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Year 2022, Volume: 51 Issue: 6, 1563 - 1576, 01.12.2022

Elif Güner Halis Aygün

https://doi.org/10.15672/hujms.1115381
Cited By: 2

Abstract

Keywords

partial metric fuzzy metric topology fuzzifying topology fixed point theorem

References

  • [1] B. Aldemir, E. Güner, E. Aydoğdu and H. Aygün, Some fixed point theorems in partial fuzzy metric spaces, Journal of the Institute of Science and Technology, 10 (4), 2889-2900, 2020.
  • [2] M.A. Alghamdi, N. Shahzad and O. Valero, On fixed point theory in partial metric spaces, Fixed Point Theory Appl. 2012 (1), 1-25, 2012.
  • [3] E. Aydoğdu, B. Aldemir, E. Güner and H. Aygün, Some properties of partial fuzzy metric topology, Advances in Intelligent Systems and Computing, Springer, Cham, 1267-1275, 2020.
  • [4] E. Aydoğdu, A. Aygünoğlu and H. Aygün, The space of continuous function between fuzzy metric spaces, Erzincan University Journal of Science and Technology 13 (3), 1132-1137, 2020.
  • [5] A. Aygünoğlu, E. Aydoğdu and H. Aygün, Construction of fuzzy topology by using fuzzy metric, Filomat 34 (2), 433-441, 2020.
  • [6] M. Bukatin, R. Kopperman, S. Matthews and H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly 116 (8), 708-718, 2009.
  • [7] V. Çetkin, E. Güner and H. Aygün, On 2S-metric spaces, Soft Computing 24 (17), 12731-12742, 2020.
  • [8] S. Gähler, 2-Metrische räume und ihre topologische struktur, Math. Nachr. 26, 115- 118, 1963.
  • [9] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (3), 395-399, 1994.
  • [10] V. Gregori, J.J. Minana and D. Miravet, Fuzzy partial metric spaces, Int J Gen Syst. 48 (3), 260-279, 2019.
  • [11] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets Syst. 115 (3), 485-489, 2000.
  • [12] E. Güner and H. Aygün, On 2-fuzzy metric spaces, in: Adv. Intell. Syst. Comput. 1197, 1258-1266, 2020.
  • [13] E. Güner and H. Aygün, On $b_2$-metric spaces, Konuralp J. Math. 9 (1), 33-39, 2021.
  • [14] S. Han, J. Wu and D. Zhang, Properties and principles on partial metric spaces, Topol. Appl. 230, 77-98, 2017.
  • [15] H. Huang and C. Wu, On the triangle inequalities in fuzzy metric spaces, Inf. Sci. 177 (4), 1063-1072, 2007.
  • [16] O. Kaleva and J. Kauhanen, A note on compactness in a fuzzy metric space, Fuzzy Sets Syst. 238, 135-139, 2014.
  • [17] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst. 12 (3), 215-229, 1984.
  • [18] I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (5), 336-344, 1975.
  • [19] B.S. Lee, S.J. Lee and K.M. Park, The completions of fuzzy metric spaces and fuzzy normed linear spaces, Fuzzy Sets Syst. 106 (3), 469-473, 1999.
  • [20] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728, 1830-197, 1994.
  • [21] K. Menger, Statistical metrics, Proc. National Acad. Sci. of the United States of America 28, 535-537, 1942.
  • [22] J.J. Miñana and A. Shostak, Fuzzifying topology induced by a strong fuzzy metric, Fuzzy Sets Syst. 300, 24-39, 2016.
  • [23] M. Mizumoto and J. Tanaka, Some properties of fuzzy numbers, in: Advances in Fuzzy Set Theory and Applications, 153-164, North-Holland, Amsterdam, 1979.
  • [24] S. Oltra and O. Valero, Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36, 1726, 2004.
  • [25] A. Roldán, J. Martinez-Moreno and C. Roldán, On interrelationships between fuzzy metric structures, Iran. J. Fuzzy Syst. 10 (2), 133-150, 2013.
  • [26] B. Schweizer ad A. Sklar, Probabilistic metric spaces, North-Holland, New York, 1983.
  • [27] S. Sedghi, N. Shobkolaei and I. Altun, Partial fuzzy metric space and some fixed point results, Commun. Math. 23 (2), 131-142, 2015.
  • [28] N. Shahzad and O. Valero, On 0-complete partial metric spaces and quantitative fixed point techniques in denotational semantics, Abstr. Appl 2013, 1-12, 2013.
  • [29] N. Shahzad and O. Valero, A Nemytskii-Edelstein type fixed point theorem for partial metric spaces, Fixed Point Theory Appl. 2015 (1), 1-15, 2015.
  • [30] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. 6 (2), 229-240, 2005.
  • [31] B.P. Varol and H. Aygün, Intuitionistic fuzzy metric groups, Int. J. Fuzzy Syst. 14 (3), 454-461, 2012.
  • [32] Y. Yue and M. Gu, Fuzzy partial (pseudo-)metric space, J. Intell. Fuzzy Syst. 27 (3), 1153-1159, 2014.
  • [33] L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (3), 338-353, 1965.
  • [34] D. Zhang and L. Xu, Categories isomorphic to FNS, Fuzzy Sets Syst. 104, 373-380, 1999.

