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International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 580918, 38 pages
http://dx.doi.org/10.1155/2009/580918
Research Article

A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

1Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroon
2Laboratoire de Mathématiques Appliquées aux Sciences Sociales, Département de Mathématiques, Faculté des Sciences, Université de Yaoundé I, B.P. 15396 Yaoundé, Cameroon
3MRSH, University of Caen, CREM-UMR 6211, CNRS, 14032 Caen Cedex, France
4Department of Mathematics, National Polytechnic Institute, P.O. Box 8390, Yaoundé, Cameroon

Received 3 July 2008; Revised 24 December 2008; Accepted 15 June 2009

Academic Editor: Andrzej Skowron

Copyright © 2009 Louis Aimé Fono et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. De Baets, E. Kerre, and B. Van de Walle, “Fuzzy preference structures and their characterization,” Journal of Fuzzy Mathematics, vol. 3, no. 2, pp. 373–381, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Dutta, “Fuzzy preferences and social choice,” Mathematical Social Sciences, vol. 13, no. 3, pp. 215–229, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
  5. L. A. Fono, H. Gwet, and S. Fotso, “On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication,” Fuzzy Sets and Systems, vol. 159, no. 17, pp. 2240–2255, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. A. Fono and N. G. Andjiga, “Utility function of fuzzy preferences on a countable set under max--transitivity,” Social Choice and Welfare, vol. 28, no. 4, pp. 667–683, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. A. Fono and N. G. Andjiga, “Fuzzy strict preference and social choice,” Fuzzy Sets and Systems, vol. 155, no. 3, pp. 372–389, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. A. Fono, Relation binaire floue et application au choix social, Thése de Doctorat, Département de Mathématiques, Faculté de Sciences, Université de Yaoundé I, Yaoundé, Cameroon, 2004.
  9. L. A. Fono and H. Gwet, “On strict lower and upper sections of fuzzy orderings,” Fuzzy Sets and Systems, vol. 139, no. 3, pp. 583–599, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Richardson, “The structure of fuzzy preferences: social choice implications,” Social Choice and Welfare, vol. 15, no. 3, pp. 359–369, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Salles, “Fuzzy Utility,” in Handbook of Utility Theory, Principles, vol. 1, pp. 321–344, Kluwer Academic Publishers, Boston, Mass, USA, 1998. View at Google Scholar
  12. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. T. Atanassov and S. Stoeva, “Intuitionistic fuzzy sets,” in Proceedings of the Polish Symposium on Interval and Fuzzy Mathematics, Poznan, Poland, 1983.
  14. H. Bustince, “Construction of intuitionistic fuzzy relations with predetermined properties,” Fuzzy Sets and Systems, vol. 109, no. 3, pp. 379–403, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Bustince and P. Burillo, “Structures on intuitionistic fuzzy relations,” Fuzzy Sets and Systems, vol. 78, no. 3, pp. 293–303, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Deschrijver and E. E. Kerre, “On the composition of intuitionistic fuzzy relations,” Fuzzy Sets and Systems, vol. 136, no. 3, pp. 333–361, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Dimitrov, “The Paretian liberal with intuitionistic fuzzy preferences: a result,” Social Choice and Welfare, vol. 23, no. 1, pp. 149–156, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. Dimitrov, “Intuitionistic fuzzy preferences: a factorization,” Advanced Studies in Contemporary Mathematics, vol. 5, no. 1, pp. 93–104, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Z. Xu, “Intuitionistic preference relations and their application in group decision making,” Information Sciences, vol. 177, no. 11, pp. 2363–2379, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  20. C. Cornelis, G. Deschrijver, and E. E. Kerre, “Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application,” International Journal of Approximate Reasoning, vol. 35, no. 1, pp. 55–95, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. L. A. Fono, H. Gwet, and B. Bouchon-Meunier, “Fuzzy implications operators for difference operations for fuzzy sets and cardinality-based measures of comparaison,” European Journal of Operational Research, vol. 183, pp. 314–326, 2008. View at Publisher · View at Google Scholar
  22. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norms, vol. 8 of Trends in Logic—Studia Logica Library, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. View at MathSciNet
  23. B. De Baets, “Coimplicators, the forgotten connectives,” Tatra Mountains Mathematical Publications, vol. 12, pp. 229–240, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet