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Intuitionistic Type-2 Fuzzy Normed Linear Space and Some of Its Basic Properties

Author

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  • Amit Biswas

    (Department of Mathematics, Kazi Nazrul University, Asansol 713340, India
    These authors contributed equally to this work.)

  • Moumita Chiney

    (Department of Mathematics, Kazi Nazrul University, Asansol 713340, India
    These authors contributed equally to this work.)

  • Syamal Kumar Samanta

    (Department of Mathematics, Visva-Bharati, Santiniketan 731235, India
    These authors contributed equally to this work.)

Abstract

An intuitionistic fuzzy set is a more generalised tool than a fuzzy set for handling unpredictability as, in an intuitionistic fuzzy set, there is scope for considering a grade of non-membership, independent of the grade of membership, only satisfying the condition that their sum is less or equal to 1. The motivation of this paper is to introduce the notion of intuitionistic type-2 fuzzy normed linear space (IT2FNLS). Here, to each vector x , we assign two fuzzy real number valued grades, one for its norm and the other for the negation of its norm. A theorem of the decomposition of the intuitionistic type-2 fuzzy norm into a family of pairs of Felbin-type fuzzy norms is established. Also, we deal with Cauchyness and convergence of sequences in the IT2FNLS. Later on, in the finite-dimensional IT2FNLS, the completeness property and compactness property are explored. Finally, we define two types of intuitionistic type-2 fuzzy continuity and examine the relations between them.

Suggested Citation

  • Amit Biswas & Moumita Chiney & Syamal Kumar Samanta, 2024. "Intuitionistic Type-2 Fuzzy Normed Linear Space and Some of Its Basic Properties," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2176-:d:1433284
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    References listed on IDEAS

    as
    1. Nabanita Konwar & Ayhan Esi & Pradip Debnath, 2019. "New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 65-83, March.
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