Min-Max Programming Problem Subject to Addition-Min Fuzzy Relation Inequalities

Abstract

A BitTorrent-like Peer-to-Peer file sharing system can be reduced into a system of addition-min fuzzy relation inequalities. Addition-min is a new composition and the solution set of addition-min fuzzy relation inequalities differs much from that of general max-t-norm fuzzy relation inequalities or equations. In order to avoid network congestion and improve the stability of data transmission, a min-max programming problem is proposed subject to addition-min fuzzy relation inequalities in this paper. Based on some relevant theorems on resolution, a novel algorithm is developed step by step to find an optimal solution of the proposed problem. Moreover, an application example is given to illustrate the feasibility and efficiency of the algorithm. At last, some further discussions are made concerning the optimal solution of the proposed problem.

Evaluation Model and Approximate Solution to Inconsistent Max‐Min Fuzzy Relation Inequalities in P2P File Sharing System

“…In what follows we shall denote the dual of order relation '<' and '≤' by the symbol '>' and '≥' , respectively. Obviously, the operator '≤' forms a partial order relation on and ( , ≤) becomes a lattice [34,36].…”

“…Fuzzy relation inequalities, as a special kind of inequalities, were also studied. It was recently found that a BitTorrent-like Peer-to-Peer (P2P) file sharing system could be reduced into a system of addition-min fuzzy relation inequalities [33][34][35][36][37][38][39]. Assume that there exist terminals, i.e., 1 , 2 , .…”

“…In [33][34][35][36], the quality requirement of download traffic of was considered as the total download speed that received file data from 1 , 2 , . .…”

Resolution of Max‐Product Fuzzy Relation Equation with Interval‐Valued Parameter

“…Fuzzy relation inequalities with addition-min composition were employed to describe the P2P file sharing system. Some properties of its solution set [38] and corresponding optimization models were studied [39][40][41]. Besides, bipolar fuzzy relation equations was another interesting research object.…”

Geometric Programming with Discrete Variables Subject to Max-Product Fuzzy Relation Constraints

“…Zhou and Ahat [17] investigated similar problem where the composition was replaced by max-product. Yang et al [18] investigated min-max programming problem subject to fuzzy relation inequality constraints with a special composition of addition-min. