Fuzzy backward reasoning system and expert system utilizing the same

An expert system for controlling a target apparatus comprising:

• supplying means for supplying n states of the target apparatus (n is an integer and larger than or equal to 2);
• reasoning means for receiving the n states as n results from said supplying means and performing fuzzy backward reasoning for a data representing the n results and causality data to generate certainties of m causes (m is an integer and larger than or equal to 2),
• wherein each of the certainties is represented in a cause matrix table having m elements, each of which is represented by an interval data, and the causality data is represented by a causality matrix table having m.times.n elements, each of which indicates a membership grade of a corresponding cause to a corresponding result and is represented by an interval data, and
• wherein in the fuzzy backward reasoning said reasoning means converts the n result data into a result matrix table having n elements, each of which is represented by an interval data, performs .epsilon.- and .epsilon.-compositions for the result and causality matrix tables to generate first and second matrix tables, generates from the first matrix table a third matrix table having m elements, each of which represent a least upper bound value of a corresponding row of the first matrix table, generates from the first and second matrix tables a check matrix table having m.times.n elements, each of which represents a possibility of influence to the certainty of a corresponding cause, and generates the cause matrix table from the first, third and check matrix tables, the cause matrix table element interval data representing a certainty of a corresponding cause;
• control means for controlling the target apparatus based on the certainties of the elements of the cause matrix table.