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principles_of_uncertainty_in_system_science

PRINCIPLES OF UNCERTAINTY IN SYSTEMS SCIENCE

George J. Klir

There are three inseparable principles: Principle of minimum uncertainty: ���.. Principle of maximum uncertainty: ���. Principal of uncertainty invariance: �

These principles may also be viewed as principles of uncertainty-based information. The common thrust of them is that they are sound information safeguards in dealing with systems problems. They guarantee that when we deal with any systems problem, we use all information available, we do not unwittingly use information that is not available, and we do not lose more information than inevitable. The three principles apply to nondeterministic systems, in which relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) is formalized with a mathematical theory suitable for each application (probability theory, possibility theory, evidence theory, etc.). The principles can be made operational only if a well-justifies measure of uncertainty in the theory employed is available. Since types and measures of uncertainty substantially differ in different uncertainty theories, the principles result in considerable different mathematical problems when we move from one theory to another. When uncertainty is reduced by taking an action (performing a relevant experiment and observing the experimental outcome, searching through an archive and finding a relevant document, etc.), the amount of information obtained by the action can be measured by the amount of uncertainty reduced � the difference between the a priori uncertainty and a posteriori uncertainty. Due to this connection between uncertainty and information, the three principles of uncertainty may also be viewed as principles of information. Information of this kind is usually called uncertainty-based information [Klir & Wierman, 1999].

Principle of Minimum Uncertainty The principle of minimum uncertainty is an arbitration principle. It facilitates the selection of meaningful solutions from a solution set obtained by solving any problem in which some initial information is inevitably lost. By this principle, we should accept only such solutions for which the amount of lost information is minimal. This is equivalent to accepting solutions with the minimum relevant uncertainty (predictive, prescriptive, etc.). A major class of problems for which the principle of minimum uncertainty is applicable are simplification problems. When a system is simplified, it is usually unavoidable to lose some information contained in the system. The amount of information that is lost in this process results in the increase of an equal amount of relevant uncertainty. Examples of relevant uncertainties are predictive, retrodictive, or prescriptive uncertainty. A sound simplification of a given system should minimize the loss of relevant information (or increase in relevant uncertainty) while achieving the required reduction of complexity. That is, we should accept only such simplifications of a given system at any desirable level of complexity for which the loss of relevant information (or the increase in relevant uncertainty) is minimal. When properly applied, the principle of minimum uncertainty guarantees that no information is wasted in the process of simplifications. Given a system formulated within a particular experimental frame, there are many distinct ways of simplifying it. Three main strategies of simplification can readily be recognized. � simplifications made by eliminating some entities from the system (variables, subsystems, etc.) � simplifications made by aggregating some entities of the system (variables, states, etc.) � simplifications made by breaking overall systems into appropriate subsystems.