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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 3 | Year 2017 | Article Id. IJMTT-V43P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P529

Second Order Fuzzy Uniform Structures


A.Kalaichelvi
Abstract

In this paper the definition of fuzzy uniformity introduced by Hutton, B. [4] is extended to the second order case. Given a first order fuzzy uniform structure (Hutton [4]) U on a set X, a second order fuzzy uniform structure U ˆ on X is constructed. Every second order fuzzy uniformity U ˆ induces a second order fuzzy topology U ). ˆ ( ˆ  It is proved that the associations U  U ˆ and U ˆ  U ) ˆ ( ˆ  are functorial.

Keywords
Fuzzy uniformity, second order Hfuzzy uniformity, second order H-uniformly continuous
References

[1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., Vol. 24 pp. 182-190, 1968.
[2] George J. Klir and Tina A. Folger, Fuzzy sets, uncertainty and informations. Prentice-Hall of India Private Limited, New Delhi, 1994.
[3] George J. Klir and Bo Yuan, Fuzzy sets and fuzzy logic : Theory and Applications, Prentice Hall of India Private Limited, New Delhi, 1997.
[4] B. Hutton, Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., Vol. 58, pp. 559-571, 1977.
[5] A. Kalaichelvi, Second order fuzzy topological space s- I, Acta Ciencia Indica, Vol. XXXIII M, No. 3, pp. 819-826, 2007.
[6] A. Kalaichelvi, Second order fuzzy topological spaces – II, International Journal of Mathematical Sciences and Applications, Vol. 1, No. 2, pp. 551-560, May 2011.
[7] A. Kalaichelvi, Second order fuzzy topological spaces – III, International Journal of Mathematical Sciences and Applications, Vol. 1, No. 2, pp. 625-633, May 2011.
[8] L.A. Zadeh, Fuzzy sets, Information and Control, Vol. 8, pp. 338- 353, 1965.

Citation :

A.Kalaichelvi, "Second Order Fuzzy Uniform Structures," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 3, pp. 238-241, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P529

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