An Analytical Method to Compute the Approximate Inverses of a Fuzzy Matrix With Max-Product Composition

This article is concerned with the problem of computing the approximate preinverses of a fuzzy matrix with max-product composition. Employing the weighted
$L_1$
distance, a variety of evaluation functions are defined according to the preselected weights, and then, an analytical method is proposed to determine all approximate preinverses of equal quality by minimizing the preselected evaluation function. Since only the approximate preinverses with fewer or preferably no zeros are acceptable for many practical applications, a criterion for selecting weights is established to ensure that the determined approximate preinverses are desirable. Some examples are given to illustrate our results.