A BRANCH‐AND‐BOUND ALGORITHM FOR THE MULTISTAGE CONTROL OF A FUZZY SYSTEM IN A FUZZY ENVIRONMENT

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Abstract
In this paper, the problem of determining a maximizing decision in the multistage control of a fuzzy system in a fuzzy environment is considered. In the fuzzy system under control, the state is assumed to be fuzzy, while the control, not fuzzy. The fuzzy environment is given by fuzzy constraints and fuzzy goals imposed on particular control stages. The number of control stages, i.e. the termination time, is assumed to be fixed and specified; the same applies to the initial state. The fuzzy decision is defined as the intersection of fuzzy goals and fuzzy constraints. For solving the above problem, a branch‐and‐bound algorithm is proposed. The algorithm is simple and relatively efficient. Two examples are given.

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