The topology of Generalized fuzzy metric spaces and Vector Image Filtering

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KAMRAN ALAM KHAN

Abstract

Khan [12] generalized the concept of Fuzzy metric space (In the sense of George and Veeramani) and introduced the notion of Generalized fuzzy n-metric spaces. In this paper, We further investigate the properties of these generalized fuzzy metric spaces and extend the Banach Fixed point theorem in this new framework. We also propose a vector image filter based on generalized fuzzy metrics.

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KHAN, K. A. (2017). The topology of Generalized fuzzy metric spaces and Vector Image Filtering. Journal of Global Research in Mathematical Archives(JGRMA), 4(11), 154–164. Retrieved from https://jgrma.com/index.php/jgrma/article/view/346
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Research Paper

References

K. Arakawa, Median filter based on fuzzy rules and its application to image restoration, Fuzzy Sets Syst. 77 (1996) 3-13.

J. Astola, P. Haavisto and Y. Neuvo, Vector Median Filters, Proc. IEEE. 78 (1990) 678-689.

J. G. Camarena, V. Gregori, S. Morillas and A. Sapena, Fast detection and removal of impulsive noise using peer groups and fuzzy metrics, Journal of Visual Communication and Image Representation 19 (2008) 20-29.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.

A. George, P. Veeramani, Some theorems in fuzzy metric spaces , J. Fuzzy Math. 3 (1995) 933-940.

A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets Syst. 90 (1997) 365-368.

M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988) 385-389.

V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002) 245-253.

V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets Syst. 115 (2000) 485-489.

K. A. Khan, On the possibility of N-topological spaces, Int. J. Math. Arc. 3 (2012) 2520-2523.

K. A. Khan, Generalized n-metric spaces and fixed point theorems, Journal of Nonlinear and Convex

Analysis 15 (2014) 1221-1229.

K. A. Khan, Generalized fuzzy metric spaces with an application to colour image filtering, Global journal of pure and applied Mathematics, 13 (2017) 3601-3616.

O. Kramosil and J.Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975) 326-334.

R. Machuca and K. Phillips, Applications of vector fields to image processing, IEEE Trans. Pattern Anal. Machine Intell. 5 (1983) 316-329.

D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets Syst. 144 (2004) 431-439.

S. Morillas, V. Gregori, G. Peris-Fajarnes and P. Latorre, A

new vector median filter based on fuzzy metrics, ICIAR05, Lecture Notes in Computer Science, 3656 (2005) 81-90.

I. Pitas and A. N. Venetsanopoulos, Nonlinear Digital Filters, Principles and Applications, Kluwer, 1992.

I. Pitas and A. N. Venetsanopoulos, Order statistics in digital image processing, Proc.IEEE, 80 (1992) 1892-1919.

K. Plataniotis and A. N. Venetsanopoulos, Vector processing in Colour Image Processing, S. J. Sangwine, ed., Chapman & Hall, London, U.K., (1998) 188-209.

K. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Applications, New York, Springer Verlag, 2000.

S. Schulte, M. Nachtegael, V. De Witte, D. Van derWeken and E. E. Kerre, A Fuzzy Impulse Noise Detection and Reduction Method, IEEE Transactions on Image Processing, 15 (2006) 1153-1162.

B. Schweizer and A. Sklar, Statistical Metric Spaces, Pacific Journal of Mathematics, 10 (1960) 313-334.

S. Sedghi and N. Shobe, Fixed point theorem in M-fuzzy metric spaces with property (E), Advances in Fuzzy Mathematics, 1 (2006) 55-65.

S. Sharma, Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 127 (2002) 345-352.

G. Sun and K. Yang, Generalized fuzzy metric spaces with properties, Research journal of Applied Sciences, Engineering and Technology 2 (2010) 673-678.

Y. Tanaka, Y. Mizuno, and T. Kado, Chaotic dynamics in the Friedmann equation, Chaos, Solitons and Fractals, 24 (2005) 407-422.

R. Vasuki, A common fixed point theorem in a fuzzy metric space, Fuzzy Sets Syst. 97 (1998) 395-397.

J. H. Wang, W. J. Liu and L. D. Lin, Histogram-Based Fuzzy Filter for Image Restoration, IEEE Transactions on Systems man and cybernetics part B.- cybernetics, 32 (2002) 230-238.

H. Xu, G. Zhu, H. Peng and D. Wang, Adaptive fuzzy switching filter for images corrupted by impulse noise, Pattern Recognition Letters, 25 (2004) 1657-1663.