Base and subbase in intuitionistic I-fuzzy topological spaces

In this paper, the concepts of the base and subbase in intuitionistic Ifuzzy topological spaces are introduced, and use them to discuss fuzzycontinuous mapping and fuzzy open mapping. We also study the baseand subbase in the product of intuitionistic I-fuzzy topological spaces,and T2separation in product intuitionistic I-fuzzy topological spaces.Finally, the relation between the generated product intuitionistic Ifuzzy topological spaces and the product generated intuitionistic Ifuzzy topological spaces are studied.

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K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
K.T. Atanassov, Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968), 182-190.
D. C¸ oker, An introduction to intuitionistic fuzzy topological space, Fuzzy Sets and Systems, (1997), 81-89.
D. C¸ oker and M. Demirci, On fuzzy inclusion in the intuitionistic sense, J. Fuzzy Math., (1996), 701-714.
D. C¸ oker and M. Demirci, On intuitionistic fuzzy points, Notes on IFS, 1-2(1995), 79-84.
D. C¸ oker and M. Demirci, An introduction to intuitionistic fuzzy topological space in ? Sostak's sense, Busefal, 67(1996), 61-66.
Jin-ming Fang, I-FTOP is isomorphic to I-FQN and I-AITOP, Fuzzy Sets and Systems (2004), 317-325.
Jin-ming Fang and Yue-li Yue, Base and Subbase in I-fuzzy Topological Spaces, Journal of Mathematical Research and Exposition 26(2006), no 1, 89-95. I.M. Hanafy,
Completely continuous functions in intuitionistic fuzzy topological spaces, Czech Math. J. 53(158)(2003) 793-803.
S.J. Lee and E.P. Lee, On the category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc, 37(2000), 63-76.
F.G. Lupi´a~nez, Quasicoincidence for intuitionistic fuzzy points, Int. J. Math. Math. Sci. (2005), 1539-1542.
F.G. Lupi´a~nez, Covering properties in intuitionistic fuzzy topological spaces, Kybernetes, (2007), 749-753. J.H. Park,
Intuitionistic fuzzy metric spaces , Chaos, Solitons and Fractals, 22(2004), -1046.
A.A. Ramadan, S.E. Abbas and A.A. Abd El-Latif, Compactness in intuitionistic fuzzy topological spaces, Int. J. Math. Math. Sci. 1(2005), 19-32.
U. H¨ohle and S.E. Rodabaugh, eds., Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The handbooks of Fuzzy Sets Series, Volume 3(1999), Kluwer Academic
Publishers (Dordrecht). A. ?Sostak, On a fuzzy topological structure, Rendiconti Circolo Mathematico Palermo (Suppl. Ser. II) 11(1985), 89-103.
Zeshui Xu and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems 35(2006), 417-433.
C.H. Yan and X.K. Wang, Intuitionistic I-fuzzy topological spaces, Czechoslovak Mathe- matical Journal 60(2010), 233-252.
Ming-sheng Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems 9(1991), -321.
Yue-li Yue and Jin-ming Fang, On induced I-fuzzy topological spaces, Journal of Mathe- matical Research and Exposition 25(2005), no 4, 665-670. (in Chinese).