Lexicographic Minimum Solution to the System of Fuzzy Relation Inequalities With Addition-Min-Product Composition

The addition-min-product fuzzy relation inequalities were recently introduced to model peer-to-peer file-sharing systems, considering scenarios where the terminals transmit their local file data at varying quality levels. Previous research primarily focused on min–max fuzzy relation programming, which assumed equal treatment for all terminals. However, this approach is inadequate when the terminals need to be differentiated or assigned fixed priority grades. To address network congestion while considering terminal priority, this study explores the lexicographic minimum solution for the addition-min-product FRIs. We propose a detailed algorithm to compute the lexicographic minimum solution, associated with a numerical illustrative example.