Introduction to Multiple State Multiple Action Decision Theory and Its Relation to Mixing Structures,
ARMY ELECTRONICS COMMAND FORT MONMOUTH N J
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A general mathematical framework is developed which addresses the problem of determining an optimal, or near optimal, course of action, when the outcome of a given course of action is known to be influenced by an evolving state of nature. In this context the advantage of knowledge of the natural state is balanced by the cost of obtaining this information. Such a structure, when considered as functioning over a given time interval, permits employment of life cycle cost versus possible gain. All the mathematical structures and related entities, and the underlying properties thereof, are developed in a manner that such tradeoff studies are possible. The theoretical development as presented is related to that of statistical game theory but with a broader set of objectives. Multiple aspects for the state of nature, and sets of permissible action are allowed, with these actions being capable of simultaneous performance. This leads to the introduction of multiple state multiple action decision theory and its basic framework, the mixing structure. The concept of sensor mixes is defined and related to the possibility of decreasing loss by the spying on the state of nature. The cost of obtaining this information is then balanced against the gain obtained by knowledge of the natural state. A resulting figure of merit may be used to determine the desirability of each sensor mix.
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