On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I-continuity

Abstract

We introduce the notions of fuzzy δ-I-open sets and fuzzy semi δ-I-continuos functions in fuzzy ideal topological space and investigate some of their properties. Additionaly, we obtain decompositions of fuzzy semi-I-continuous functions and fuzzy α-I-continuous functions by using fuzzy δ-I-open sets. 

Keywords

• Fuzzy δ-I-open sets,fuzzy semi δ-I-continuity,fuzzy α-I-continuity

Bulanık Delta-I-Açık Kümeler ve Bulanık Alfa-I-Sürekliliğin Dağılımı Üzerine

Abstract

Bulanık ideal topolojik uzaylarda bulanık delta-I-açık küme ve bulanık yarı delta-I-sürekli fonksiyon kavramlarını tanımladık ve bunların bazı özelliklerini araştırdık. Ayrıca, bulanık delta-I-açık kümeleri kullanarak bulanık alfa-I-sürekli ve bulanık yarı-I-sürekli fonksiyonların ayrışımını elde ettik.

Keywords

• Bulanık delta-I-açık kümeler, bulanık yarı delta-I-süreklilik, bulanık alfa-I- süreklilik

References

1. Zadeh L.A., 1965. Fuzzy sets, Inform Control, 8: 338-53.
2. Chang C.L., 1968. Fuzzy topological spaces, Jourmal Mathematic Analysis Applied, 24: 182-90.
3. Lowen R., 1976. Fuzzy topological spaces and fuzzy compactness, Journal Mathematic Analysis Applied, 56: 621-633.
4. Kuratowski K., 1966. Topology, Vol. 1, Academic Press, New York, USA, p. 309.
5. Vaidyanathaswamy R., 1960. Set Topology, Chelsea Publishing Company, New York, USA, p.135.
6. Vaidyanathaswamy R., 1945. The localization theory in set topology, Proceedings of the Indian Academy of Sciences, 20: 51-61.
7. Janković D., Hamlett T.R., 1990. New topologies from old via ideals, American Mathematic Monthly, 97 (4): 295-310.
8. Açıkgöz A., Yüksel Ş., 2007. Some new sets and decompositions of AI-R continuity, α-I-continuity, continuity via idealization, Acta Mathematica Hungaria, 114: 79-89.

9. Açıkgöz A., Noiri T., Yüksel Ş., 2004. A decomposition of continuity in ideal topological spaces, Acta Mathematica Hungaria, 105 (4): 285-289.
10. Açıkgöz A., Noiri T., Yüksel Ş., 2004. On α-I-continuous and α-I-open functions, Acta Mathematica Hungaria, 105 (1-2): 27-37.
11. Sarkar D., 1997. Fuzzy ideal theory, fuzzy local function and generated fuzzy topology, Fuzzy Sets and Systems, 87: 117-23.
12. Mahmoud R.A., 1997. Fuzzy ideals, fuzzy local functions and fuzzy topology, Journal Fuzzy Mathematic Los Angels, 5 (1): 165-172.
13. Nasef A.A., Mahmoud R.A., 2002. Some topological applications via fuzzy ideals, Chaos, Solitons & Fractals, 13: 825-831.
14. Nasef A.A., Hatır E., 2009. On fuzzy pre-I-open sets and a decomposition of fuzzy I-continuity, Chaos, Solitons & Fractals, 40: 1185-1189.
15. Wong C.K., 1974. Fuzzy points and local properties of fuzzy topology, Journal Mathematic Analysis Applied, 46: 316-28.
16. Pau P.M., Liu Y.M., 1980. Fuzzy topology I, neighbourhood structure of a fuzzy point and Moore- Smith convergence, Journal Mathematic Analysis Applied, 76 (2): 571-599.
17. Chankraborty M.K., Ahsanullah T.M.G., 1991. Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems, 45: 189-97.
18. Yüksel Ş., Gürsel Çaylak E., Açıkgöz A., 2009. On fuzzy α-I-continuous and fuzzy α-I-open functions, Chaos, Solitons and Fractal, 41: 1691-1696.
19. Hatır E., Jafari S., 2007. Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization, Chaos, Solitans & Fractals, 34: 1220-1224.
20. Eser Gürsel Çaylak e-mail: [e-mail]
21. Ahu Açıkgöz e-mail: [e-mail]