| Title of paper:
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Self-contradiction degrees in intuitionistic fuzzy sets
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| Author(s):
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| Elena Castiñeira
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| Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte
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| ecastineira@fi.upm.es
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| Susana Cubillo
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| Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte
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| Carmen Torres
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| Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte
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| Victoria Zarzosa
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| Dept. Matematica Aplicada, Univ. Politecnica de Madrid, 28660 Boadilla del Monte
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| Presented at:
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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.
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| Published in:
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Conference proceedings, pages 455-460
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| Download:
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 PDF (284 Kb, Info)
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| Abstract:
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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.
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| Keywords:
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Intuitionistic fuzzy sets, intuitionistic fuzzy generators and fuzzy negations, degrees of contradiction
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| References:
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- 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.
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| Citations:
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