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On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity

Year 2011, Volume: 24 Issue: 4, 731 - 738, 21.01.2011

Cemil Yıldız , Fadhil Abbas

Abstract

 The concepts of fuzzy regular-I-closed set and fuzzy semi-I-regular set in fuzzy ideal topological spaces are investigated and some of their properties are obtained.

Keywords

Topological Spaces Fuzzy Regular Sets

References

  • Zadeh L. A., “Fuzzy sets”, Inform. And control, 8: 338-353, (1965).
  • Yüksel S., Gürsel Caylak E. , Acikgöz A. , “On Fuzzy α -I-continuous and fuzzy α -I-open functions”, Chaos, Solitons &Fractals, 41: 1691- 1696 (2009).
  • Nasef A. A. , Mahmoud R. A. , “Some topological applications via fuzzy ideals”, Chaos, Solitons & Fractals, 13: 825-831 (2002).
  • Yalvac T. H., “Fuzzy sets and functions on fuzzy spaces”, Journal of Mathematical Analysis and Applications, 126(2): 409-423 (1987).
  • Wong C. K.,. “Fuzzy points and local properties of fuzzy topology”, Journal of Mathematical Analysis and Applications, 46: 316-328 (1974).
  • Vaidyannathaswamy R, “The localization theory in set topology”, Proceedings of the Indian National Science Academy, (20): 51-61 (1945).
  • Sarkar D, “Fuzzy ideal theory, fuzzy local function and generated fuzzy topology”, Fuzzy Sets and Systems, 87: 117-123 (1997).
  • Nasef A. A., Hatir E, “On fuzzy pre-I-open sets and a decomposition of fuzzy-I-continuity”, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.08.073 (2007).
  • Azad K. K, “On fuzzy semi continuity, fuzzy almost continuity”, Journal of Mathematical Analysis and Applications, 82: 14-23 (1981).
  • Bin Shahana A. S., “On fuzzy strong semi continuity and fuzzy pre continuity”, Fuzzy Sets and Systems, 44: 303-308 (1991).
  • Chankraborty M. K., Ahsanullah T. M. G., “Fuzzy topology on fuzzy sets and tolerance topology”, Fuzzy Sets and Systems, 45: 189-97 (1991).
  • Chang C, “Fuzzy topological spaces”, Journal of Mathematical Analysis and Applications, 24: 182- 9 (1968).
  • Hatir E, Jafari S, “Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization”, Chaos, Solitons & Fractals, 34: 1220-1224 (2007).
  • Jankovic D, Hamlet T. R., “New topologies from old via ideals”, The American Mathematical Monthly, 97(4): 295-310 (1990).
  • Lowen R., “Fuzzy topological spaces and fuzzy compactness”, Journal of Mathematical Analysis and Applications, 56: 621-633 (1976).
  • Kuratowski K., “Topology”, Vol.1 (transl.) Academic Press, New York (1966).

Year 2011, Volume: 24 Issue: 4, 731 - 738, 21.01.2011

Cemil Yıldız , Fadhil Abbas

Abstract

References

  • Zadeh L. A., “Fuzzy sets”, Inform. And control, 8: 338-353, (1965).
  • Yüksel S., Gürsel Caylak E. , Acikgöz A. , “On Fuzzy α -I-continuous and fuzzy α -I-open functions”, Chaos, Solitons &Fractals, 41: 1691- 1696 (2009).
  • Nasef A. A. , Mahmoud R. A. , “Some topological applications via fuzzy ideals”, Chaos, Solitons & Fractals, 13: 825-831 (2002).
  • Yalvac T. H., “Fuzzy sets and functions on fuzzy spaces”, Journal of Mathematical Analysis and Applications, 126(2): 409-423 (1987).
  • Wong C. K.,. “Fuzzy points and local properties of fuzzy topology”, Journal of Mathematical Analysis and Applications, 46: 316-328 (1974).
  • Vaidyannathaswamy R, “The localization theory in set topology”, Proceedings of the Indian National Science Academy, (20): 51-61 (1945).
  • Sarkar D, “Fuzzy ideal theory, fuzzy local function and generated fuzzy topology”, Fuzzy Sets and Systems, 87: 117-123 (1997).
  • Nasef A. A., Hatir E, “On fuzzy pre-I-open sets and a decomposition of fuzzy-I-continuity”, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.08.073 (2007).
  • Azad K. K, “On fuzzy semi continuity, fuzzy almost continuity”, Journal of Mathematical Analysis and Applications, 82: 14-23 (1981).
  • Bin Shahana A. S., “On fuzzy strong semi continuity and fuzzy pre continuity”, Fuzzy Sets and Systems, 44: 303-308 (1991).
  • Chankraborty M. K., Ahsanullah T. M. G., “Fuzzy topology on fuzzy sets and tolerance topology”, Fuzzy Sets and Systems, 45: 189-97 (1991).
  • Chang C, “Fuzzy topological spaces”, Journal of Mathematical Analysis and Applications, 24: 182- 9 (1968).
  • Hatir E, Jafari S, “Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization”, Chaos, Solitons & Fractals, 34: 1220-1224 (2007).
  • Jankovic D, Hamlet T. R., “New topologies from old via ideals”, The American Mathematical Monthly, 97(4): 295-310 (1990).
  • Lowen R., “Fuzzy topological spaces and fuzzy compactness”, Journal of Mathematical Analysis and Applications, 56: 621-633 (1976).
  • Kuratowski K., “Topology”, Vol.1 (transl.) Academic Press, New York (1966).
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Cemil Yıldız

Fadhil Abbas

Publication Date January 21, 2011
Published in Issue Year 2011 Volume: 24 Issue: 4

Cite

APA Yıldız, C., & Abbas, F. (2011). On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity. Gazi University Journal of Science, 24(4), 731-738.
AMA Yıldız C, Abbas F. On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity. Gazi University Journal of Science. December 2011;24(4):731-738.
Chicago Yıldız, Cemil, and Fadhil Abbas. “On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity”. Gazi University Journal of Science 24, no. 4 (December 2011): 731-38.
EndNote Yıldız C, Abbas F (December 1, 2011) On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity. Gazi University Journal of Science 24 4 731–738.
IEEE C. Yıldız and F. Abbas, “On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity”, Gazi University Journal of Science, vol. 24, no. 4, pp. 731–738, 2011.
ISNAD Yıldız, Cemil - Abbas, Fadhil. “On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity”. Gazi University Journal of Science 24/4 (December 2011), 731-738.
JAMA Yıldız C, Abbas F. On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity. Gazi University Journal of Science. 2011;24:731–738.
MLA Yıldız, Cemil and Fadhil Abbas. “On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity”. Gazi University Journal of Science, vol. 24, no. 4, 2011, pp. 731-8.
Vancouver Yıldız C, Abbas F. On Fuzzy Regular-I-Closed Sets, Fuzzy Semi-I-Regular Sets, Fuzzy ABI-Sets and Decompositions of Fuzzy Regular-I-Continuity, Fuzzy AI - Continuity. Gazi University Journal of Science. 2011;24(4):731-8.