Document Type : Research Paper


Department of Mathematics and Computer Science, Faculty of Sciences Dhar El mahraz, Sidi Mohamed Ben Abdellah University, B.P. 1769-Atlas Fez, Morocco.


This paper studies the concept of fuzzy generalized topologies, which are generalizations of smooth topologies and Chang's fuzzy topologies. A basis of fuzzy generalized topological space will be defined as functions from the family of all fuzzy subsets of a non-empty set $ X $ to $ [0, 1] $ and  some basic properties of their structure will be obtained. Some characterizations of  the basis of fuzzy generalized topology, fuzzy generalized cotopology and the product of fuzzy generalized topological spaces will also be shown.


Main Subjects

[1] K.K. Azad, Fuzzy hausdorff spaces and fuzzy perfect mappings, Journal of mathematical analysis and applications, 82 (2) (1981), pp. 297-305.
[2] R. Belohlávek, Fuzzy closure operators, Journal of mathematical analysis and applications, 262 (2) (2001), pp. 473-489.
[3] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182-190.
[4] K.C. Chattopadhyay, R.N. Hazra and S.K. Samanta, Gradation of openness: fuzzy topology, Fuzzy sets and Systems, 49 (2) (1992), pp. 237-242.
[5] N.R. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and systems, 107 (3) (1999), pp. 349-354.
[6] R.N. Hazra, S.K. Samanta and K.C. Chattopadhyay, Fuzzy topology redefined, Fuzzy sets and Systems, 45 (1) (1992), pp. 79-82.
[7] C. Kalaivani, Fuzzy proper functions, Diss. Ph. D. Thesis. Alagappa University, Karaikudi-630 004, India, (2012).
[8] C. Kalaivani and R. Roopkumar, Fuzzy perfect mappings and qcompactness in smooth fuzzy topological spaces, Fuzzy Information and Engineering, 6 (1) (2014), pp. 115-131.
[9] A. Mhemdi, The category of soft topological spaces and the T0- reflection, Journal of Mathematics and Computer Science, 22 (1) (2021), pp. 1-8.
[10] W.K. Min, Fuzzy generalized topological spaces, Journal of the Korean Institute of Intelligent Systems, 19 (3) (2009), pp. 404-407.
[11] D. Molodtsov, Soft set theory-first results, Computers & mathematics with applications, 37 (4-5) (1999), pp. 19-31.
[12] P. Mukherjee and C. Park, On fuzzy soft bitopological spaces, Mathematicas and Computer Sciences Journal, 10 (7) (2015), pp. 2-9.
[13] C.K. Park, W.K. Min and M.H. Kim, Weak smooth α-structure of smooth topological spaces, Communications of the Korean Mathematical Society, 19 (1) (2004), pp. 143-153.
[14] W. Peeters, Subspaces of smooth fuzzy topologies and initial smooth fuzzy structures, Fuzzy sets and Systems, 104 (3) (1999), pp. 423-433.
[15] A.A. Ramadan, Smooth topological spaces, Fuzzy sets and Systems, 48 (3) (1992), pp. 371-375.
[16] A.F. Sayed, On characterizations of some types of fuzzy soft sets in fuzzy soft bitopological spaces, Journal of Advances in Mathematics and Computer Science, 24 (3) (2017), pp. 1-12.
[17] A.F. Sayed, Some separation axioms in fuzzy soft bitopological spaces, J. Math. Comput. Sci., 8 (1) (2017), pp. 28-45.
[18] A.F. Sayed, On fuzzy soft b-open sets in fuzzy soft bitopological space, Journal of Mathematics and Computer Science, 21 (2020), pp. 31-44.
[19] M. Shakthiganesan and R. Vembu, On the product of smooth fuzzy topological spaces, Novi Sad J. Math, 46 (2) (2016), pp. 13-31.
[20] R. Srivastava, On separation axioms in a newly defined fuzzy topology, Fuzzy sets and systems, 62 (3) (1994), pp. 341-346.
[21] S.S. Thakura, C.P. Rathorb and M. Thakura, Generalized e-closed sets and generalized e-continuity in intuitionistic fuzzy topology, Journal of Mathematics and Computer Science, 25 (3) (2022), pp. 219-231.