Issue:Self-contradiction degrees in intuitionistic fuzzy sets - Revision history

Vassia Atanassova at 13:30, 22 July 2010

2010-07-22T13:30:52Z

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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.		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		\| keywords = [[Intuitionistic fuzzy sets]], intuitionistic fuzzy generators and fuzzy negations, degrees of contradiction
	\| references =		\| references =
	# Atanassov, K.T. (1999) “[[Intuitionistic Fuzzy Sets: Theory and Applications\|Intuitionistic fuzzy sets]]”, (Physica-Verlag, Heidelberg, New York).		# Atanassov, K.T. (1999) “[[Intuitionistic Fuzzy Sets: Theory and Applications\|Intuitionistic fuzzy sets]]”, (Physica-Verlag, Heidelberg, New York).

Vassia Atanassova at 13:27, 22 July 2010

2010-07-22T13:27:11Z

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	\| conference = ~~3rd~~ Conference of the [[European Society for Fuzzy Logic and Technology]], ~~Zittau~~, ~~Germany~~, September 10-12, ~~2003~~		\| conference = 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.
	\| issue = Conference proceedings, pages ~~164~~-~~167~~		\| issue = Conference proceedings, pages 455-460
	\| file = EUSFLAT-2005-455-460.pdf		\| file = EUSFLAT-2005-455-460.pdf
	\| format = PDF		\| format = PDF

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
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[[Category:Publications in 2005 year|{{PAGENAME}}]]
{{issue/title
| title = Self-contradiction degrees in intuitionistic fuzzy sets
| shortcut = eusflat-2005-455-460
}}
{{issue/author
| author = Elena Castiñeira
| institution = Dept. Matematica Aplicada, Univ. Politecnica de Madrid
| address = 28660 Boadilla del Monte
| email-before-at = ecastineira
| email-after-at = fi.upm.es
}}
{{issue/author
| author = Susana Cubillo
| institution = Dept. Matematica Aplicada, Univ. Politecnica de Madrid
| address = 28660 Boadilla del Monte
| email-before-at =
| email-after-at =
}}
{{issue/author
| author = Carmen Torres
| institution = Dept. Matematica Aplicada, Univ. Politecnica de Madrid
| address = 28660 Boadilla del Monte
| email-before-at =
| email-after-at =
}}
{{issue/author
| author = Victoria Zarzosa
| institution = Dept. Matematica Aplicada, Univ. Politecnica de Madrid
| address = 28660 Boadilla del Monte
| email-before-at =
| email-after-at =
}}
{{issue/data
| conference = 3rd Conference of the [[European Society for Fuzzy Logic and Technology]], Zittau, Germany, September 10-12, 2003
| issue = Conference proceedings, pages 164-167
| file = EUSFLAT-2005-455-460.pdf
| format = PDF
| size = 284
| 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: Theory and Applications|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 =
| see-also =
}}