Dynamic Picture Fuzzy Sets and Its Applications

Traditional picture fuzzy sets (PFSs) cannot capture temporal dynamics in dynamic uncertainty scenarios. This paper proposes dynamic picture fuzzy sets (DPFSs) and corresponding similarity measures. DPFSs integrate a discrete time set into the PFS framework, retaining the four-dimensional membership structure (positive, neutral, negative, refusal) while modeling time-dependent variations, and their basic operations and key properties are rigorously proven. Six types of dynamic similarity measures (Hamming, Euclidean, Minkowski, Chebyshev, Lambert, absolute sum-difference) are constructed, which are divided into Type-I (excluding refusal degree) and Type-II (including refusal degree), and time weights with a decay factor are incorporated to emphasize the cumulative effect of recent data. Two practical applications validate the effectiveness of the proposed methods: time-aware supplier selection (a multi-criteria decision-making scenario) can consistently identify the optimal alternative by amplifying the advantages of recent performance, and type 2 diabetes risk assessment (a medical diagnosis scenario) can capture dynamic symptom progression to provide clinically meaningful risk classifications, with both applications showing high consistency across different measures.