An Overview of Interval Analysis Techniques and Their Fuzzy Extensions in Multi-Criteria Decision-Making: What’s Going on and What’s Next?

Due to the diversity of information, many decision-making problems cannot be solved based on a single criterion. The complexity of assessment objects and the limitations of individual cognition cause the opinions given by experts uncertain, which further aggravates decision-making difficulties. Although fuzzy sets and intuitionistic fuzzy sets are proposed to express vague information, they still have the problem of losing information. As a tool to express uncertain information, interval techniques can effectively prevent the loss of information and improve the accuracy of decision-making. In this regard, many scholars applied interval analysis techniques and their fuzzy extensions to solve multi-criteria decision-making (MCDM) problems. This study reviews 195-related articles published from 2007 to 2022, and analyzes the research progress of interval analysis techniques and their fuzzy extensions in MCDM problems. Through bibliometrics analyses, publication and citation trends as well as productive countries can be intuitively and quantitatively obtained. Then, we review theories and methods regarding the combination of interval techniques and MCDM methods, and find that interval-valued fuzzy sets are extensively discussed and combined with TOPSIS. Next, real-world applications of these publications are reviewed, and we obtain that interval techniques are mainly used in supply chain selection. Finally, we propose future directions regarding interval techniques in MCDM problems. It is hoped that this study would be helpful for scholars and practitioners to carry out further research.