CONTINUITY OF FUZZY PROPER FUNCTIONS ON SOSTAK`S I-FUZZY TOPOLOGICAL SPACES

- Journal title : Communications of the Korean Mathematical Society
- Volume 26, Issue 2, 2011, pp.305-320
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2011.26.2.305

Title & Authors

CONTINUITY OF FUZZY PROPER FUNCTIONS ON SOSTAK`S I-FUZZY TOPOLOGICAL SPACES

Roopkumar, Rajakumar; Kalaivani, Chandran;

Roopkumar, Rajakumar; Kalaivani, Chandran;

Abstract

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of ostak`s I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.

Keywords

fuzzy proper function;ostak`s I-fuzzy topology;smooth fuzzy continuity;

Language

English

Cited by

References

1.

H. Aygun and S. E. Abbas, Some good extensions of compactness in Sostak's L-fuzzy topology, Hacet. J. Math. Stat. 36 (2007), no. 2, 115-125.

2.

M. K. Chakraborty and T. M. G. Ahsanullah, Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems 45 (1992), no. 1, 103-108.

4.

A. K. Chaudhuri and P. Das, Some results on fuzzy topology on fuzzy sets, Fuzzy Sets and Systems 56 (1993), no. 3, 331-336.

5.

M. Demirci, Neighborhood structures of smooth topological spaces, Fuzzy Sets and Systems 92 (1997), no. 1, 123-128.

6.

M. Demirci, Three topological structures of smooth topological spaces, Fuzzy Sets and Systems 101 (1999), no. 1, 185-190.

7.

M. Demirci, On several types of compactness in smooth topological spaces, Fuzzy Sets and Systems 90 (1997), no. 1, 83-88.

8.

M. K. El Gayyar, E. E. Kerre, and A. A. Ramadan, Almost compactness and near compactness in smooth topological spaces, Fuzzy Sets and Systems 62 (1994), no. 2, 193-202.

9.

M. A. Fath Alla and F. S. Mahmoud, Fuzzy topology on fuzzy sets: functions with fuzzy closed graphs and strong fuzzy closed graphs, J. Fuzzy Math. 9 (2001), no. 3, 525-533.

10.

S. Ganguly and S. Saha, A note on compactness in a fuzzy setting, Fuzzy Sets and Systems 34 (1990), no. 1, 117-124.

11.

R. N. Hazra and S. K. Samanta, and K. C. Chattopadhyay, Fuzzy topology redefined, Fuzzy Sets and Systems 45 (1992), no. 1, 79-82.

12.

R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56 (1976), no. 3, 621-633.

13.

R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl. 64 (1978), no. 2, 446-454.

15.

P. P. Ming and L. Y. Ming, Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), no. 2, 571-599.

16.

P. P. Ming and L. Y. Ming, Fuzzy topology, II. Product and quotient spaces, J. Math. Anal. Appl. 77 (1980), no. 1, 20-37.

17.

W. Peeters, Subspaces of smooth fuzzy topologies and initial smooth fuzzy structures, Fuzzy Sets and Systems 104 (1999), no. 3, 423-433.

18.

A. A. Ramadan, M. A. Fath Alla, and S. E. Abbas, Smooth Fuzzy topology on fuzzy sets, J. Fuzzy Math. 10 (2002), no. 1, 59-68.

19.

A. P. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (2) Suppl. No. 11 (1985), 89-103.

20.

A. P. Sostak, On some modification of fuzzy topologies, Mat. Vesnik 41 (1989), no. 1, 51-64.

21.

R. Srivastava, On separation axioms in a newly defined fuzzy topology, Fuzzy Sets and Systems 62 (1994), no. 3, 341-346.

22.

R. Srivastava, S. N. Lal, and A. K. Srivastava, Fuzzy Hausdorff topological spaces, J. Math. Anal. Appl. 81 (1981), no. 2, 497-506.

23.

R. Srivastava, S. N. Lal, and A. K. Srivastava, Fuzzy $T_1$ -topological spaces, J. Math. Anal. Appl. 102 (1984), no. 2, 442-448.