# Introduction

## A Theory of Three-way Decisions

A theory of three-way decisions is formulated based on the notions of acceptance, rejection and noncommitment. It is an extension of the commonly used binary-decision model with an added third option. Three-way decisions play a key role in everyday decision-making and have been widely used in many fields and disciplines.

The concept of three-way decisions was first introduced in rough set theory for interpreting the positive, negative and boundary regions. One can construct rules for acceptance from the positive region and rules for rejection from the negative region. When neither a decision of an acceptance nor a decision of rejection can be made, a third option of noncommitment is chosen. Recent investigations of three-way decisions move beyond rough set theory, with a long-term goal of developing a more general theory based on a tripartition of a universal set. A tripartition consists of three pair-wise disjoint subsets of the universe and their union is the universe. Depending on the construction and interpretation of a tripartition, it is possible to derive many concreted models, including rough sets, interval sets, three-valued approximations of a fuzzy set (e.g., shadowed sets), three-valued approximations of a many-valued logic, and many others.

Yao, Y.Y., An Outline of a Theory of Three-way Decisions. In: Yao, J., Yang, Y., Slowinski, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1-17. Springer, Heidelberg (2012).