Interval-solutions with respect to a given solution in fuzzy-relation-inequality system

Fuzzy-relation-inequality (FRI) systems with maximum-minimum operations have been recently introduced to model a Peer-to-Peer (P2P) network system. Each feasible scheme in such a P2P network is exactly a solution of the relevant FRI system. For embodying the stability of a feasible scheme, the biggest fluctuation allowed to a given solution is considered. In detail, considering the upward, downward and two-way fluctuation, we introduce and study the lower interval-solution, the upper interval-solution and the including interval-solution, respectively, with respect to a given solution. The corresponding biggest allowed fluctuations are named lower width, upper width and including width. The lower interval-solution could be found trivially. We propose some detailed approaches for finding the upper interval-solution and the including interval-solution, respectively. Several examples have been presented to verify the proposed resolution methods.