The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such interpretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets.

The article discusses the topic of combining various numerical indicators (indexes, models, scales, etc.) into a new synthetic index, which will allow for effective decision making within the expert system. Mentioned problem already has a well-researched solution based on aggregation operators. However, the aggregation-based approach did not create a new, consistent decision-making index. Moreover, some problems may occur because the interaction between input data is omitted during the aggregation. The methods proposed in this paper will focus on the possibility of maintaining interactions between attributes. The described methods will then be applied to the real-life problem of monitoring and assessment of maintenance in an enterprise.

The uncertainty is a common problem in many areas of science. The best-studied variant is incomplete data where the values of some attributes are unknown. It turns out that even in this situation, many known classification methods fail. The objective of the work is to develop an effective classification method for uncertain data including pre-processing and uncertainty aware similarity-based algorithms. The problem of uncertainty is particularly important in medical diagnostics where incompleteness and uncertainty is often a natural and permanent feature of the data. The paper presents the evaluation of the proposed methods on two publicly available data sets and compare the effectiveness of the previous results.