On partial fuzzy metric-preserving functions

Document Type : Research Paper


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


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.


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Volume 14, Issue 10
October 2023
Pages 43-55
  • Receive Date: 04 October 2022
  • Revise Date: 01 June 2023
  • Accept Date: 19 July 2023