A new approach to fuzzy partial metric spaces

Year 2022, Volume: 51 Issue: 6, 1563 - 1576, 01.12.2022

Elif Güner Halis Aygün

https://doi.org/10.15672/hujms.1115381
Cited By: 2

Abstract

In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization of crisp partial metric spaces in the fuzzifying view with the distance between ordinary points. For this aim, we first present the concept of fuzzy partial metric spaces by considering the distance as non-negative, upper semi-continuous, normal and convex fuzzy numbers by giving examples. We obtain some useful inequalities under some restrictions in fuzzy partial metric spaces. Then we discuss the relationships with the other metric structures and we point out Banach's fixed point theorem as an application of the proposed properties and relations. Finally, we show that fuzzy partial metric spaces induce some $\alpha$-level topology, Lowen fuzzy topology, and fuzzifying topology.

Keywords

partial metric fuzzy metric topology fuzzifying topology fixed point theorem

References

  • [1] B. Aldemir, E. Güner, E. Aydoğdu and H. Aygün, Some fixed point theorems in partial fuzzy metric spaces, Journal of the Institute of Science and Technology, 10 (4), 2889-2900, 2020.
  • [2] M.A. Alghamdi, N. Shahzad and O. Valero, On fixed point theory in partial metric spaces, Fixed Point Theory Appl. 2012 (1), 1-25, 2012.
  • [3] E. Aydoğdu, B. Aldemir, E. Güner and H. Aygün, Some properties of partial fuzzy metric topology, Advances in Intelligent Systems and Computing, Springer, Cham, 1267-1275, 2020.
  • [4] E. Aydoğdu, A. Aygünoğlu and H. Aygün, The space of continuous function between fuzzy metric spaces, Erzincan University Journal of Science and Technology 13 (3), 1132-1137, 2020.
  • [5] A. Aygünoğlu, E. Aydoğdu and H. Aygün, Construction of fuzzy topology by using fuzzy metric, Filomat 34 (2), 433-441, 2020.
  • [6] M. Bukatin, R. Kopperman, S. Matthews and H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly 116 (8), 708-718, 2009.
  • [7] V. Çetkin, E. Güner and H. Aygün, On 2S-metric spaces, Soft Computing 24 (17), 12731-12742, 2020.
  • [8] S. Gähler, 2-Metrische räume und ihre topologische struktur, Math. Nachr. 26, 115- 118, 1963.
  • [9] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (3), 395-399, 1994.
  • [10] V. Gregori, J.J. Minana and D. Miravet, Fuzzy partial metric spaces, Int J Gen Syst. 48 (3), 260-279, 2019.
  • [11] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets Syst. 115 (3), 485-489, 2000.
  • [12] E. Güner and H. Aygün, On 2-fuzzy metric spaces, in: Adv. Intell. Syst. Comput. 1197, 1258-1266, 2020.
  • [13] E. Güner and H. Aygün, On $b_2$-metric spaces, Konuralp J. Math. 9 (1), 33-39, 2021.
  • [14] S. Han, J. Wu and D. Zhang, Properties and principles on partial metric spaces, Topol. Appl. 230, 77-98, 2017.
  • [15] H. Huang and C. Wu, On the triangle inequalities in fuzzy metric spaces, Inf. Sci. 177 (4), 1063-1072, 2007.
  • [16] O. Kaleva and J. Kauhanen, A note on compactness in a fuzzy metric space, Fuzzy Sets Syst. 238, 135-139, 2014.
  • [17] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst. 12 (3), 215-229, 1984.
  • [18] I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (5), 336-344, 1975.
  • [19] B.S. Lee, S.J. Lee and K.M. Park, The completions of fuzzy metric spaces and fuzzy normed linear spaces, Fuzzy Sets Syst. 106 (3), 469-473, 1999.
  • [20] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728, 1830-197, 1994.
  • [21] K. Menger, Statistical metrics, Proc. National Acad. Sci. of the United States of America 28, 535-537, 1942.
  • [22] J.J. Miñana and A. Shostak, Fuzzifying topology induced by a strong fuzzy metric, Fuzzy Sets Syst. 300, 24-39, 2016.
  • [23] M. Mizumoto and J. Tanaka, Some properties of fuzzy numbers, in: Advances in Fuzzy Set Theory and Applications, 153-164, North-Holland, Amsterdam, 1979.
  • [24] S. Oltra and O. Valero, Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36, 1726, 2004.
  • [25] A. Roldán, J. Martinez-Moreno and C. Roldán, On interrelationships between fuzzy metric structures, Iran. J. Fuzzy Syst. 10 (2), 133-150, 2013.
  • [26] B. Schweizer ad A. Sklar, Probabilistic metric spaces, North-Holland, New York, 1983.
  • [27] S. Sedghi, N. Shobkolaei and I. Altun, Partial fuzzy metric space and some fixed point results, Commun. Math. 23 (2), 131-142, 2015.
  • [28] N. Shahzad and O. Valero, On 0-complete partial metric spaces and quantitative fixed point techniques in denotational semantics, Abstr. Appl 2013, 1-12, 2013.
  • [29] N. Shahzad and O. Valero, A Nemytskii-Edelstein type fixed point theorem for partial metric spaces, Fixed Point Theory Appl. 2015 (1), 1-15, 2015.
  • [30] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. 6 (2), 229-240, 2005.
  • [31] B.P. Varol and H. Aygün, Intuitionistic fuzzy metric groups, Int. J. Fuzzy Syst. 14 (3), 454-461, 2012.
  • [32] Y. Yue and M. Gu, Fuzzy partial (pseudo-)metric space, J. Intell. Fuzzy Syst. 27 (3), 1153-1159, 2014.
  • [33] L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (3), 338-353, 1965.
  • [34] D. Zhang and L. Xu, Categories isomorphic to FNS, Fuzzy Sets Syst. 104, 373-380, 1999.
There are 34 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Elif Güner 0000-0002-6969-400X

