About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 260457, 11 pages
http://dx.doi.org/10.1155/2012/260457
Research Article

Generalized Caratheodory Extension Theorem on Fuzzy Measure Space

Department of Mathematics, Faculty of Arts and Sciences, University of Gaziantep, 27310 Gaziantep, Turkey

Received 23 April 2012; Revised 28 June 2012; Accepted 10 October 2012

Academic Editor: Alberto D'Onofrio

Copyright © 2012 Mehmet Şahin 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. A. H. Q. A. Al-Tai, “On the fuzzy convergence,” Journal of Applied Mathematics, vol. 2011, Article ID 147130, 8 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. S. Alkhazaleh and A. R. Salleh, “Fuzzy soft multiset theory,” Abstract and Applied Analysis, vol. 2012, Article ID 350603, 20 pages, 2012. View at Publisher · View at Google Scholar
  3. A. A. L. Sangalli, “Lattices of fuzzy objects,” International Journal of Mathematics and Mathematical Sciences, vol. 19, no. 4, pp. 759–766, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. B. Ahmad and A. Kharal, “On fuzzy soft sets,” Advances in Fuzzy Systems, vol. 2009, Article ID 586507, 6 pages, 2009. View at Zentralblatt MATH
  5. B. Ahmad and A. Kharal, “Fuzzy sets, fuzzy S-open and S-closed mappings,” Advances in Fuzzy Systems, vol. 2009, Article ID 303042, 5 pages, 2009. View at Zentralblatt MATH
  6. B. T. Bilalov, S. Farahani, and F. A. Guliyeva, “The intuitionistic fuzzy normed space of coefficients,” Abstract and Applied Analysis, vol. 2012, Article ID 969313, 11 pages, 2012. View at Publisher · View at Google Scholar
  7. S. K. Elegan and D. Baleanu, “Set-valued fixed-point theorem for generalized contractive mapping on fuzzy metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 832807, 7 pages, 2012. View at Publisher · View at Google Scholar
  8. F. Polat, “The centre of the spaces of Banach lattice-valued continuous functions on the generalized Alexandroff duplicate,” Abstract and Applied Analysis, vol. 2011, Article ID 604931, 5 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. F.-G. Shi, “(L,M)-fuzzy σ-algebras,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 356581, 11 pages, 2010. View at Publisher · View at Google Scholar
  10. G. Zhang, “Some theorems on fuzzy number valued fuzzy measure and fuzzy number valued fuzzy measure space,” in Proceedings of the 5th Conference of fuzzy Mathematics and system society of China, pp. 78–81, Chengdu, China, 1990.
  11. G. Q. Zhang, “Fuzzy number valued fuzzy measure and Fuzzy number valued fuzzy integral on the -fuzzy sets,” Chinese Quaterly Journal of Mathematics, vol. 6, no. 2, 1991.
  12. G. Q. Zhang, “Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set,” Fuzzy Sets and Systems, vol. 49, no. 3, pp. 357–376, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. Tanaka and P. F. Mcloughlin, “Construction of a lattice on the completion space of an algebra and an isomorphism to its Carathéodory extension,” Far East Journal of Mathematical Sciences, vol. 43, no. 2, pp. 153–164, 2010.
  14. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Zentralblatt MATH
  15. L. A. Zadeh, “Calculus of fuzzy restrictions,” in Fuzzy Sets and Their Applications to Cognitive and Decision Processes, L. A. Zadeh, K. S. Fu, K. Tanaka, and M. Shimura, Eds., pp. 1–39, Academic Press, New York, NY, USA, 1975. View at Zentralblatt MATH
  16. M. Sahin, Generalized σ-algebras and Generalizedfuzzy Measures [Ph.D. thesis], Trabzon, Turkey, 2004.
  17. M. Şahin, “Generalized fuzzy sets,” Proceedings of the Jangjeon Mathematical Society, vol. 8, no. 2, pp. 153–158, 2005. View at Zentralblatt MATH
  18. M. Sahin and Z. Yapar, “Measure in generalized fuzzy sets,” Far East Journal of Mathematical Sciences, vol. 24, no. 2, pp. 217–226, 2007. View at Zentralblatt MATH
  19. N. Nakajima, “Generalized fuzzy sets,” Fuzzy Sets and Systems, vol. 32, no. 3, pp. 307–314, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. F. Zheng and X. Lian, “Common fixed point theorems for commutating mappings in fuzzy metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 729758, 5 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Z. Y. Wang and G. J. Klir, Fuzzy Measure Theory, Springer, 1993.
  22. A. Mukherjea and K. Pothoven, Real and Functional Analysis, Part A Real Analysis, vol. 27, Plenum Press, New York, NY, USA, 1984.
  23. A. W. Knapp, Advanced Real Analysis: Along with a Companion Volume Basic Real Analysis, 2005.
  24. L. Xuecheng and Z. Guangquan, “Lattice-valued fuzzy measure and lattice-valued fuzzy integral,” Fuzzy Sets and Systems, vol. 62, no. 3, pp. 319–332, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. Şahin, “On Carathedory extension theorem on fuzzy measure spaces,” Far East Journal of Mathematical Sciences, vol. 26, no. 2, pp. 311–317, 2007.
  26. G. Birkhoff, Lattice Theory, AMS Colloquim Publications, Providence, RI, USA, 3rd edition, 1967.
  27. G. Grätzer, General Lattice Theory, 1978.
  28. J. Tanaka, “Hahn decomposition theorem of signed fuzzy measure,” Advances in Fuzzy Sets and Systems, vol. 3, no. 3, pp. 315–323, 2008. View at Zentralblatt MATH
  29. M. Sahin and M. Demir, “Lattice valued caratheodory extension theorem,” Archives des Sciences, vol. 65, no. 7, pp. 89–106, 2012.