Interval Solution to Fuzzy Relation Inequality With Application in P2P Educational Information Resource Sharing Systems

Max-min fuzzy relation inequalities have recently been introduced to describe the peer-to-peer (P2P) educational information resource sharing systems. It is well known that the complete solution set of the max-min fuzzy relation system is fully determined by its minimal solutions. However, solving all the minimal solutions has been proven to be equivalent to the set-covering problem, which is NP-hard. Without solving the complete solution set, some specific solutions can be obtained through the corresponding fuzzy relation optimization problems. However, these solutions are usually unstable and fragile. Any minor fluctuations to the components of these specific solutions will cause them to be no longer feasible. In this work, we define and study the widest interval solution of a max-min fuzzy relation inequality system for the first time. The interval solution allows the solution to fluctuate within some range. The fluctuation range is determined by the width of the interval solution. We propose a novel resolution method for searching for the widest interval solution. The resolution method is carried out by detailed procedures and illustrated by a numerical example.