Sains Malaysiana 51(2)(2022): 609-618

http://doi.org/10.17576/jsm-2022-5102-24

Intuitionistic Anti Fuzzy Normal Subrings over Normed Rings

(Subgelang Normal Kabur Anti Berintuisi terhadap Gelang Norma)

NOUR ABED ALHALEEM* & ABD GHAFUR AHMAD

Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Received: 8 March 2021/Accepted: 4 July 2021

ABSTRACT

In this paper, we initiate the notion of intuitionistic anti fuzzy normed normal subrings and generalize various related properties. We extend the notion of intuitionistic fuzzy normed subrings to intuitionistic anti fuzzy normed normal subrings. Further, we study the algebraic nature of direct product of intuitionistic anti fuzzy normed normal subrings and establish and examine some imperative properties of such products. We also provide some essential operations specially subset, complement and intersection relating to direct product of intuitionistic anti fuzzy normed normal subrings. Then, we generalize the relation between the intuitionistic characteristic function and direct product of intuitionistic anti fuzzy normed normal subrings.

Keywords: Direct product of intuitionistic anti fuzzy normed normal subrings; intuitionistic anti fuzzy normed normal subring; intuitionistic fuzzy normed normal subring

ABSTRAK

Dalam makalah ini, kami mempelopori tanggapan subgelang normal norma anti kabur berintuisi dan menyamaratakan pelbagai sifat berkaitan. Kami kembangkan tanggapan subgelang normal norma kabur berintuisi kepada subgelang normal norma anti kabur berintuisi. Seterusnya, kami mengkaji sifat aljabar bagi hasil darab langsung subgelang normal norma anti kabur berintuisi dan memantapkan serta mengkaji beberapa sifat penting hasil darab tersebut. Kami juga memberikan beberapa operasi asas terutamanya subset, pelengkap dan persilangan yang berkaitan dengan hasil darab langsung subgelang normal norma anti kabur berintuisi. Kemudian kami permudahkan hubungan antara fungsi cirian berintuisi dengan hasil darab langsung subgelang normal norma anti kabur berintuisi.

Kata kunci: Hasil darab langsung subgelang normal bernorma anti kabur berintuisi; subgelang normal bernorma anti kabur berintuisi; subgelang normal bernorma kabur berintuisi

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*Corresponding author; email: p102361@siswa.ukm.edu.my