Solving on widest-interval solutions with the maximum width for a system of max-min fuzzy relational inequalities

The system of max-min fuzzy relational inequalities (FRI) was established to model the problems of instructional information resource allocation and peer-to-peer file-sharing systems. Considering the instability and fragility of the optimal solution, researchers design the widest-interval solution of the max-min FRI to allow the solution to fluctuate within a certain range. As a result, there are still numerous, or even infinite, widest-interval solutions in the system. To better demonstrate the differences among the various widest-interval solutions, this paper proposes the widest-interval solutions with the maximum width for the system. The widest-interval solutions with the maximum width, as its name indicates, have the largest interval width compared to other solutions. Consequently, it can contribute to the robust solution and stable system behavior. Built upon new theoretical insights, a novel solution method is developed to obtain widest-interval solutions with the maximum width. A numerical illustration is presented to demonstrate the detailed procedure of this method.