# Binary Relations

• Po-Lung Yu
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 30)

## Abstract

As mentioned in Section 1.1, if the preference over Y is clear and complete enough to identify a certain y* ∈ Y as the best choice, then x* ∈ f −1(y*) will be a final choice of the decision problem. If one can specify a υalue function υ(y): YR 1, so that υ(y 1) >υ(y 2) implies that y 1 is prefered to y 2, then the decision problem reduces to max υ(f(x)) over xX. Unfortunately, such a value function proves difficult to obtain in practice. Before we make strong assumptions to construct a “reasonable” value function (Chapter 5), it may be more important for us to understand what “preference” is and what its basic characteristics are. We shall study these in terms of binary relations that encompass real-valued functions as special cases.

## Keywords

Partial Order Binary Relation Preference Information Weak Order Transitivity Property
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

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