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INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA

Year 2017, Volume: 30 Issue: 1, 413 - 429, 14.03.2017

Ebru Yiğit Hakan Efe

Abstract

In this paper we give some examples of intuitionistic fuzzy metrics in the sense of Park [17]. All the examples have been classified with respect to their construction. At the same time, most of the well-known intuitionistic fuzzy metrics are given in this paper. Also, some important intuitionistic fuzzy metrics, by the help of classical metrics and some definite special kinds of functions are shown.

Keywords

continuous t-norm continuous t-conorm intuitionistic fuzzy metric stationary intuitionistic fuzzy metric.

References

  • C. Alaca, D. Turkoglu, C. Yildiz,Common fixed points of compatible maps in intuitionistic fuzzy metric spaces, Southeast Asian Bull. Math., 32, (2008), 21-33.
  • C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons& Fractals, 29(5), (2006), 1073-1078.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986), 87-96.
  • Z. Deng, Fuzzy pseudo-metric spaces, Journal of Mathematical Analysis and Applications, 86(1), (1982), 74-95.
  • H. Efe, C. Yildiz, On the Hausdorff intuitionistic fuzzy metric on compact sets, International Journal of Pure and Applied Mathematics, 31(2), (2006), 143-155.
  • H. Efe, E. Yiğit, On strong intuitionistic fuzzy metrics, J. Nonlinear Sci. Appl., 9(2016), 4016-4038.
  • M. A. Erceg, Metric spaces in fuzzy set theory, Journal of Mathematical Analysis and Applications, 69(1), (1979), 205-230.
  • A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(3), (1994), 395-399.
  • A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy sets and systems, 90(3), (1997), 365-368.
  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3), (1988), 385-389.
  • V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, 115(3), (2000), 485-489.
  • V. Gregori, S. Romaguera, A. Sapena, On t-uniformly continuous mappings in fuzzy metric spaces, The Journal of Fuzzy Mathematics, 12(1), (2004), 237-243.
  • V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144(3), (2004), 411-420.
  • V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems, 170(1), (2011), 95-111.
  • H. M. Golshan, H. Naraghi, M. Kazemi, t-Best approximation in fuzzy and intuitionistic fuzzy metric spaces, Journal of Nonlinear Analysis and Optimization: Theory, (2011).
  • R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht, (1996).
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons& Fractals, 22(5), (2004), 1039-1046.
  • A. S. Piera, A contribution to the study of fuzzy metric spaces, Applied General Topology, 2(1), (2001), 63-75.
  • S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems, 130(3), (2002), 399-404.
  • B. Schweizer, A.Sklar, Statistical metric spaces, Pacific J. Math, 10(3), (1960), 313-334.
  • D. Turkoglu, C. Alaca, C. Yildiz, Compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces, Demonstratio Math., 39, (2006), 671-684.
  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965), 338-353.

Year 2017, Volume: 30 Issue: 1, 413 - 429, 14.03.2017

Ebru Yiğit Hakan Efe

Abstract

References

  • C. Alaca, D. Turkoglu, C. Yildiz,Common fixed points of compatible maps in intuitionistic fuzzy metric spaces, Southeast Asian Bull. Math., 32, (2008), 21-33.
  • C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons& Fractals, 29(5), (2006), 1073-1078.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986), 87-96.
  • Z. Deng, Fuzzy pseudo-metric spaces, Journal of Mathematical Analysis and Applications, 86(1), (1982), 74-95.
  • H. Efe, C. Yildiz, On the Hausdorff intuitionistic fuzzy metric on compact sets, International Journal of Pure and Applied Mathematics, 31(2), (2006), 143-155.
  • H. Efe, E. Yiğit, On strong intuitionistic fuzzy metrics, J. Nonlinear Sci. Appl., 9(2016), 4016-4038.
  • M. A. Erceg, Metric spaces in fuzzy set theory, Journal of Mathematical Analysis and Applications, 69(1), (1979), 205-230.
  • A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(3), (1994), 395-399.
  • A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy sets and systems, 90(3), (1997), 365-368.
  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3), (1988), 385-389.
  • V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, 115(3), (2000), 485-489.
  • V. Gregori, S. Romaguera, A. Sapena, On t-uniformly continuous mappings in fuzzy metric spaces, The Journal of Fuzzy Mathematics, 12(1), (2004), 237-243.
  • V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144(3), (2004), 411-420.
  • V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems, 170(1), (2011), 95-111.
  • H. M. Golshan, H. Naraghi, M. Kazemi, t-Best approximation in fuzzy and intuitionistic fuzzy metric spaces, Journal of Nonlinear Analysis and Optimization: Theory, (2011).
  • R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht, (1996).
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons& Fractals, 22(5), (2004), 1039-1046.
  • A. S. Piera, A contribution to the study of fuzzy metric spaces, Applied General Topology, 2(1), (2001), 63-75.
  • S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems, 130(3), (2002), 399-404.
  • B. Schweizer, A.Sklar, Statistical metric spaces, Pacific J. Math, 10(3), (1960), 313-334.
  • D. Turkoglu, C. Alaca, C. Yildiz, Compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces, Demonstratio Math., 39, (2006), 671-684.
  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965), 338-353.
There are 22 citations in total.

Details

Journal Section Mathematics
Authors

Ebru Yiğit This is me

Hakan Efe This is me

Publication Date March 14, 2017
Published in Issue Year 2017 Volume: 30 Issue: 1

Cite

APA Yiğit, E., & Efe, H. (2017). INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science, 30(1), 413-429.
AMA Yiğit E, Efe H. INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science. March 2017;30(1):413-429.
Chicago Yiğit, Ebru, and Hakan Efe. “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”. Gazi University Journal of Science 30, no. 1 (March 2017): 413-29.
EndNote Yiğit E, Efe H (March 1, 2017) INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science 30 1 413–429.
IEEE E. Yiğit and H. Efe, “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”, Gazi University Journal of Science, vol. 30, no. 1, pp. 413–429, 2017.
ISNAD Yiğit, Ebru - Efe, Hakan. “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”. Gazi University Journal of Science 30/1 (March 2017), 413-429.
JAMA Yiğit E, Efe H. INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science. 2017;30:413–429.
MLA Yiğit, Ebru and Hakan Efe. “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”. Gazi University Journal of Science, vol. 30, no. 1, 2017, pp. 413-29.
Vancouver Yiğit E, Efe H. INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science. 2017;30(1):413-29.