The goal of multi-dimensional fuzzy analysis consists in discovering different properties in multi-dimensional fuzzy distributions represented either extensionally (database) or intensionally (knowledge base). In this paper we show how this approach can be applied to such problems as decision making and knowledge discovery in databases. For uniform and efficient representation of fuzzy knowledge and data we propose a technique of sectioned matrices. For carrying out logical inference we use a new operation of fuzzy resolution which is a generalization of the conventional resolution. With the help of this operation we find fuzzy prime disjunctions which later are used for making decisions in concrete situations. For discovering hidden dependencies in data a new fuzzy covering method is used.