Previous |  Up |  Next

Article

Title: Intuitionistic $I$-fuzzy topological spaces (English)
Author: Yan, Cong-hua
Author: Wang, Xiao-ke
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 1
Year: 2010
Pages: 233-252
Summary lang: English
.
Category: math
.
Summary: The main purpose of this paper is to introduce the concept of intuitionistic ${\rm I}$-fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic $I$-fuzzy topological spaces and the category of intuitionistic $I$-fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic $I$-fuzzy topology is proposed, and the connections among generated intuitionistic $I$-fuzzy topological spaces, fuzzifying topological spaces and $I$-fuzzy topological spaces are discussed. Finally, the properties of the operators ${\rm I}\omega $, $\iota $ are obtained. (English)
Keyword: intuitionistic $I$-fuzzy topological space
Keyword: intuitionistic fuzzy point
Keyword: intuitionistic $I$-fuzzy quasi-coincident neighborhood space
Keyword: fuzzifying topology
Keyword: $I$-fuzzy topology
MSC: 54A40
MSC: 54E15
idZBL: Zbl 1224.54022
idMR: MR2595086
.
Date available: 2010-07-20T16:32:11Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/140565
.
Reference: [1] Atanassov, K. T.: Intuitionistic fuzzy sets.Fuzzy Sets Syst. 20 (1986), 87-96. Zbl 0631.03040, MR 0852871
Reference: [2] Atanassov, K. T.: Intuitionistic Fuzzy Sets.Springer Heidelberg (1999). Zbl 0939.03057, MR 1718470
Reference: [3] Birkhoff, G.: Lattice Theory (third revised edition).Am. Math. Soc. Colloquium Pub. 25 Providence (1967). MR 0227053
Reference: [4] Chang, C. L.: Fuzzy topological spaces.J. Math. Anal. Appl. 24 (1968), 182-190. Zbl 0167.51001, MR 0236859, 10.1016/0022-247X(68)90057-7
Reference: [5] Çoker, D.: An introduction to intuitionistic fuzzy topological space.Fuzzy Sets Syst. 88 (1997), 81-89. MR 1449497
Reference: [6] Çoker, D., Demirci, M.: On intuitionistic fuzzy points.Notes IFS 1-2 (1995), 79-84. MR 1417217
Reference: [7] Çoker, D., Demirci, M.: An introduction to intuitionistic fuzzy topological space in Šostak's sense.BUSEFAL 67 (1996), 61-66.
Reference: [8] Çoker, D., Demirci, M.: On fuzzy inclusion in the intuitionistic sense.J. Fuzzy Math. 4 (1996), 701-714. MR 1410641
Reference: [9] Hanafy, I. M.: Completely continuous functions in intuitionistic fuzzy topological spaces.Czech Math. J. 53(158) (2003), 793-803. Zbl 1080.54503, MR 2018831, 10.1023/B:CMAJ.0000024523.64828.31
Reference: [10] Höhle, U., Rodabaugh, S. E., eds.: Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory. The Handbooks of Fuzzy Sets Series, Vol. 3.Kluwer Academic Publishers Dordrecht (1999). MR 1788899
Reference: [11] Fang, Jin-ming: $I$-FTOP is isomorphic to $I$-{\bf FQN} and $I$-{\bf AITOP}.Fuzzy Sets Syst. 147 (2004), 317-325. MR 2089295
Reference: [12] Fang, Jinming, Yue, Yueli: Base and subbase in $I$-fuzzy topological spaces.J. Math. Res. Expo. 26 (2006), 89-95. Zbl 1101.54005
Reference: [13] Lee, S. J., Lee, E. P.: On the category of intuitionistic fuzzy topological spaces.Bull. Korean Math. Soc. 37 (2000), 63-76. MR 1752195
Reference: [14] Lupiáñez, F. G.: Quasicoincidence for intuitionistic fuzzy points.Int. J. Math. Math. Sci. 10 (2005), 1539-1542. MR 2177859, 10.1155/IJMMS.2005.1539
Reference: [15] Lupiáñez, F. G.: Covering properties in intuitionistic fuzzy topological spaces.Kybernetes 36 (2007), 749-753. MR 2371364, 10.1108/03684920710749811
Reference: [16] Park, J. H.: Intuitionistic fuzzy metric spaces.Chaos Solitons Fractals 22 (2004), 1039-1046. Zbl 1060.54010, MR 2078831, 10.1016/j.chaos.2004.02.051
Reference: [17] Ramadan, A. A., Abbas, S. E., El-Latif, A. A. Abd: Compactness in intuitionistic fuzzy topological spaces.Int. J. Math. Math. Sci. 1 (2005), 19-32. MR 2146013
Reference: [18] Rodabaugh, S. E.: Powerset operator foundations for Poslat fuzzy set theories and topologies.Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory. The handbooks of Fuzzy Sets Series, Vol. 3 Kluwer Academic Publishers Dordrecht (1999), 91-116. Zbl 0974.03047, MR 1788901
Reference: [19] Šostak, A.: On a fuzzy topological structure.Rend. Circ. Math. Palermo (Suppl. Ser. II) 11 (1985), 89-103. MR 0897975
Reference: [20] Xu, Zeshui, Yager, R. R.: Some geometric aggregation operators based on intuitionistic fuzzy sets.Int. J. Gen. Syst. 35 (2006), 417-433. Zbl 1113.54003, MR 2243887, 10.1080/03081070600574353
Reference: [21] Ying, Ming-sheng: A new approach for fuzzy topology (I).Fuzzy Sets Syst. 9 (1991), 303-321. MR 1095905
Reference: [22] Yue, Yue-li, Fang, Jin-ming: On induced $I$-fuzzy topological spaces.J. Math. Res. Exp. 25 (2005), 665-670 Chinese. MR 2184241
.

Files

Files Size Format View
CzechMathJ_60-2010-1_20.pdf 281.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo