Fuzzy statistics-aided inference in experimental design

Abstract

Conducting research based on active influence on the examined object or process requires distinguishing an explained quantity, measured quantitatively, the possible changes of which will be considered as influencing it through a group of quantities considered as explanatory quantities. This approach implicitly postulates the existence of a cause-and-effect relationship between the explanatory quantities and the explained quantity. In practice, especially industrial practice, explanatory quantities are often called controlled factors. Knowledge of possible cause-and-effect relationships can be graded, from the most comfortable situation of the existence of appropriate binding equations and their exact solutions, through the existence of binding equations but without knowing the exact solutions, to the absence of such equations. While in the first case, experimental research serves to refine the results originally calculated for idealized models, in the second case, it is a necessary stage of identifying the parameters of the postulated model, and in the third case, it is a necessary stage of collecting data for which the simplest possible forecasting model will be constructed

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