Note on Intuitionistic Fuzzy Metric-like Spaces with Application in Image Processing

Tatjana Došenović, Dušan Rakić, Nebojša Ralević and Biljana Carić ()
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Tatjana Došenović: Faculty of Technology, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia
Dušan Rakić: Faculty of Technology, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia
Nebojša Ralević: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Biljana Carić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

Mathematics, 2024, vol. 12, issue 15, 1-19

Abstract: Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G -Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G -Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing.

Keywords: fixed point; intuitionistic fuzzy metric space; t -norm; image processing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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