Optimization method for solving complex fuzzy equations

A formal mathematical model of a complex equation based on a composition (convolution) of fuzzy correspondences is proposed. The direct and inverse problems (the problem of fuzzy diagnostics) are formulated. The concept of reducing the initial problem to an extreme one is investigated, which makes it possible to find a guaranteed solution to the inverse problem. A practical approbation of the proposed methodology for analyzing and obtaining solutions to complex equations in a fuzzy inverse formulation is carried out.