Linear Programming Subject to the Secondary Maximum Minimum Fuzzy Relation Inequalities Constraint

A study focuses on a linear programming problem that involved a special fuzzy relation inequality (FRI) system, herein referred to as a secondary maximum minimum (SecMaxMin) FRI system. The SecMax-Min FRI system defines the conditions for attaining secondary maximum values within the inequalities. A linear programming problem, constrained by the SecMax-Min FRI, serves as an effective tool for formulating the minimum total cost of a wireless peer-to-peer network system. It takes into account the availability of candidate server peers for each user peer. In this research, the characteristics of the SecMax-Min FRI system are systematically presented, and algorithms for solving the associated programming problem are rigorously deduced. Furthermore, illustrative examples are offered to validate the efficiency and feasibility of the algorithms proposed.