METHODS OF TAKING INTO ACCOUNT UNCERTAINTY IN CONSTRUCTION OF LINGUISTIC SCALES

Abstract

The report presents the main aspects of the problem of constructing linguistic scales when applying metric classification in intelligent measuring systems. The measurement results obtained at the output of the measurement channels of the system are converted into a form that can be used in the future for fuzzy calculations, decision-making, diagnosis of the state of objects, as well as the need to adjust the parameters of objects. To obtain the final result, a metric classification is used, according to which a scale with a fuzzy linguistic variable is built on a metric medium, which allows to determine the equivalence class to which the measurement result corresponds.It is shown that when establishing linguistic scales it is necessary to take into account the following components of uncertainty: uncertainty from the vagueness of the semantic rule, which determines the boundaries of the term set of a linguistic variable, uncertainty from incomplete identification of the object of measurement (definitive uncertainty); uncertainty from the instability of the latent parameter to be measured; instrumental uncertainty.It is established that when constructing linguistic scales, two methods of taking into account uncertainty can be used, which in turn correspond to two algorithms of fuzzy classifier operation. The first method is that the uncertainty components related to the scale and the object of measurement are used to construct the scale, and the instrumental component of uncertainty is used to design the measurement result as a fuzzy number. Then, according to the algorithm of the fuzzy classifier, the composition of the membership functions of the term set of the linguistic variable and the fuzzy number is found, and the required equivalence class is found by the center of gravity of the composition result. The second method is to find the total uncertainty for all components and take it into account when constructing a linguistic scale. Then the equivalence class is determined by the maximum cross section of the membership functions of the term set of the linguistic scale with the measurement result, or by the maximum and minimum cross section. Most often, to solve such a problem, a fuzzy appendix to the MatLab package is used, which determines the activated equivalence classes, the membership functions of which are modified in accordance with the maximum and minimum cross-section. Therefore, the authors of the report chose the second method of taking into account the uncertainty and analyzed the relationship between the fuzzy index of membership functions of individual terms of the linguistic variable and the total uncertainty.