Regular PapersNo Access

SELF-CONTRADICTION AND CONTRADICTION BETWEEN TWO ATANASSOV'S INTUITIONISTIC FUZZY SETS

SUSANA CUBILLO

Department of Applied Mathematics, Technical University of Madrid, 28660 Boadilla del Monte, Madrid, Spain

Search for more papers by this author

CARMEN TORRES

Department of Applied Mathematics, Technical University of Madrid, 28660 Boadilla del Monte, Madrid, Spain

Search for more papers by this author

, and

ELENA CASTIÑEIRA

Department of Applied Mathematics, Technical University of Madrid, 28660 Boadilla del Monte, Madrid, Spain

Search for more papers by this author

https://doi.org/10.1142/S0218488508005297Cited by:10 (Source: Crossref)

Abstract

The paper focuses on the study of the contradiction between two Atanassov's intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction between two Atanassov's intuitionistic fuzzy sets are achieved.

This work is partially supported by CICYT (Spain) under Project TIN 2005-08943-C02-01 and by UPM-CAM (Spain) under Project R05/11240.

Keywords:

References

K. T. Atanassov , Intuitionistic Fuzzy Sets ( Physica-Verlag , Heidelberg, New York , 1999 ) . Crossref, Google Scholar
H. Bustince, J. Kacprzyk and V. Mohedano, Fuzzy Sets and Systems 114, 485 (2000), DOI: 10.1016/S0165-0114(98)00279-6. Crossref, Web of Science, Google Scholar
E. Castiñeira, S. Cubillo and S. Bellido, Degrees of contradiction in fuzzy sets theory, Proceedings IPMU'02 (2002) pp. 171–176. Google Scholar
E. Castiñeira, S. Cubillo and S. Bellido, Contradiction entre dos conjuntos, Actas ESTYLF'02 (2002) pp. 379–383. Google Scholar
E. Castiñeiraet al., Self-contradiction degrees in intuitionistic fuzzy sets, Proceedings of Joint EUSFLAT-LFA 2005 (2005) pp. 455–460. Google Scholar
E. Castiñeira, S. Cubillo and C. Torres, Mathware and Soft Computing (2006). Google Scholar
S. Cubillo and E. Castiñeira, Contradiction in intuitionistic fuzzy sets, Proceedings IPMU'04 (2004) pp. 2180–2186. Google Scholar
G. Deschrijver, C. Cornelis and E. Kerre, Intuitionistic fuzzy connectives revisited, Proceedings IPMU'02 (2002) pp. 1839–1844. Google Scholar
J. A. Goguen, Journal of Mathematical Analysis and Applications 18(1), 623 (1967), DOI: 10.1016/0022-247X(67)90189-8. Web of Science, Google Scholar
E. Trillas, Sobre funciones de negatión en la teoría de conjuntos difusos, Stochastica III/1 (1979) 47-60 (in Spanish). Reprinted (English version) (1998) in Advances of Fuzzy Logic, eds. S. Barro et al., pp. 31-43 (Ed. Universidad de Santiago de Compostela) . Google Scholar
E. Trillas, C. Alsina and J. Jacas, Soft Computing 3(4), 197 (1999). Crossref, Google Scholar
E. Trillas and S. Cubillo, On non-contradictory input/output couples in Zadeh's CRI, Proceedings NAFIPS (1999) pp. 28–32. Google Scholar