Halis Aygün 0000-0003-3263-3884

Publication Date December 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 6

Cite

APA Güner, E., & Aygün, H. (2022). A new approach to fuzzy partial metric spaces. Hacettepe Journal of Mathematics and Statistics, 51(6), 1563-1576. https://doi.org/10.15672/hujms.1115381
AMA Güner E, Aygün H. A new approach to fuzzy partial metric spaces. Hacettepe Journal of Mathematics and Statistics. December 2022;51(6):1563-1576. doi:10.15672/hujms.1115381
Chicago Güner, Elif, and Halis Aygün. “A New Approach to Fuzzy Partial Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 51, no. 6 (December 2022): 1563-76. https://doi.org/10.15672/hujms.1115381.
EndNote Güner E, Aygün H (December 1, 2022) A new approach to fuzzy partial metric spaces. Hacettepe Journal of Mathematics and Statistics 51 6 1563–1576.
IEEE E. Güner and H. Aygün, “A new approach to fuzzy partial metric spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, pp. 1563–1576, 2022, doi: 10.15672/hujms.1115381.
ISNAD Güner, Elif - Aygün, Halis. “A New Approach to Fuzzy Partial Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 51/6 (December 2022), 1563-1576. https://doi.org/10.15672/hujms.1115381.
JAMA Güner E, Aygün H. A new approach to fuzzy partial metric spaces. Hacettepe Journal of Mathematics and Statistics. 2022;51:1563–1576.
MLA Güner, Elif and Halis Aygün. “A New Approach to Fuzzy Partial Metric Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, 2022, pp. 1563-76, doi:10.15672/hujms.1115381.
Vancouver Güner E, Aygün H. A new approach to fuzzy partial metric spaces. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1563-76.

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A new approach to fuzzy partial metric spaces
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https://doi.org/10.15672/hujms.1115381

https://dergipark.org.tr/en/pub/hujms