How to take care of routine decision-making, and leave important decisions to an expert: case study

One of the possible applications of control to decision making is as follows. Usually, our decision is based on the values of the characteristics x_i that we do not measure directly. We can measure the values of some other characteristics y_j that are related to x_i, and we know the rules (formulated in terms of a natural language) that describe the relationship between these two classes of characteristics. If we apply fuzzy control technique to measured values of y_j, we get estimates for x_i. By comparing these estimates with the desired bounds, we make a decision. This method works fine if the estimates for x_i are radically different from the bounds. If the estimates are close to the bounds, then, since these estimates are only approximate, we may make a wrong decision. To prevent that, we take into consideration that the membership functions (used to estimate x_i) are only approximately known. As a result, we can compute the explicit interval of possible values of x_i, and by comparing this interval with the bound, either make a decision (if the entire interval is inside or outside these bounds), or (if some points from the interval are inside, and some are outside) refer the decision-making to an expert