This paper describes a federated learning model capable to process imprecise and missing data. Federation learning is a technique to solve the problem of data governance and privacy by training algorithms without exchanging the data itself. The performance of the proposed method is demonstrated on medical data of breast cancer cases. Results for different data loss scenarios and corresponding measures of classification quality are presented and discussed.

The article deals with the problem of selecting the most appropriate attributes for a given classification method with the use of inclusion and similarity measures for interval-valued fuzzy sets. These types of measures with uncertainty were introduced using partial or linear order. The article introduces a modified IV-Relief algorithm using the above-mentioned measures. The theoretical considerations were supported by the analysis of the effectiveness of the proposed algorithm on a well-known dataset on breast cancer diagnostics. The proposed methods make it possible to extend the recognized classification methods so that they operate on uncertain data.

The problem of measuring the degree of entropy based on precedence indicator and similarity measures under conditions of uncertainty or imprecision was studied. So we call back to the notion of precedence and similarity measures of interval-valued fuzzy sets (IVFSs) and we construct an entropy measure with uncertainty by applying for IVFSs of different orders. In addition, we discuss the impact of entropy measures reflecting the uncertainty in the decision-making problem that employed these new measures in the problem of missing values.

In this contribution we propose new methodology to compare interval-valued fuzzy cardinal numbers (IVFCN). The new methods are based on interval subsethood measures which take into account widths of the intervals. An application of introduced methodology is presented on an example of decision algorithm for medical diagnosis support.