Sensitivity analysis on generalized fuzzy relation equations

Concerns a fuzzy relation equation xoA=b where x and b are input and output vectors and A is a state matrix with max-min operator `o´. The authors extend their previous work by relaxing the condition that the elements in vector b are strictly distinct and allowing the same values of membership to exist in b. They propose a solution procedure from the defined quasi-characteristic matrix that not only determines the solution set but also defines the types of solution set before the solution set is determined. Therefore, it provides an insight into the structure of fuzzy relation equations. Also by means of the quasi-characteristic matrix, the authors perform a sensitivity analysis on A to determine the set of state-matrices which has the same solution set with respect to the given output-vector