On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces
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Authors
Xia Li
- Department of Mathematics and Sciences, Hebei GEO University, Shijiazhuang 050031, China.
Meifang Guo
- Department of Mathematics and Sciences, Hebei GEO University, Shijiazhuang 050031, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, 300387, China.
Abstract
The purpose of this article is to evaluate the definition of a class of intuitionistic fuzzy metric space
which was presented by Park [J. H. Park, Chaos Solitons Fractals, 22 (2004), 1039-1046]. This review is
also appropriate to the definition of a class of intuitionistic fuzzy normed space which was presented by
Saadati and Park [R. Saadati, J. H. Park, Chaos Solitons Fractals, 27 (2006), 331-344].
Share and Cite
ISRP Style
Xia Li, Meifang Guo, Yongfu Su, On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 9, 5441--5448
AMA Style
Li Xia, Guo Meifang, Su Yongfu, On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces. J. Nonlinear Sci. Appl. (2016); 9(9):5441--5448
Chicago/Turabian Style
Li, Xia, Guo, Meifang, Su, Yongfu. "On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces." Journal of Nonlinear Sciences and Applications, 9, no. 9 (2016): 5441--5448
Keywords
- Fuzzy metric space
- fuzzy normed space
- intuitionistic fuzzy metric space
- intuitionistic fuzzy normed space.
MSC
References
-
[1]
M. Abbas, B. Ali, W. Sintunavarat, P. Kumam, Tripled fixed point and tripled coincidence point theorems in intuitionistic fuzzy normed spaces, Fixed Point Theory Appl., 2012 (2012), 16 pages
-
[2]
C. Alaca, D. Turkoghlu, C. Yildiz, , Chaos Solitons Fractals, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29 (2006), 1073--1078
-
[3]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96
-
[4]
S. Chauhan, S. Bhatnagar, S. Radenović, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Matematiche (Catania), 68 (2013), 87--98
-
[5]
S. Chauhan, S. Radenović, M. Imdad, C. Vetro, Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 795--810
-
[6]
Y. J. Cho, J. Martínez-Moreno, A. Roldán, C. Roldán, Coupled coincidence point theorems in (intuitionistic) fuzzy normed spaces, J. Inequal. Appl., 2013 (2013), 11 pages.
-
[7]
D. Çoker , An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81--89
-
[8]
C. Di Bari, C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), 973--982
-
[9]
H. Efe, E. Yiğitb, On strong intuitionistic fuzzy metrics, J. Nonlinear Sci. Appl., 9 (2016), 4016--4038
-
[10]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395--399
-
[11]
D. Gopal, M. Imdad, C. Vetro, M. Hasan, Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces, J. Nonlinear Anal. Appl., 2012 (2012), 11 pages
-
[12]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385--389
-
[13]
C. Ionescu, S. Rezapour, M. E. Samei, Fixed points of some new contractions on intuitionistic fuzzy metric spaces, Fixed Point Theory Appl., 2013 (2013), 8 pages
-
[14]
Z. Jiang, Y. J. Wang, C.-C. Zhu, Fixed point theorems for contractions in fuzzy normed spaces and intuitionistic fuzzy normed spaces , Fixed Point Theory Appl., 2013 (2013), 10 pages
-
[15]
Z. Kadelburg, S. Radenović, A note on some recent best proximity point results for non-self mappings , Gulf J. Math., 1 (2013), 36--41
-
[16]
I. Kramosil, J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika (Prague), 11 (1975), 336--344
-
[17]
A. Latif, M. Hezarjaribi, P. Salimi, N. Hussain, Best proximity point theorems for \(\alpha-\psi\)-proximal contractions in intuitionistic fuzzy metric spaces, J. Inequal. Appl., 2014 (2014), 19 pages
-
[18]
W. Long, S. Khaleghizadeh, P. Selimi, S. Radenović, S. Shukla, Some new fixed point results in partial ordered metric spaces via admissible mappings, Fixed Point Theory Appl., 2014 (2014), 18 pages
-
[19]
A. Mohamad , Fixed-point theorems in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 34 (2007), 1689--1695
-
[20]
S. A. Mohiuddine, M. A. Alghamdi, Stability of functional equation obtained through a fixed-point alternative in intuitionistic fuzzy normed spaces, Adv. Difference Equ., 2012 (2012), 16 pages
-
[21]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039--1046
-
[22]
J. S. Park, Y. C. Kwun, J. H. Park, A fixed point theorem in the intuitionistic fuzzy metric spaces , Far East J. Math. Sci. (FJMS), 16 (2005), 137--149
-
[23]
M. Rafi, M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric, Iran. J. Fuzzy Syst., 3 (2006), 23--29
-
[24]
R. Saadati, P. Kumam, S. Y. Jang , On the tripled fixed point and tripled coincidence point theorems in fuzzy normed spaces, Fixed Point Theory Appl., 2014 (2014), 16 pages
-
[25]
R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces , Chaos Solitons Fractals, 27 (2006), 331--344
-
[26]
P. Salimi, C. Vetro, P. Vetro , Some new fixed point results in non-Archimedean fuzzy metric spaces, Nonlinear Anal. Model. Control, 18 (2013), 344--358
-
[27]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 314--334
-
[28]
Y. H. Shen, D. Qiu, W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Lett., 25 (2012), 138--141
-
[29]
W. Sintunavarat, Y. J. Cho, P. Kumam, Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory Appl., 2011 (2011), 13 pages
-
[30]
C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 162 (2011), 84--90
-
[31]
C. Vetro, D. Gopal, M. Imdad, Common fixed point theorems for (\(\varphi,\psi\))-weak contractions in fuzzy metric spaces, Indian J. Math., 52 (2010), 573--590
-
[32]
C. Vetro, P. Vetro, Common fixed points for discontinuous mappings in fuzzy metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), 295--303
-
[33]
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338--353