On Fuzzy Topological Spaces Involving Boolean Algebraic Structures
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Authors
P. K. Sharma
- Post Graduate Department of Mathematics, D.A.V. College, Jalandhar city, Punjab, India
Abstract
The notion of fuzzy set was introduced by L.A. Zadeh as a generalization of the notion of classical set or crisp set. Fuzzy topological spaces were introduced by C.L. Chang and studied by many eminent authors like R. Lowen and C.K. Wong. A. Rosenfeld applied the notion of fuzzy set to algebra and introduced fuzzy subgroup of a group. Shaoquan Sun introduced the notion of fuzzy Boolean subalgebra in a Boolean algebra. In this paper, we will study fuzzy topology by involving the Boolean algebraic structure on it and introduce the notion of Boolean algebraic fuzzy topological spaces. We will examine many properties of these spaces and obtain many results.
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ISRP Style
P. K. Sharma, On Fuzzy Topological Spaces Involving Boolean Algebraic Structures, Journal of Mathematics and Computer Science, 15 (2015), no. 4, 252-260
AMA Style
Sharma P. K., On Fuzzy Topological Spaces Involving Boolean Algebraic Structures. J Math Comput SCI-JM. (2015); 15(4):252-260
Chicago/Turabian Style
Sharma, P. K.. "On Fuzzy Topological Spaces Involving Boolean Algebraic Structures." Journal of Mathematics and Computer Science, 15, no. 4 (2015): 252-260
Keywords
- Fuzzy topological space (FTS)
- fuzzy Boolean subalgebra (FBSA)
- Boolean algebraic fuzzy topological space (BAFTS)
- fuzzy point (FP).
MSC
References
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C. L. Chang, Fuzzy Topological Spaces, J. Math. Anal. Appl., 24 (1968), 182–190.
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[2]
R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness, J. Math. Anal. Appl., 56 (1976), 621–633.
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A. Parvathi, K. N. Meenakshi, Fuzzy Topological Boolean Algebras, Indian J. pure appl. Math. , 28(12) (1997), 1639-1648.
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A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971), 512–517.
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Shaoquan Sun, Fuzzy subalgebras and Fuzzy ideals of Boolean algebra, Fuzzy Systems and Mathematics, 20(1) (2006), 90-94.
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Shaoquan Sun, Generalized Fuzzy Subalgebras of Boolean Algebras, Proceedings of the 2009 International Workshop on Information Security and Application (IWISA 2009) Qingdao, November 21-22, China (2009)
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