On some topological properties of intuitionistic $2$-fuzzy $n$-normed linear spaces

Yıl 2020, Cilt: 49 Sayı: 1, 208 - 220, 06.02.2020

Ljubiša D. R. Kočinac Vakeel Ahmad Khan K.m.a.s. Alshlool H. Altaf

https://doi.org/10.15672/hujms.546973

Cited By: 1

Öz

Motivated by the notion of $n$-norm due to Gähler, in this article we define the concept of intuitionistic $2$-fuzzy $n$-normed space in general setting of $t$-norm as a generalization of intuitionistic fuzzy normed space  in the sense of Bag and Samanta. Further we define the notion of $\alpha$-$n$-norm corresponding to intuitionistic $2$-fuzzy $n$-norm. In addition, we discuss some basic properties of convergence and completeness for intuitionistic $2$-fuzzy $n$-normed spaces.

Anahtar Kelimeler

intuitionistic fuzzy set, fuzzy set, $2$-fuzzy $n$-normed space, $t$-norm, $t$-conorm

Kaynakça

• [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. Fuzzy Math. 11 (3), 687–705, 2003.
• [4] T. Bag and S.K. Samanta, Finite dimensional intuitionistic fuzzy normed linear spaces, 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, Lineare 2-normierte Räume, Math. Nachr. 28 (1-2), 1–43, 1964.
• [7] S. Gähler, Untersuchungen über verallgemeinerte m-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, On n-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 linear n-normed spaces, Demonstratio Math. 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 fuzzy 2-normed space and some related concepts, Chaos Solitons Fract. 42 (1), 224–234, 2009.
• [14] A.L. Narayanan and S. Vijayabalaji, Fuzzy n-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 to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problem, J. Inequal. Appl. 14, 2012.
• [17] M.H.M. Rashid and Lj.D.R. Kočinac, Ideal convergence in 2-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 Solitons Fract. 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 of 2-fuzzy 2-normed linear spaces, Bull. Malays. Math. Sci. Soc. 32 (2), 211–221, 2009.
• [21] L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (3), 338–353, 1965.