| Title of paper:
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Approximations of crisp set and intuitionistic fuzzy set based on intuitionistic fuzzy normal subgroup
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| Author(s):
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| Prasenjit Mandal
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| Bhalukdungri Jr High School, Raigara, Purulia (W.B.), 723153, India
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| prasenjitmandal08@yahoo.com
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| A. S. Ranadive
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| Department of Pure and Applied Mathematics, Guru Ghasidas University, Bilaspur (C.G.), India
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| asranadive04@yahoo.co.in
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 23, 2017, Number 4, pages 91—105
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| Download:
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 PDF (157 Kb Kb, File info)
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| Abstract:
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We consider a group G, with identity element e, as a universal set and assume that the knowledge about objects is restricted by an intuitionistic fuzzy normal subgroup [math]\displaystyle{ A=(\mu_A,\nu_A) }[/math] of G. For each α, β ∈ [0, 1] such that α + β ≤ 1, the set [math]\displaystyle{ U (A, \alpha, \beta) = U (\mu_A , \alpha) \cap U (\nu_A, \beta) }[/math] is a congruence relation on G, where [math]\displaystyle{ U (\mu_A , \alpha) = \{ (x,y) \in G \times G: \mu_A(xy^{-1}) \geq \alpha \} }[/math] and [math]\displaystyle{ U (\nu_A , \beta) = \{ (x,y) \in G \times G: \nu_A(xy^{-1}) \leq \beta \} }[/math]. In this paper, the notion of U (A, α, β)-lower and U (A, α, β)-upper approximation of a non-empty subset of G and an intuitionistic fuzzy set of G are introduced and some important properties of the above approximations are presented.
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| Keywords:
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Rough set, Fuzzy set, Intuitionistic fuzzy set, Intuitionistic fuzzy normal subgroup, Congruence relation, Lower and Upper approximations of crisp and fuzzy sets.
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| AMS Classification:
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03E72, 06F35, 08A72, 03E99.
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