Stability of a majority efficient solution of a vector linear trajectorial problem

The multicriteria problem of majority choice on a system of subsets of a finite set with linear partial criteria (MINSUM) is considered. Sufficient and necessary conditions of preserving majority efficiency by an efficient trajectory under " small " perturbations of vector criterion coefficients have been found. Lower and upper attainable estimates of the stability radius of a majority efficient trajectory have been obtained. In the papers [1,2] stability of different types of efficient solutions (optimal by Pareto, Smale, and Slater) of a vector trajectorial problem was investigated. Sufficient and necessary conditions of local stability (the property of a trajectory to preserve appropriate efficiency under " small " independent perturbations of vector criterion parameters) of such solutions were presented. Lower attainable estimates of stability radii of such trajectories, and formulas in several cases, were obtained. A summary of these results can be found in [3]. In this work the parralel results have been obtained for a majority efficient solution being an element of the Pareto set. Note that the papers [4–14] are devoted to various types of stability of the whole Pareto set of vector discrete optimization problems. 1 Definitions and properties As in [1], we consider a class of vector discrete optimization problems described with the following model.