On strong intuitionistic fuzzy metrics

Volume 9, Issue 6, pp 4016--4038 http://dx.doi.org/10.22436/jnsa.009.06.47

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Authors

Hakan Efe - Department of Mathematics, Faculty of Science, Gazi University Teknikokullar, Ankara, 06500, Turkey. Ebru Yigit - Graduate School of Natural and Applied Science, Gazi University Teknikokullar, Ankara, 06500, Turkey.

Abstract

In this paper we give some properties of a class of intuitionistic fuzzy metrics which is called strong. This new class includes the class of stationary intuitionistic fuzzy metrics. So we examine the relationship between strong intuitionistic fuzzy metric and stationary intuitionistic fuzzy metric.

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Keywords

• Continuous t-norm
• continuous t-conorm
• intuitionistic fuzzy metric
• strong intuitionistic fuzzy metric
• stationary intuitionistic fuzzy metric.

MSC

•  54A40
•  54B20
•  54E35

References

• [1] C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29 (2006), 1073-1078.


• [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Sys., 20 (1986), 87-96.


• [3] D. Çoker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets Sys., 88 (1997), 81-89.


• [4] Z. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86 (1982), 74-95.


• [5] M. A. Erceg , Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205-230.


• [6] J. G. García, S. Romaguera , Examples of non-strong fuzzy metrics, Fuzzy Sets Sys., 162 (2011), 91-93.


• [7] A. George, P. Veeramani , On some results in fuzzy metric spaces, Fuzzy Sets Sys., 64 (1994), 395-399.


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


• [9] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets Sys., 90 (1997), 365-368.


• [10] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Sys., 27 (1988), 385-389.


• [11] V. Gregori, S. Romaguera, P. Veeramani, A note on intuitionistic fuzzy metric spaces , Chaos Solitons Fractals, 28 (2006), 902-905.


• [12] V. Gregori, S. Morillas, A. López-Crevillén , On continuity and uniform continuity in fuzzy metric spaces, In Proceedings of the Workshop in Applied Topology WIAT'09, (2009), 85-91.


• [13] O. Kaleva, S. Seikkala , On fuzzy metric spaces, Fuzzy Sets Sys., 12 (1984), 215-229.


• [14] I. Kramosil, J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344.


• [15] R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht (1996)


• [16] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046.


• [17] S. Romaguera , On completion of fuzzy metric spaces, Fuzzy Sets Sys., 130 (2002), 399-404.


• [18] R. Saadati, J. H. Park , On the intuitionistic fuzzy topological spaces , Chaos Solitons Fractals, 27 (2006), 331-344.


• [19] A. Sapena, S. Morillas, On strong fuzzy metrics, In Proceedings of the Workshop in Applied Topology WIAT'09, (2009), 135-141.


• [20] A. Savchenko, A remark on stationary fuzzy metric spaces, Carpathian Math. Publ., 3 (2011), 124-129.


• [21] B. Schweizer, A. Sklar , Statistical metric spaces, Pacific J. Math, 10 (1960), 313-334.


• [22] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.