Uniqueness of solution in FLP under parameter perturbations
Given is the following interval linear programming problem: \[ (1)\quad \min cx,\quad s.t.\quad Ax\leq B\quad and\quad x\geq 0, \] in which the coefficients on the right hand side (i.e. the components of the vector B) are intervals. The authors establish necessary and sufficient conditions for all the problems due to (1), with varying vector b (b\(\in B)\), having the same unique optimal solution. Subsequently, the authors propose to use this result in the stability (sensitivity) analysis of the solution of a fuzzy linear programming problem with varying values of some parameters in the membership functions of the fuzzy goal and the constraints. This is possible because in such a case the fuzzy linear programming problem resolves itself into a certain crisp equivalent problem of the form (1). It should be said, however, that this concerns only the uniqueness of the solution of the problem dual to this equivalent one. The authors do not draw any conclusions about the properties of the optimal solution of the original problem, although both the title of the paper and the abstract seem to announce such conclusions.
scientific article; zbMATH DE number 4133854