On partial fuzzy metric-preserving functions

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Arts and Science, Kocaeli University, 41380, Kocaeli, Turkey

Abstract

The target of this paper is to present partial fuzzy metric-preserving functions and characterize the functions $f:[0,1]\to[0,1]$ with this aspect. We give a characterization for partial fuzzy  metric-preserving functions considering the different t-norms. Also, we show that the topology induced by partial fuzzy metric does not preserve under these functions with  an example. Then we  give a characterization of those partial fuzzy metric-preserving functions which preserve completeness and contractivity under some conditions. Finally, we discussed the relation between fuzzy  metric preserving and partial fuzzy preserving functions.

Keywords

[1] B. Aldemir, E. Guner, E. Aydogdu, and H. Aygun, Some fixed point theorems in partial fuzzy metric spaces, J. Inst. Sci. Technol. 10 (2020), 2889–2900.
[2] M. A. Alghamdi, N. Shahzad, and O. Valero, On fixed point theory in partial metric spaces, Fixed Point Theory Appl.175 (2012).
[3] E. Aydogdu, B. Aldemir, E. Guner, and H. Aygun, Some properties of partial fuzzy metric topology, Int. Conf. Intell. Fuzzy Syst., Springer, Cham, 2020, pp. 1267–1275.
[4] H. Aygun, E. Guner, J.J. Minana, and O. Valero, Fuzzy partial metric spaces and fixed point theorem, Mathematics 10 (2022), no. 17, 3092.
[5] J. Borsik and J. Dobos, Functions whose composition with every metric is a metric, Math. Slovaca 31 (1981), 3–12.
[6] I. Demir, Fixed point theorems in complex valued fuzzy b-metric spaces with application to integral equations, Miskolc Math. Notes 22 (2021), no. 1, 153–171.
[7] I. Demir, Some soft topological properties and fixed soft element results in soft complex valued metric spaces, Turk. J. Math. 45 (2021), no. 2, 971–987.
[8] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), no. 3, 395–399.
[9] V. Gregori, J.J. Minana, and D. Miravet, Fuzzy partial metric spaces, Int. J. Gen. Syst. 48 (2019), no. 3, 260–279.
[10] V. Gregori, J.J. Minana, and O. Valero, A technique for fuzzifying metric spaces via metric preserving mappings, Fuzzy Sets Syst. 330 (2018), 1–15. 
[11] V. Gregori, S. Morillas, and A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy Sets Syst. 161 (2010), no. 16, 2193–2205.
[12] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets Syst. 115 (2000), no. 3, 485–489.
[13] E. Guner and H. Aygun, A new approach to fuzzy partial metric spaces, Hacettepe J. Math. Statist. 51 (2022), no. 6, 1563–1576.
[14] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334.
[15] S. Massanet and O. Valero, New results on metric aggregation, Proc. 16th Spanish Conf. Fuzzy Technol. Fuzzy Logic, Eur. Soc. Fuzzy Logic Technol., Valladolid, 2012, pp. 558–563.
[16] S. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994), no.1, 183–197.
[17] J.J. Minana and O. Valero, On partial metric preserving functions and their characterization, Filomat 34 (2020), no. 7, 2315–2327.
[18] S. Onbasıoglu, and B. Pazar Varol, Intuitionistic fuzzy metric-like spaces and fixed-point results, Mathematics 11 (2023), no. 8, 1902.
[19] T. Pedraza, J. Rodrıguez-Lopez, and O. Valero, Aggregation of fuzzy quasi-metrics, Inf. Sci. 581 (2021), 362–389.
[20] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983.
[21] S. Sedghi, N. Shobkolaei, and I. Altun, Partial fuzzy metric space and some fixed point results, Commun. Math. 23 (2015), no. 2, 131–142.
[22] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topology 6 (2005), no. 2, 229–240.
[23] L. A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), no. 3, 338–353.
Volume 14, Issue 10
October 2023
Pages 43-55
  • Receive Date: 04 October 2022
  • Revise Date: 01 June 2023
  • Accept Date: 19 July 2023