A Heuristic Method to Compute the Approximate Postinverses of a Fuzzy Matrix

This paper considers the problem of computing the approximate inverses of a fuzzy matrix under max-min composition. A polynomial-time algorithm is proposed to construct an approximate postinverse by minimizing an evaluation function, which balances two different distance measures. The obtained approximate postinverse contains no zero columns unless the given fuzzy matrix itself contains zero rows. Subsequently, the techniques for solving fuzzy relational equations are applied to obtain all the approximate postinverses of equal quality.