The geometry of three-way decision

摘要

A theory of three-way decision concerns the art, science, and practice of thinking, problem solving, and information processing in threes. It explores the effective uses of triads of three things, for example, three elements, three parts, three perspectives, and so on. In this paper, I examine geometric structures, graphical representations, and semantical interpretations of triads in terms of basic geometric notions of dots, lines, triangles, circles, as well as more complex structures derived from these basic notions. I use examples from different disciplines and fields to illustrate the uses of these structures and their physical interpretations for triadic thinking, triadic computing, and triadic processing. Following the principles of triadic thinking, this paper blends together three common ways to think, namely, numerical thinking, textual thinking, and visual thinking.