# 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).