On some topological properties of intuitionistic2-fuzzyn-normed linear spaces

Objective & Hypothesis:Motivated by the notion ofn-norm due to Gähler, in this article we define the conceptof intuitionistic2-fuzzyn-normed space in general setting oft-norm as a generalizationof intuitionistic fuzzy normed space in the sense of Bag and Samanta.

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Key Findings & Data:Further we definethe notion ofα-n-norm corresponding to intuitionistic2-fuzzyn-norm.

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Conclusion & Impact:In addition, wediscuss some basic properties of convergence and completeness for intuitionistic2-fuzzyn-normed spaces.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

Motivated by the notion ofn-norm due to Gähler, in this article we define the conceptof intuitionistic2-fuzzyn-normed space in general setting oft-norm as a generalizationof intuitionistic fuzzy normed space in the sense of Bag and Samanta. Further we definethe notion ofα-n-norm corresponding to intuitionistic2-fuzzyn-norm. In addition, wediscuss some basic properties of convergence and completeness for intuitionistic2-fuzzyn-normed spaces.

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Cite This Article

KOCİNAC, L., KHAN, V., ALSHLOL, K., ALTAF, H. (2022). On some topological properties of intuitionistic2-fuzzyn-normed linear spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 208–220. https://ajindex.com/articles/530060

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References (1)

K.T. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets Syst.20(1), 87–96, 1986. [2]K.T. Atanassov,More on intuitionistic fuzzy sets, Fuzzy Sets Syst.33(1), 37–45,1989. [3]T. Bag and S.K. Samanta,Finite dimensional fuzzy normed linear spaces, J. FuzzyMath.11(3), 687–705, 2003. [4]T. Bag and S.K. Samanta,Finite dimensional intuitionistic fuzzy normed linearspaces, Ann. Fuzzy Math. Inform.6(2), 45–57, 2013. [5]D. Çoker,An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets Syst.88(1), 81–89, 1997. [6]S. Gähler,Lineare2-normierte Räume, Math. Nachr.28(1-2), 1–43, 1964. [7]S. Gähler,Untersuchungen über verallgemeinertem-metrische Räume, Math. Nachr.40(1-3), 165–189, 1969. [8]R. Giles,A computer program for fuzzy reasoning, Fuzzy Sets Syst.4(3), 221–234,1980. [9]H. Gunawan and M. Mashadi,Onn-normed spaces, Internat. J. Math. Math. Sci.27(10), 631–639, 2001. [10]L. Hong and J.-Q. Sun,Bifurcations of fuzzy nonlinear dynamical systems, Commun.Nonlinear Sci. Numer. Simul.11(1), 1–12, 2006. [11]S.S. Kim and Y.J. Cho,Strict convexity in linearn-normed spaces, DemonstratioMath.29(4), 739–744, 1996. [12]A. Misiak,n-inner product spaces, Math. Nachr.140(1), 299–319, 1989. [13]M. Mursaleen and Q.M. Danish Lohani,Intuitionistic fuzzy2-normed space and somerelated concepts, Chaos Solitons Fract.42(1), 224–234, 2009. [14]A.L. Narayanan and S. Vijayabalaji,Fuzzyn-normed linear spaces, Internat. J. Math.Math. Sci.24, 3963–3977, 2005. [15]J.H. Park,Intuitionistic fuzzy metric spaces, Chaos Solitons Fract.22(5), 1039–1046,2004. [16]C. Park and C. Alaca,An introduction to2-fuzzyn-normed linear spaces and a newperspective to the Mazur-Ulam problem, J. Inequal. Appl.14, 2012. [17]M.H.M. Rashid and Lj.D.R. Kočinac,Ideal convergence in2-fuzzy 2-normed spaces,Hacet. J. Math. Stat.46(1), 145–159, 2017. [18]R. Saadati and J.H. Park,On the intuitionistic fuzzy topological spaces, Chaos SolitonsFract.27(2), 331–344, 2006. [19]B. Schweizer and A. Sklar,Statistical metric spaces, Pacific J. Math.10(1), 313–334,1960. [20]R.M. Somasundaram and T. Beaula,Some aspects of2-fuzzy 2-normed linear spaces,Bull. Malays. Math. Sci. Soc.32(2), 211–221, 2009. [21]L.A. Zadeh,Fuzzy sets, Inform. and Control8(3), 338–353, 1965.