{"title":"Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces","authors":"R. Uthayakumar, D. Easwaramoorthy","volume":68,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1161,"pagesEnd":1169,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15298","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.<\/p>\r\n","references":"[1] L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965) 338\u2013353. \r\n[2] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric Spaces,\r\nKybernetika, 11(5) (1975) 336\u2013344.\r\n[3] A. George and P. Veeramani, On some results in fuzzy metric spaces,\r\nFuzzy Sets and Systems, 64 (1994) 395\u2013399.\r\n[4] A. George and P. Veeramani, On some results of analysis for fuzzy\r\nmetric spaces, Fuzzy Sets and Systems, 90 (1997) 365\u2013368.\r\n[5] V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric\r\nspaces, Fuzzy Sets and Systems, 125 (2002) 245\u2013252.\r\n[6] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals,\r\n22 (2004) 1039\u20131046.\r\n[7] C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy\r\nmetric spaces, Chaos, Solitons and Fractals, 29 (2006) 1073\u20131078.\r\n[8] A. Mohamad, Fixed-point theorems in intuitionistic fuzzy metric spaces,\r\nChaos, Solitons and Fractals, 34 (2007) 1689\u20131695.\r\n[9] B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and\r\nCompany, New York, 1983.\r\n[10] J.E. Hutchinson, Fractals and self similarity, Indiana University Mathematics\r\nJournal, 30 (1981) 713\u2013747.\r\n[11] M. Barnsley, Fractals Everywhere, 2nd ed., Academic Press, USA, 1993.\r\n[12] M. Barnsley, Super Fractals, Cambridge University Press, New York,\r\n2006.\r\n[13] D. Easwaramoorthy and R. Uthayakumar, Analysis on Fractals in Fuzzy\r\nMetric Spaces, Fractals, 19(3) (2011) 379\u2013386.\r\n[14] R. Uthayakumar and D. Easwaramoorthy, Hutchinson-Barnsley Operator\r\nin Fuzzy Metric Spaces, International Journal of Engineering and Natural\r\nSciences, 5(4) (2011) 203\u2013207.\r\n[15] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of\r\nMathematics, 10 (1960) 313\u2013334.\r\n[16] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic\r\nfuzzy metric spaces, Chaos, Solitons and Fractals, 28 (2006) 902\u2013905.\r\n[17] J. Rodriguez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on\r\ncompact sets, Fuzzy Sets and Systems, 147 (2004) 273\u2013283.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 68, 2012"}