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The geometry of three-way decision

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Abstract

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.

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  1. Department of Computer Science, University Of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Yiyu Yao

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Correspondence to Yiyu Yao.

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This article belongs to the Topical Collection: 30th Anniversary Special Issue

I would like to thank Professor Hamido Fujita for his constructive and supportive comments on three-way decision and his encouragement for writing the paper for the special issue. I am grateful to reviewers for their encouraging comments and suggestions. This work was partially supported by a Discovery Grant from NSERC, Canada.

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Yao, Y. The geometry of three-way decision. Appl Intell 51, 6298–6325 (2021). https://doi.org/10.1007/s10489-020-02142-z

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  • DOI: https://doi.org/10.1007/s10489-020-02142-z

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