One of the main objectives of science and engineering is to help people select the most beneficial decisions. To make these decisions,
- we must know people's preferences,
- we must have the information about different events -- possible consequences of different decisions, and
- since information is never absolutely accurate and precise, we must also have information about the degree of certainty.
- For preferences, a < b means that b is preferable to a. This relation is used in decision theory.
- For events, a < b means that a can influence b. This causality relation is used in space-time physics.
- For uncertain statements, a < b means that a is less certain than b. This relation is used in logics describing uncertainty such as fuzzy logic.
In this paper, we consider the general problem of how to combine two ordered spaces A and B into one. We also analyze which properties of orders are preserved under the resulting products.