Some New Results on Partial Fuzzy Metric Spaces

Authors

  • Amenah Kareem Yousif Department of mathematics, College of Education for pure Sciences, University of Thi-Qar, Iraq
  • Mohammed Jassim Mohammed Department of Mathematics, College of Sciences, University of Basrah, Iraq

DOI:

https://doi.org/10.32792/jeps.v14i3.544

Keywords:

Partial fuzzy co-metric spaces, strong partial fuzzy metric spaces, strong Partial fuzzy co-metric space, t-conorm.

Abstract

   In this work, we introduce a different interpretation of the notion of a partial fuzzy metric, which we refer to as a partial fuzzy co-metric. We define a partial fuzzy co-metric from a t-conorm and compare it with partial fuzzy metric, in contrast to the conventional approach to the theory of partial fuzzy metric spaces, which is based on the use of a t-norm. Here, we limit the scope of our analysis to Sedghi's definition of partial fuzzy metrics. Additionally, we proposed and compared the ideas of strong partial fuzzy co-metric spaces and strong partial fuzzy metric spaces. We also presented a few examples of these novel ideas.

References

[ 1] Zadeh L. A.," Fuzzy sets," Inform. Control, 8), 338–353, 1965.

[ 2] Kramoosil I., and Michalek J.," Fuzzy metric and statistical metric spaces," Kybernetika 11 336-344, 1975.

[ 3] George A., and Veeramani P.," On some results in fuzzy metric spaces," Fuzzy Sets and Systems 64 (3) 395-399, 1994.

[ 4] Matthews S.G.," Partial Metric Topology," Annals of the New York Academy of Sciences 728 183-197, 1994.

[ 5] Amal M. Hashim, "Fixed Point of Generalized Weakly Contractive Maps in Partial Metric Spaces,", Jnanabha, Vol. 46, 155-166, 2016.

[ 6] Amal M. Hashim, Athraa F. Abd Ali, "A Suzuki Type Fixed Point Theorems for a Generalized Hybrid maps on a Partial Hausdorff Metric Spaces," Basrah Journal of Science (A), Vol. 35 (1), 51-60, 2017.

[ 7] Amal M. Hashim, Haneen A. Bakry," Fixed points theorems for ciric' mappings in partial b-metric space," Basrah Journal of Science, Vol.37(1), 16-24, 2019.

[ 8] Camarena J.G., Gregori V., Morillas S., and Sapena A.," Two-step fuzzy logic-based method for impulse noise detection in colour images," Pattern Recognition Letters 31 (13) 1842-1849, 2010.

[ 9] Grecova S., and Morillas S.," Perceptual similarity between color images using fuzzy metrics," Journal of Visual Communication and Image Representation 34 230-235, 2016.

[ 10] Gregori V., Minana J.J., and Morillas S.,"Some questions in fuzzy metric spaces," Fuzzy Sets and Systems 204 71-85, 2012.

[ 11] Yue, Y., Gu, M.," Fuzzy partial (pseudo-) metric space," J. Intell. Fuzzy Syst. 27(3), 1153–1159, 2014.

[ 12] Sedghi S., Shobkolaei N., and Altun I., "Partial fuzzy metric space and some fixed point results," Communications in Mathematics, 23, 131-142, 2015.

[ 13] Gregori, V., Minana, J.J., Miravet, D., "Fuzzy partial metric spaces," Int. J. Gen. Syst. 48(3), 260–279 ,2019.

[ 14] Noori F. AL-Mayhi and I. H. Radhi, "Some problems related to fuzzy metric space," University of ALQadissiya, 2012.

[ 15] Olga G., Juan J. Minana, A. Sostak and Oscar Valero, "On t-Conorm based fuzzy (pseudo) metrics," Axioms, 9(3), 78, 2020.

[ 16] Klement, E.P.; Mesiar, R.; Pap, E," Triangular norms, Position paper II, General constructions and parametrized families," Fuzzy Sets Syst. 145, 411–438, 2004.

Downloads

Published

2024-09-01

Issue

Vol. 14 No. 3 (2024): JOURNAL OF EDUCATION FOR PURE SCIENCE- UNIVERSITY OF THI-QAR

Section

Articles

License

Copyright (c) 2024 Journal of Education for Pure Science- University of Thi-Qar

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright Policy

Authors retain copyright of their articles published in the Journal of Education for Pure Science (JEPS).

By submitting their work, authors grant the journal a non-exclusive license to publish, distribute, and archive the article in all formats and media.

License

All articles published in JEPS are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

This license permits unrestricted use, distribution, and reproduction in any medium, provided that the original author(s) and the source are properly credited.

Author Rights

Authors have the right to:

  • Share their articles on personal websites, institutional repositories, and academic platforms

  • Reuse their work in future research and publications

  • Distribute the published version without restriction

Journal Rights

The journal retains the right to:

  • Publish and archive the articles

  • Include them in indexing and archiving systems such as LOCKSS and CLOCKSS

  • Promote and disseminate the published work

Responsibility

The contents of all articles are the sole responsibility of the authors. The journal, editors, and editorial board are not responsible for any errors, opinions, or statements expressed in the published articles.

Open Access Statement

JEPS provides immediate open access to its content, supporting the principle that making research freely available to the public enhances global knowledge exchange.

This work is licensed under a Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/