On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I-continuity
Year 2010,
Volume: 5 Issue: 1, 147 - 153, 27.06.2010
Şaziye Yüksel
,
Eser Çaylak
Ahu Açıkgöz
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.
References
- Zadeh L.A., 1965. Fuzzy sets, Inform Control, 8: 338-53.
- Chang C.L., 1968. Fuzzy topological spaces, Jourmal Mathematic Analysis Applied, 24: 182-90.
- Lowen R., 1976. Fuzzy topological spaces and fuzzy compactness, Journal Mathematic Analysis Applied, 56: 621-633.
- Kuratowski K., 1966. Topology, Vol. 1, Academic Press, New York, USA, p. 309.
- Vaidyanathaswamy R., 1960. Set Topology, Chelsea Publishing Company, New York, USA, p.135.
- Vaidyanathaswamy R., 1945. The localization theory in set topology, Proceedings of the Indian Academy of Sciences, 20: 51-61.
- Janković D., Hamlett T.R., 1990. New topologies from old via ideals, American Mathematic Monthly, 97 (4): 295-310.
- 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.
- Açıkgöz A., Noiri T., Yüksel Ş., 2004. A decomposition of continuity in ideal topological spaces, Acta Mathematica Hungaria, 105 (4): 285-289.
- Açıkgöz A., Noiri T., Yüksel Ş., 2004. On α-I-continuous and α-I-open functions, Acta Mathematica Hungaria, 105 (1-2): 27-37.
- Sarkar D., 1997. Fuzzy ideal theory, fuzzy local function and generated fuzzy topology, Fuzzy Sets and Systems, 87: 117-23.
- Mahmoud R.A., 1997. Fuzzy ideals, fuzzy local functions and fuzzy topology, Journal Fuzzy Mathematic Los Angels, 5 (1): 165-172.
- Nasef A.A., Mahmoud R.A., 2002. Some topological applications via fuzzy ideals, Chaos, Solitons & Fractals, 13: 825-831.
- 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.
- Wong C.K., 1974. Fuzzy points and local properties of fuzzy topology, Journal Mathematic Analysis Applied, 46: 316-28.
- 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.
- Chankraborty M.K., Ahsanullah T.M.G., 1991. Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems, 45: 189-97.
- 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.
- Hatır E., Jafari S., 2007. Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization, Chaos, Solitans & Fractals, 34: 1220-1224.
- Eser Gürsel Çaylak e-mail: esergursel@mynet.com
- Ahu Açıkgöz e-mail: ahuacikgoz@aksaray.edu.tr
Bulanık Delta-I-Açık Kümeler ve Bulanık Alfa-I-Sürekliliğin Dağılımı Üzerine
Year 2010,
Volume: 5 Issue: 1, 147 - 153, 27.06.2010
Şaziye Yüksel
,
Eser Çaylak
Ahu Açıkgöz
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.
References
- Zadeh L.A., 1965. Fuzzy sets, Inform Control, 8: 338-53.
- Chang C.L., 1968. Fuzzy topological spaces, Jourmal Mathematic Analysis Applied, 24: 182-90.
- Lowen R., 1976. Fuzzy topological spaces and fuzzy compactness, Journal Mathematic Analysis Applied, 56: 621-633.
- Kuratowski K., 1966. Topology, Vol. 1, Academic Press, New York, USA, p. 309.
- Vaidyanathaswamy R., 1960. Set Topology, Chelsea Publishing Company, New York, USA, p.135.
- Vaidyanathaswamy R., 1945. The localization theory in set topology, Proceedings of the Indian Academy of Sciences, 20: 51-61.
- Janković D., Hamlett T.R., 1990. New topologies from old via ideals, American Mathematic Monthly, 97 (4): 295-310.
- 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.
- Açıkgöz A., Noiri T., Yüksel Ş., 2004. A decomposition of continuity in ideal topological spaces, Acta Mathematica Hungaria, 105 (4): 285-289.
- Açıkgöz A., Noiri T., Yüksel Ş., 2004. On α-I-continuous and α-I-open functions, Acta Mathematica Hungaria, 105 (1-2): 27-37.
- Sarkar D., 1997. Fuzzy ideal theory, fuzzy local function and generated fuzzy topology, Fuzzy Sets and Systems, 87: 117-23.
- Mahmoud R.A., 1997. Fuzzy ideals, fuzzy local functions and fuzzy topology, Journal Fuzzy Mathematic Los Angels, 5 (1): 165-172.
- Nasef A.A., Mahmoud R.A., 2002. Some topological applications via fuzzy ideals, Chaos, Solitons & Fractals, 13: 825-831.
- 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.
- Wong C.K., 1974. Fuzzy points and local properties of fuzzy topology, Journal Mathematic Analysis Applied, 46: 316-28.
- 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.
- Chankraborty M.K., Ahsanullah T.M.G., 1991. Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems, 45: 189-97.
- 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.
- Hatır E., Jafari S., 2007. Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization, Chaos, Solitans & Fractals, 34: 1220-1224.
- Eser Gürsel Çaylak e-mail: esergursel@mynet.com
- Ahu Açıkgöz e-mail: ahuacikgoz@aksaray.edu.tr