A Decade of Picture Fuzzy Sets in Multi-Criteria Decision-Making: A Comprehensive Review of Trends, Gaps, and Future Directions

Abstract

Picture fuzzy sets (PFSs) are extensively utilized in medical diagnostics and multi-criteria decision-making (MCDM) due to their enhanced flexibility, distinguishing capability, and applicability in handling uncertainty and hesitation, particularly in complex domains such as healthcare, transportation, environmental decision-making, artificial intelligence (AI), and machine learning. Guided by four research questions, this review employed descriptive statistics to analyse the extent of research focused on PFSs. An intensive literature search was performed across leading publishers, including IEEE Xplore, SpringerLink, ScienceDirect, the Association for Computing Machinery (ACM), and the Multidisciplinary Digital Publishing Institute (MDPI). Findings revealed significant scholarly efforts to adopt PFSs in healthcare (22.6%), transportation (24.5%), environmental decision-making (7.5%), AI and machine learning (5.7%), and other domains (39.6%). Research from 2013 to 2024 demonstrated notable advancements in mathematical operations and extensions (25%), aggregation operators and similarity measures (30%), hybrid approaches and MCDM applications (20%), domain-specific implementations (15%), and theoretical developments (10%). MCDM emerged as a prominent tool for enhancing decision-making across diverse fields. The study highlights the need to explore additional areas of application for PFSs, particularly in refining distance measures to further enhance their utility.