Heterogeneous formal context and its decomposition by heterogeneous fuzzy subsets

Fuzzy relations are the mappings which are intensively studied in decision, reasoning, or data analysis. We propose a method for decomposition of heterogeneous formal context by heterogeneous fuzzy subsets, which allows representing the heterogeneous structure of truth degrees for each object, heterogeneous structure of truth degrees for each attribute and heterogeneous structure of truth degrees for relationship between each pair of object and attribute. We formulate and prove the properties of decomposition in heterogeneous extension of Formal concept analysis. We put emphasis on the role of special heterogeneous formal concepts which are generated from heterogeneous singleton fuzzy subsets. We illustrate our novel results in our running example of personal requirements for accommodation as the natural continuation of our previous studies.