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| For any Intuitionistic fuzzy set <math>A = {<x, \mu_A(x), \nu_A(x) | x \in E>}</math> of a set <math>E</math>, we define a <math>(\alpha, \beta)</math>-cut of <math>A</math> as the crisp subset <math>x \in E | \mu_A(x) \ge \alpha, \nu_A(x) \le \beta}</math> of <math>E</math>. In this paper some interesting properties of <math>(\alpha, \beta)</math>-cut of [[Intuitionistic fuzzy ideal]]s of a ring were discussed. | | For any Intuitionistic fuzzy set <math>A = {<x, \mu_A(x), \nu_A(x) | x \in E>}</math> of a set <math>E</math>, we define a <math>(\alpha, \beta)</math>-cut of <math>A</math> as the crisp subset <math>\{ x \in E | \mu_A(x) \geq \alpha, \nu_A(x) \leq \beta \}</math> of <math>E</math>. In this paper some interesting properties of <math>(\alpha, \beta)</math>-cut of [[Intuitionistic fuzzy ideal]]s of a ring were discussed. |
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| | keywords = [[Intuitionistic fuzzy set]], Intuitionistic fuzzy ideal, (α,β)-cut | | | keywords = [[Intuitionistic fuzzy set]], Intuitionistic fuzzy ideal, (α,β)-cut |
Revision as of 12:00, 30 May 2016
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http://ifigenia.org/wiki/issue:nifs/16/3/22-27
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| Title of paper:
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(α,β)-cut of intuitionistic fuzzy ideals
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| Author(s):
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| Dhiren Kumar Basnet
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| Department of Mathematics, Assam University, Silchar-788011, Assam, India
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| dkbasnet@rediffmail.com
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| Published in:
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"Notes on IFS", Volume 16 (2010) Number 3, pages 22—27
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| Download:
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 PDF (161 Kb, File info)
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| Abstract:
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For any Intuitionistic fuzzy set [math]\displaystyle{ A = {\lt x, \mu_A(x), \nu_A(x) | x \in E\gt } }[/math] of a set [math]\displaystyle{ E }[/math], we define a [math]\displaystyle{ (\alpha, \beta) }[/math]-cut of [math]\displaystyle{ A }[/math] as the crisp subset [math]\displaystyle{ \{ x \in E | \mu_A(x) \geq \alpha, \nu_A(x) \leq \beta \} }[/math] of [math]\displaystyle{ E }[/math]. In this paper some interesting properties of [math]\displaystyle{ (\alpha, \beta) }[/math]-cut of Intuitionistic fuzzy ideals of a ring were discussed.
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| Keywords:
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Intuitionistic fuzzy set, Intuitionistic fuzzy ideal, (α,β)-cut
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| References:
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- Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy sets and systems, 20 (1986), no. 1, 87–96.
- Banerjee B. and Basnet. D. K., “Intuitionistic Fuzzy Subrings and Ideals”, J. of Fuzzy Mathematics, Vol. 11, No. 1, 2003 , 139 – 155.
- Basnet D. K., “Intuitionistic Fuzzy Ideals”, J. of Fuzzy Mathematics, Vol. 15, No. 4, 2007, 811 – 819.
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