Intuitionistic fuzzy normed prime and maximal ideals

Motivated by the new notion of intuitionistic fuzzy normed ideal, we present and investigate some associated properties of intuitionistic fuzzy normed ideals. We describe the intrinsic product of any two intuitionistic fuzzy normed subsets and show that the intrinsic product of intuitionistic fuzzy...

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Published inAIMS mathematics Vol. 6; no. 10; pp. 10565 - 10580
Main Authors Alhaleem, Nour Abed, Ahmad, Abd Ghafur
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
intuitionistic fuzzy normed ideal
intuitionistic fuzzy normed maximal ideal
intuitionistic fuzzy normed prime ideal
intuitionistic fuzzy normed ring
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021613

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Abstract Motivated by the new notion of intuitionistic fuzzy normed ideal, we present and investigate some associated properties of intuitionistic fuzzy normed ideals. We describe the intrinsic product of any two intuitionistic fuzzy normed subsets and show that the intrinsic product of intuitionistic fuzzy normed ideals is a subset of the intersection of these ideals. We specify the notions of intuitionistic fuzzy normed prime ideal and intuitionistic fuzzy normed maximal ideal, we present the conditions under which a given intuitionistic fuzzy normed ideal is considered to be an intuitionistic fuzzy normed prime (maximal) ideal. In addition, the relation between the intuitionistic characteristic function and prime and maximal ideals is generalized. Finally, we characterize relevant properties of intuitionistic fuzzy normed prime ideals and intuitionistic fuzzy normed maximal ideals.
AbstractList Motivated by the new notion of intuitionistic fuzzy normed ideal, we present and investigate some associated properties of intuitionistic fuzzy normed ideals. We describe the intrinsic product of any two intuitionistic fuzzy normed subsets and show that the intrinsic product of intuitionistic fuzzy normed ideals is a subset of the intersection of these ideals. We specify the notions of intuitionistic fuzzy normed prime ideal and intuitionistic fuzzy normed maximal ideal, we present the conditions under which a given intuitionistic fuzzy normed ideal is considered to be an intuitionistic fuzzy normed prime (maximal) ideal. In addition, the relation between the intuitionistic characteristic function and prime and maximal ideals is generalized. Finally, we characterize relevant properties of intuitionistic fuzzy normed prime ideals and intuitionistic fuzzy normed maximal ideals.
Author Alhaleem, Nour Abed
Ahmad, Abd Ghafur
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CorporateAuthor Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
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SubjectTerms intuitionistic fuzzy normed ideal
intuitionistic fuzzy normed maximal ideal
intuitionistic fuzzy normed prime ideal
intuitionistic fuzzy normed ring
Title Intuitionistic fuzzy normed prime and maximal ideals
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