Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces
The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.
[1] L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965) 338–353.
[2] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric Spaces,
Kybernetika, 11(5) (1975) 336–344.
[3] A. George and P. Veeramani, On some results in fuzzy metric spaces,
Fuzzy Sets and Systems, 64 (1994) 395–399.
[4] A. George and P. Veeramani, On some results of analysis for fuzzy
metric spaces, Fuzzy Sets and Systems, 90 (1997) 365–368.
[5] V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric
spaces, Fuzzy Sets and Systems, 125 (2002) 245–252.
[6] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals,
22 (2004) 1039–1046.
[7] C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy
metric spaces, Chaos, Solitons and Fractals, 29 (2006) 1073–1078.
[8] A. Mohamad, Fixed-point theorems in intuitionistic fuzzy metric spaces,
Chaos, Solitons and Fractals, 34 (2007) 1689–1695.
[9] B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and
Company, New York, 1983.
[10] J.E. Hutchinson, Fractals and self similarity, Indiana University Mathematics
Journal, 30 (1981) 713–747.
[11] M. Barnsley, Fractals Everywhere, 2nd ed., Academic Press, USA, 1993.
[12] M. Barnsley, Super Fractals, Cambridge University Press, New York,
2006.
[13] D. Easwaramoorthy and R. Uthayakumar, Analysis on Fractals in Fuzzy
Metric Spaces, Fractals, 19(3) (2011) 379–386.
[14] R. Uthayakumar and D. Easwaramoorthy, Hutchinson-Barnsley Operator
in Fuzzy Metric Spaces, International Journal of Engineering and Natural
Sciences, 5(4) (2011) 203–207.
[15] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of
Mathematics, 10 (1960) 313–334.
[16] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic
fuzzy metric spaces, Chaos, Solitons and Fractals, 28 (2006) 902–905.
[17] J. Rodriguez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on
compact sets, Fuzzy Sets and Systems, 147 (2004) 273–283.
[1] L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965) 338–353.
[2] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric Spaces,
Kybernetika, 11(5) (1975) 336–344.
[3] A. George and P. Veeramani, On some results in fuzzy metric spaces,
Fuzzy Sets and Systems, 64 (1994) 395–399.
[4] A. George and P. Veeramani, On some results of analysis for fuzzy
metric spaces, Fuzzy Sets and Systems, 90 (1997) 365–368.
[5] V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric
spaces, Fuzzy Sets and Systems, 125 (2002) 245–252.
[6] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals,
22 (2004) 1039–1046.
[7] C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy
metric spaces, Chaos, Solitons and Fractals, 29 (2006) 1073–1078.
[8] A. Mohamad, Fixed-point theorems in intuitionistic fuzzy metric spaces,
Chaos, Solitons and Fractals, 34 (2007) 1689–1695.
[9] B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and
Company, New York, 1983.
[10] J.E. Hutchinson, Fractals and self similarity, Indiana University Mathematics
Journal, 30 (1981) 713–747.
[11] M. Barnsley, Fractals Everywhere, 2nd ed., Academic Press, USA, 1993.
[12] M. Barnsley, Super Fractals, Cambridge University Press, New York,
2006.
[13] D. Easwaramoorthy and R. Uthayakumar, Analysis on Fractals in Fuzzy
Metric Spaces, Fractals, 19(3) (2011) 379–386.
[14] R. Uthayakumar and D. Easwaramoorthy, Hutchinson-Barnsley Operator
in Fuzzy Metric Spaces, International Journal of Engineering and Natural
Sciences, 5(4) (2011) 203–207.
[15] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of
Mathematics, 10 (1960) 313–334.
[16] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic
fuzzy metric spaces, Chaos, Solitons and Fractals, 28 (2006) 902–905.
[17] J. Rodriguez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on
compact sets, Fuzzy Sets and Systems, 147 (2004) 273–283.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64296", author = "R. Uthayakumar and D. Easwaramoorthy", title = "Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces", abstract = "The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.
", keywords = "Contraction, Iterated Function System, Hutchinson- Barnsley Operator, Intuitionistic Fuzzy Metric Space, Hausdorff Intuitionistic Fuzzy Metric.", volume = "6", number = "8", pages = "1234-8", }
