This work proposes fuzzy logics system with use of math apparatus of type-2 interval fuzzy sets. The present paper formulates the task of developing a formal approach, which would enable analyzing fuzzy systems in terms of their capability to describe uncertainties of input information using interval membership functions. In contrast with the type-1 fuzzy sets-based systems, which result in membership value in the form of a single digit, the type-2 fuzzy sets allow to obtain an interval of values of the final linguistic variable. This interval is the result of the uncertainties, which are present in the incoming data, as well as of the uncertainties, related to the nature of presentation of expertise. These peculiarities allow the interval fuzzy sets-based system to function operating with less informative incoming data as well as in case of data omission. These conditions make function of the type-1 fuzzy logical systems impossible. That is why use of the fuzzy logics systems with interval functions is seen expedient compared to the usual type-1 systems. However, such models may result in wide interval output. In case the resulting output of the model may not be used to solve a task or is not satisfactory for the developer, it is better to get to use of the three-dimension membership functions while obtaining the outcome as a linguistic interpretation. This work also describes the stages of building fuzzy knowledge base using the common rule of use of experimental data. This work also proposes an approach to evaluate the parameters of gauss type-2 membership interval functions by defining the membership functions permissible measuring ranges which allow for adequate modelling. As long as use of the interval membership function provides for the fuzzy system output value with certain interval, taking into account certain vector of input values, this work provides expert recommendations on how to evaluate the interval output.

A type-2 interval generalizing fuzzy model is proposed for monitoring complex systems’ states. A set-theoretic approach is proposed to generalize the results of type-2 fuzzy models with interval membership functions. The study of the correspondence of expert assessments to the output value of the generalizing fuzzy model over the observation interval is presented. Examples of the use of generalizing fuzzy model type-2 in the task of monitoring the conditions of an artesian well are given. It is shown that in order to improve the quality of decisions made, the expert needs to pay attention to the value of the interval output of the generalizing type-2 fuzzy model. Recommendations are presented to experts to improve decision-making regarding the estimation of the output interval of the generalizing model.