An optimization problem on the image set of a (max, min) fuzzy operator

The paper deals with the unsolvability of (max, min) linear equation systems with coefficients in the unit interval (for fuzzy systems), or in an arbitrary real interval (general case). If the system has no solution, then the nearest vector to the right-hand side of the system for which the system is solvable is computed. A polynomial algorithm for the problem is presented. The method is illustrated by numerical examples.