Pattern detection and cluster analysis with clustering validation using novel knowledge and accuracy measures for hesitant fuzzy sets

Hesitant fuzzy sets (HFSs) extend traditional fuzzy sets by allowing multiple membership values for each element. This paper introduces a new knowledge measure for HFSs, rigorously validated through systematic axiomatic analysis. Numerical examples demonstrate the measure’s effectiveness in capturing ambiguity and facilitating linguistic comparisons. Building on this knowledge measure, a hesitant fuzzy accuracy measure is proposed, that gives distinct values for different pairs of hesitant fuzzy elements (HFEs). Further, the proposed accuracy measure is utilized in pattern detection problems, showcasing its efficacy. Furthermore, the proposed measures are utilized in cluster analysis, using real-world data on flood impacts in Indian states (۲۰۱۲-۲۰۲۱). A clustering validation index, namely the contiguous density region index (CDR index) is also introduced in the context of HFSs. Comparative analysis reveals the proposed accuracy measure’s superior clustering performance, particularly at low confidence levels. This research contributes to the advancement of HFS theory and explores its potential applications in pattern recognition, cluster analysis and clustering validation.

کلیدواژه ها:

Hesitant Fuzzy Set ، Knowledge measure ، Accuracy measure ، Pattern detection ، Cluster analysis ، Cluster validation ، CDR index