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  • On Algebraic Properties of k-Q-Anti Fuzzy Normed Rings

    Author(s)
    Premkumar Munusamy
    Department of Mathematics, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai-600119, Tamil Nadu, India.

    J. Juliet Jeyapackiam
    Department of Mathematics, Jayaraj Annapackiam CSI College of Engineering Nazareth, Tuticorin-628617, India.

    Abdul Salam
    Gulf Asian English School, Sharjah, United Arab Emirates.

    H. Girija Bai
    Department of Mathematics, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai-600119, Tamil Nadu, India.

    Y. Immanuel
    Department of Mathematics, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai-600119, Tamil Nadu, India.

    A. Prasanna
    PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.

    ISBN 978-81-967669-0-0 (Print)
    ISBN 978-81-967669-1-7 (eBook)
    DOI: 10.9734/bpi/mono/978-81-967669-0-0

    In this paper, the concept of \(\mathit{k}\) - \(\mathit{Q}\) - Anti fuzzy normed ring is introduced and some basic properties related to it are established. That our definition of normed rings on \(\mathit{k}\) - \(\mathit{Q}\) - Anti fuzzy sets leads to a algebraic structure which we call a \(\mathit{k}\) - \(\mathit{Q}\) - Anti Fuzzy Normed Rings. We also defined \(\mathit{k}\) - \(\mathit{Q}\) - Anti Fuzzy Normed Rings homomorphism,  Anti Fuzzy Normed Subring,  Fuzzy Normed Ideal, \(\mathit{k}\) - \(\mathit{Q}\) - Fuzzy Normed Prime Ideal and \(\mathit{k}\) - \(\mathit{Q}\) - Anti Fuzzy Normed Maximal Ideal of a Normed ring respectively. We show that the some algebraic properties of normed ring theory on a \(\mathit{k}\) - \(\mathit{Q}\) - fuzzy sets, prove theorem and given relevant examples.

     

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