Fuzzy sharing problem (Q1263511)

A generalization of the sharing problem viewed as a method of finding an equitable distribution of resources presented in the paper pertains to modelling sink nodes of the network with membership functions. The objective is to maximize the smallest value of all membership functions representing the degree of satisfaction for the flux among all sink nodes: maximize min \(y_ t(f(t))\), \(t\in T\). Here \(y_ t\) denotes a degree of satisfaction for the flux while T stands for a set of all sink nodes of the network. Furthermore, the membership function \(y_ t(f(t))\) takes the form of a piecewise linear function. The provided algorithm is polynomially bounded.