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INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA

Yıl 2017, Cilt: 30 Sayı: 1, 413 - 429, 14.03.2017

Ebru Yiğit Hakan Efe

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • 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.

Yıl 2017, Cilt: 30 Sayı: 1, 413 - 429, 14.03.2017

Ebru Yiğit Hakan Efe

Öz

Kaynakça

  • 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Bölüm Mathematics
Yazarlar

Ebru Yiğit Bu kişi benim

Hakan Efe Bu kişi benim

Yayımlanma Tarihi 14 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 30 Sayı: 1

Kaynak Göster

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. Mart 2017;30(1):413-429.
Chicago Yiğit, Ebru, ve Hakan Efe. “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”. Gazi University Journal of Science 30, sy. 1 (Mart 2017): 413-29.
EndNote Yiğit E, Efe H (01 Mart 2017) INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA. Gazi University Journal of Science 30 1 413–429.
IEEE E. Yiğit ve H. Efe, “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”, Gazi University Journal of Science, c. 30, sy. 1, ss. 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 (Mart 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 ve Hakan Efe. “INTUITIONISTIC FUZZY METRICS DEDUCED BY COMBINATION OF SEVERAL DISTANCE CRITERIA”. Gazi University Journal of Science, c. 30, sy. 1, 2017, ss. 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.