Finding minimal solutions to the system of addition-min fuzzy relational inequalities

In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables.

Automated summary

This paper studies the properties of minimal solutions in an addition-min fuzzy relational inequalities system and proposes an iterative algorithm to find these minimal solutions. The proposed algorithm not only efficiently finds the minimal solutions, but also discovers multiple minimal solutions in different iterative sequences of variables.