| Title of paper:
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Radical structures of intuitionistic fuzzy polynomial ideals of a ring
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| Author(s):
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| P. K. Sharma
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| Post Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
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| pksharma@davjalandhar.com
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| Gagandeep Kaur
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| Research Scholar, IKG PT University, Jalandhar, Punjab, India
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| taktogagan@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 85–96
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| DOI:
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https://doi.org/10.7546/nifs.2018.24.4.85-96
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| Download:
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 PDF (198 Kb Kb, File info)
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| Abstract:
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In this paper we investigate the radical structure of an intuitionistic fuzzy polynomial ideal [math]\displaystyle{ A_x }[/math] induced by an intuitionistic fuzzy ideal [math]\displaystyle{ A }[/math] of a ring and study its properties. Given an intuitionistic fuzzy ideal [math]\displaystyle{ B }[/math] of a ring [math]\displaystyle{ R^{\prime} }[/math] and a homomorphism [math]\displaystyle{ f : R \rightarrow R^{\prime} }[/math], we show that if [math]\displaystyle{ f_x : R[x] \rightarrow R^{\prime}[x] }[/math] is the induced homomorphism of [math]\displaystyle{ f }[/math], that is, [math]\displaystyle{ f_x (\sum_{i = 0}^n a_i^{x_i}) = \sum_{i = 0}^n (f(a_i)) x_i }[/math], then [math]\displaystyle{ f_x^{-1} [(\sqrt{B})_x] = (\sqrt{f^{-1}(B)})_x }[/math].
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| Keywords:
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Complex trapezoidal intuitionistic fuzzy number (CTrIFN), Trapezoidal intuitionistic fuzzy number (TrIFN).
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| AMS Classification:
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03E72, 05C72, 05C65, 47N60.
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| References:
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- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Heidelberg.
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- Burillo, P., Bustince, H., & Mohedano, V. (1994). Some definition of intuitionistic fuzzy number, Fuzzy Based Expert Systems, Sofia, Bulgaria, 1994, 28–30.
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