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.
All these types of information naturally lead to partial orders: - 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 many practical situations, we are analyzing a complex system that consists of several subsystems. Each subsystem can be described as a separate ordered space. To get a description of the system as a whole, we must therefore combine these ordered spaces into a single space that describes the whole system.
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Technical Report: UTEP-CS-11-28
Published in International Journal of Innovative Management, Information & Production (IJIMIP), 2011, Vol. 2, No. 4, pp. 10-28.