Maximum-interval solutions of the given solution for system of addition-min fuzzy relational inequalities

Abstract

For a given solution to the addition-min fuzzy relational inequalities (FRIs) system, the maximum amplitude (the largest possible deviation from the given solution) and maximum-amplitude solution are proposed to measure its stability. In this paper, we formulate a single-variable optimization model and present some properties to the maximum amplitude. Based on these properties, an algorithm is proposed, which can quickly obtain the maximum amplitude and maximum-amplitude solution of the problem without decomposing the system into multiple subproblems. Additionally, the minimal solution associated with the maximum-amplitude solution can be derived by using the existing algorithm. By examining the relationship between the obtained minimal solution and the given solution, we are able to derive the maximum-interval solution. This maximum-interval solution is generally more “stable” than the maximum-amplitude solution for the addition-min FRIs system.