, and in both cases some properties are found. Keywords: Intuitionistic fuzzy sets, intuitionistic fuzzy generators and fuzzy negations, degrees of contradiction References: Atanassov, K.T. (1999) “Intuitionistic fuzzy sets”, (Physica-Verlag, Heidelberg, New York). Bustince, H., Kacprzyk, J. and Mohedano, V. (2000) “Intuitionistic fuzzy generators - Application to intuitionistic fuzzy complementation”, Fuzzy Sets and Systems 114, 485-504. Casti˜neira, E., Cubillo, S. and Bellido, S. (2002) “Degrees of Contradiction in Fuzzy Sets Theory”, Proceedings IPMU’02, Annecy (France), 171-176. Castiñeira, E., Cubillo, S. and Bellido, S. (2002) “Contradiccion entre dos conjuntos”, Actas ESTYLF’02, Le´on (Spain), 379-383 (in Spanish). Cubillo, S., Castiñeira, E. (2004) “Contradiciton in Intuitionistic Fuzzy Sets”, Proceedings IPMU’04, Perugia (Italy), 2180-2186. Deschrijver, G., Cornelis, C. and Kerre, E. (2002), “Intuitionistic fuzzy connectives revisited”, Proceedings IPMU’02, 1839-1844. Goguen, J.A. (1967) “L-Fuzzy Sets”, Journal of Mathematical Analysis and Applications 18(1), 623-668. Trillas, E. (1979) “Sobre funciones de negacion en la teoria de conjuntos difusos”, Stochastica III/1, 47-60 (in Spanish). Reprinted (English version) (1998) in Avances of Fuzzy Logic (eds. S. Barro et altri), 31-43 (Ed. Universidad de Santiago de Compostela). Trillas, E., Alsina, C. and Jacas, J. (1999), “On Contradiction in Fuzzy Logic”, Soft Computing, 3(4), 197-199. Trillas, E. and Cubillo, S. (1999), “On Non-Contradictory Input/Output Couples in Zadeh’s CRI”, Proceedings NAFIPS, 28-32, New York. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.