A Study of Hausdorff Measure in Fuzzy Soft Metric Spaces
DOI:
https://doi.org/10.29304/jqcm.2022.14.4.1097Keywords:
Fuzzy soft set, Continuous t-conorm, Fuzzy soft metric space, Generalized Hausdorff measure, Fuzzy distance functionAbstract
In fields such as mathematics, statistics, computer science, etc., the theory of fuzzy metric spaces is crucial. In this work, a new significant characteristics of the space of fuzzy soft metric are presented, following Kider's (2020) proposal of the fuzzy soft metric model. furthermore, to study hyperspaces in terms of this specific fuzzy soft metric notion. A fuzzy soft distance between two fuzzy soft compact sets is created. A formulation has been proposed for establishing a Hausdorff fuzzy soft metric on the collection of non-empty fuzzy soft compact subsets. Additionally, a variety of essential features of the Hausdorff fuzzy soft metric concept are described.
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References
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[4] Q. Zhang, J. Hu, J. Feng, A. Liu, and Y. Li, “New similarity measures of Pythagorean fuzzy sets and their applications,” IEEE Access, vol. 7, pp. 138192–138202, 2019.
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[8] P. Dutta, “Medical diagnosis via distance measures on picture fuzzy sets,” Adv. Model. Anal. A, vol. 54, no. 2, pp. 657–672, 2017.
[9] I. Kramosil and J. Michálek, “Fuzzy metrics and statistical metric spaces,” Kybernetika, vol. 11, no. 5, pp. 336–344, 1975.
[10] A. George and P. Veeramani, “On some results in fuzzy metric spaces,” Fuzzy sets Syst., vol. 64, no. 3, pp. 395–399, 1994.
[11] A. George and P. Veeramani, “On some results of analysis for fuzzy metric spaces,” Fuzzy sets Syst., vol. 90, no. 3, pp. 365–368, 1997.
[12] L. D. R. Kočinac, “Selection properties in fuzzy metric spaces,” Filomat, vol. 26, no. 2, pp. 305–312, 2012.
[13] S. Kumar and D. Miheţ, “G-completeness and M-competeness in fuzzy metric spaces: A note on a common fixed point theorem,” Acta Math. Hungarica, vol. 126, no. 3, pp. 253–257, 2010.
[14] V. Gregori and S. Romaguera, “On completion of fuzzy metric spaces,” Fuzzy sets Syst., vol. 130, no. 3, pp. 399–404, 2002.
[15] V. Gregori, J. A. Mascarell, and A. Sapena, “On completion of fuzzy quasi-metric spaces,” Topol. Appl., vol. 153, no. 5–6, pp. 886–899, 2005.
[16] V. Gregori, S. Morillas, and A. Sapena, “On a class of completable fuzzy metric spaces,” Fuzzy sets Syst., vol. 161, no. 16, pp. 2193–2205, 2010.
[17] V. Gregori, J.-J. Miñana, and S. Morillas, “A note on local bases and convergence in fuzzy metric spaces,” Topol. Appl., vol. 163, pp. 142–148, 2014.
[18] J.-F. Tian, M.-H. Ha, and D.-Z. Tian, “Tripled fuzzy metric spaces and fixed point theorem,” Inf. Sci. (Ny)., vol. 518, pp. 113–126, 2020.
[19] A. Khalid and M. Abbas, “Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory,” Int. J. Fuzzy Syst., vol. 17, no. 3, pp. 490–497, 2015.
[20] J. Rodrı́guez-López and S. Romaguera, “The Hausdorff fuzzy metric on compact sets,” Fuzzy sets Syst., vol. 147, no. 2, pp. 273–283, 2004.
[21] J. Kider, “Some Properties of Fuzzy Soft Metric Space,” Al-Qadisiyah J. Pure Sci., vol. 25, no. 3, pp. 46–61, 2020.
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Published
2022-12-02
How to Cite
Mohammedali, M. N., Sadiq, F. A., & Sabri, R. I. (2022). A Study of Hausdorff Measure in Fuzzy Soft Metric Spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(4), Stat. Page 11–18. https://doi.org/10.29304/jqcm.2022.14.4.1097
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Statistic Articles
