The matrix representation of fuzzy knowledge and its application to the expert systems design

An approach to the diagnostic type expert systems design based on the special matrix representation of fuzzy predicates in the attribute model of the problem domain is presented. Intensive representation of predicates by means of sectional matrices is an analogue of the conjunctive normal form. Rules, positive examples and negative examples (in general, all fuzzy) can be used to form knowledge base. Diagnostics problem is thought of as finding some attribute values provided that the information about other attribute values is available. Logical inference is based on an equivalent transformation of the matrix to that containing all prime disjuncts by using the operation < xk > of fuzzy resolution. Two strategies to carry out such transformation are described. On the basis of formalism presented the expert system shell EDIP is developed, the first version of that is non-fuzzy and the second one allows working with fuzzy data and conclusions.