ISSN ONLINE(2319-8753)PRINT(2347-6710)
Madhulika Shukla Associate professor, Department of Applied Mathematics, GGITS Engineering College, Jabalpur (M.P.) India |
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We define and characterize a fuzzy pairwise strongly pre-continuous mappings on a fuzzy bitopological space. We investigate some of their properties. We establish some equivalent conditions of fuzzy pairwise strongly precontinuous mappings on a fuzzy bitopological space.
Keywords |
(τi, τj)-fuzzy preopen, (τi, τj)-fuzzy preclosed, (τi, τj)-fuzzy semi-open, (τi, τj)-fuzzy semi-closed, (τi, τj)- fuzzy pairwise precontinuous, (τi, τj) -fuzzy pairwise semicontinuous, (τi, τj) -fuzzy pairwise stongly pre-continuous, (τi, τj)-fuzzy pairwise strongly preclosed. |
INTRODUCTION |
In 1981, K.K. Azad [4] introduced the concept of semi-open sets in fuzzy topology. A.S. Bin Shahana [1] has defined the concept of fuzzy pre-open sets in fuzzy topological spaces. |
In 1989, A. Kandil [5] introduced the notation of fuzzy bitopological space. Further in 1996, S.S. Thakur and R. Malviya [9] defined fuzzy semi-open and fuzzy semi-continuous in fuzzy bitopological space. Sampath kumar [10] defined a (τi, τj)-fuzzy pre-open set and characterized a fuzzy pairwise precontinuous mappings on a fuzzy bitopological space. Further M. Shrivastava, J.K.m maitra And M. Shukla [7] in 2006 defined fuzzy strongly pre-continuous mapping in fuzzy topological space |
In this article we have established equivalent conditions for a mapping to be fuzzy pairwise strongly pre-continuous mapping in fuzzy bitopological space. Further we have studied some properties of fuzzy pairwise pre-continuous mapping. |
PRELIMINARIES |
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FUZZY PAIRWISE STRONGLY PRE-CONTINUOUS MAPPINGS |
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Concluding remark: |
1. We have introduced and studied new kind of map fuzzy pairwise Strongly pr-econtinuos maps on fuzzy bitopological spaces. |
2. We defined the relation between fuzzy pairwise pre continuous and fuzzy pairwise strongly continuous map. We investigated some of their properties. |
3. We proved that the fuzzy pairwise storgly pre-continuous map is stronger form of fuzzy paqairwise pre-continuous map by use of example. |
4. We have established some significant properties of fuzzy pairwise strogly pre-continuous maps. |
5. We introduce and study new kind of fuzzy pairwise strongly pre-closed and investigate of their properties. |
References |
1. A. S. Bin Shahana, On fuzzy strong semi-continuity and fuzzy pre continuity, Fuzzy Sets and Systems, 44 (1991), 303-308.
2. C. L. Chang ., Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182-190. 3. H.S. Lee, J.S. Lee and Y.B. Im, Fuzzy pairwise strong pre-irresolute continuous mappings. J. Appl. Math & Informatics. 28(2010), 1561-1571. 4. K.K. Azad ., On fuzzy semi continuity, fuzzy almost continuity and fuzzy weak continuity. J. Math. Anal. Appl. 82 (1981), 14-32. 5. Kandil, Biproximities and fuzzy bitopological spaces, Simon Stevin. 63(1989) 45-66. 6. L. A. Zadeh , Fuzzy Sets, Inform. And control, 8 (1965), 338-353. 7. M. Shrivastava . J.K. Maitra J.K. and M. Shukla., On fuzzy strongly pre continuous mappings, VISLESANA, 10-B (2) (2006), 109-117. 8. M. Shukla , Fuzzy pairwise strongly -continuois mapping in J. Comp. & Maths. Sci. Vol. 3, No.6, (2012), pp 631-636. 9. S. S. Thakur and R. Malviya., Semi-open sets and semi-continuity in fuzzy bitopological spaces. Fuzzy Sets and Systems. 79 (1996) 251-256. 10. S. Sampath kumar . On fuzzy pairwise -continuous and fuzzy pairwise pre-continuity. Fuzzy Sets and Systems. 62 (1994), 231-238. |