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Intuitionistic fuzzy 2-normed space and some related concepts

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  • Mursaleen, M.
  • Danish Lohani, Q.M.

Abstract

Motivated by the notion of 2-norm due to Gähler [Gähler S. Lineare 2-normietre Räume. Math Nachr 28;1965:1–43], in this paper we define the concept of intuitionistic fuzzy 2-normed space which is a generalization of the notion of intuitionistic fuzzy normed space due to Saadati and Park [Saadati R, Park JH, On the intuitionistic fuzzy topological spaces. Chaos Solitons & Fractals 2006;27:331–44]. Further we establish some topological results in this new set up.

Suggested Citation

  • Mursaleen, M. & Danish Lohani, Q.M., 2009. "Intuitionistic fuzzy 2-normed space and some related concepts," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 224-234.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:224-234
    DOI: 10.1016/j.chaos.2008.11.006
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    References listed on IDEAS

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    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    3. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
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    Cited by:

    1. Mausumi Sen & Pradip Debnath, 2011. "Statistical convergence in intuitionistic fuzzy n-normed linear spaces," Fuzzy Information and Engineering, Springer, vol. 3(3), pages 259-273, September.
    2. Mursaleen, M. & Danish Lohani, Q.M., 2009. "Baire’s and Cantor’s theorems in intuitionistic fuzzy 2-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2254-2259.
    3. Mursaleen, M. & Lohani, Q.M. Danish & Mohiuddine, S.A., 2009. "Intuitionistic fuzzy 2-metric space and its completion," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1258-1265.
    4. Ali Hassan Abbaker Abd Alla, 2019. "An Application of Fixed Point Theorems in Fuzzy Metric Space," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 37-41, February.

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