a fuzzy backward reasoning system which includes a memory section for storing a causality table having n × m elements , a first generating section for reading out the causality table from the memory section and generating basic and auxiliary matrix tables and an input effect matrix table , a second generating section for generating a minimum matrix table and a third generating section for generating from the basic and auxiliary tables a check matrix table . the invention further includes a modifying section for modifying the checking matrix table to selectively reset each flag therein in accordance with corresponding elements of the basic and minimum matrix tables and a fourth generating section for generating from elements having the flags set of the checking matrix table and the basic and minimum matrix tables a cause matrix table , wherein cause matrix table element interval data represents a certainty of a corresponding cause .