1 INTUITIONISTIC FUZZY NORMED IDEAL AND ITS CHARACTER- ISTICS Tekalign Ashale 1,†,‡ https://orcid.org/0000-0001-9424-3318 Tekalign Ashale Ashale, T. 1 Jimma University; tekalign.ashale@ju.edu.et Abstract A single paragraph of about 200 words maximum. For research ar- ticles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but with- out headings: (1) Background: place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: describe briefly the main methods or treatments applied; (3) Results: summarize the article’s main find- ings; (4) Conclusion: indicate the main conclusions or interpretations. The ab- stract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions. Intuitionist Fuzzy Normed Ring ; Intuitionist fuzzy normed Ideal ; Fuzzy Prime Ideal ; Fuzzy Normed Prime Ideal.) 1 Introduction After Zadeh [1] formulate the interception of fuzzy set as ageneralization of acrisp set,that use to establishment of the fuzzy set theory,in 1971 RosenField [2] extended and formulated the notion of fuzzy subgroup of agroup. Later,in [3] Liu introduced the definition of fuzzy ring,fuzzy subring,fuzzy ideals and some related concepts.Swamy in [5],Mukherje and Sen in[7]) and Zhag Yue [8] introduced fuzzy ideals and fuzzy prime ideals,characterized Regular Rings andnotherian Rings by Fuzzy Ideals,determined all fuzzy ideals of a ring of intigers.in 1997 Atanassov [9]presented the idea of the intuitionistic fuzzy set a way to handle uncertainty, while fuzzy set deals with the degree of member- ship of an element in a given set, intuitionistic fuzzy sets assign both degrees of membership and non-membership with an addition that sum of these de- grees should not exceeds 1. In 1992 [10],Dix et al. introduced the notion of intuitionistic fuzzy groups, followed by a study of the properties of intuition- istic fuzzy subgroups and intuitionistic fuzzy subrings conducted by Hur et al. in[11]. Marashdeh and Salleh generalized Dibs notion for fuzzy rings based on the notion of fuzzy space in [14] by applying the notion of fuzzy space to intuitionistic fuzzy space and to introduce related concepts to present a new formulation of intuitionistic fuzzy group and intuitionistic fuzzy ring. In [26],a generalisation of the notion of fuzzy homomorphism and fuzzy normal sub- group based on.fuzzy spaces to intuitionistic fuzzy hyperhomomorphism based on intuitionistic fuzzy spaces to introduce the concept of an intuitionistic fuzzy quotient hypergroup induced by an intuitionistic fuzzy normal subhypergroup. Complex intuitionistic fuzzy ideals were defined and its characteristics were in- vestigated by Alsarahead and Ahmad in [14] and some of its applications were studied in [16] bycombining complex intuitionistic fuzzy sets and graph theory which can be used in the utilization of the complex intuitionistic fuzzy graphs in decision making problems. After studies by Naimark [22]of normed rings, Arens presented [17] the generalization of normed rings and Gelfand defined commutative normed rings in [18] and presented the notion of commutative normed rings. In[19] Jarden characterized the ultrametric absolute value and investigated the properties of normed rings. Gupta and Qi [29] studied T-norms and T-conorm, T-norm, T-conorm and negation function was described as a set of T-operators, some typical T-operators and their mathematical properties were given.in 2016,[28]Backhadech,et al.introduced intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring using intuitionistic fuzzy points and membership and non-membership function. Properties of fuzzy normed ring theory were established by Emniyet and Sahin [24] in 2018,they defined fuzzy normed homomorphism, fuzzy normed subring and fuzzy normed ideal and showed some algebraic properties of normed ring theory on fuzzy sets. Af- Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 20 August 2021 doi:10.20944/preprints202108.0415.v1 © 2021 by the author(s). Distributed under a Creative Commons CC BY license.