SOLUTION ALGORITHMS FOR FUZZY RELATIONAL EQUATIONS WITH MAX-PRODUCT COMPOSITION

The conditions for the existence of an inverse solution to the max-min composition of fuzzy relational equations have been well documented s ince the original work by Sanchez [30, 31]. These same existence theor ems have been extended to the t-norm composition of relational equatio ns, in which the max-product composition is a member [5, 13, 26]. Seve ral studies [8, 15, 24, 33, 34, 38] have shown that the max-min operat or may not always be the most desirable fuzzy relational composition a nd in fact the max-product operator was superior in these instances. T his paper reviews the algorithms necessary to determine the complete s olution of the inverse for fuzzy relational equations with max-product composition. (C) 1998 Published by Elsevier Science B.V.