Abstract: A fuzzy backward reasoning system which includes a memory section for storing a causality table having n.times.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.