A review of three-way decision: Triadic understanding, organization, and perspectives

A theory of three-way decision is about thinking, problem-solving, and computing in threes or through triads. In this paper, we review fifteen years of research on three-way decision by using the philosophy-theory-application triad and the who-what-when triad. First, we discuss the philosophy, theory, and application of three-way decision. At the philosophy level, we delve into the philosophical roots and fundamental nature of three-way decision to reveal the underlying philosophical thinking. At the theory level, we provide an insightful analysis of the theory and methodology of three-way decision. At the application level, we examine the integration of three-way decision with other theories and their applications and effectiveness in real-world scenarios. Second, we focus on bibliometrics analytics by using the who-what-when triad, which attempts to answer a fundamental question of “who did what when”. We propose a $3\times 3$ model by applying the $3\times 3$ method of three-way decision. The first 3 is the author-topic-time triad. The second 3 represents a three-level analysis for each of the first three: (1) categorizing authors into the three levels of prolific authors, frequent authors, and occasional authors, (2) classifying topics into the three levels of the core topics, emerging topics, and to-be-explored topics, and (3) dividing articles into the three levels of initial investigations, further developments, and most recent studies. Finally, we perform a bibliometrics analysis of three-way decision articles by using the $3\times 3$ model of three-way decision. The results not only reveal the current status and trend of three-way decision research but also provide a road map for future research.