Vietoris-Rips Complex Induced by Intuitionistic Fuzzy Distance Measure

This paper proposes a method to extract qualitative information from uncertain datasets using the intuitionistic fuzzy distance measure within the context of Topological Data Analysis (TDA). TDA is a field that seeks to extract topological features from datasets, focusing on qualitative rather than quantitative information, such as the number of connected components, loops, and voids. TDA assigns a shape to the given data called simplicial complexes, which can be constructed in various ways. One such method is the Vietoris-Rips Complex, which is generated by distance measures. In this paper, we propose an Intuitionistic Fuzzy Vietoris-Rips Complex (IFVRC) generated by an intuitionistic fuzzy distance measure to demonstrate the effectiveness of this approach in solving machine learning problems. Our experimental results using classification example demonstrate that IFDMs can be used to extract qualitative information with Intuitionistic Fuzzy Sets (IFSs).