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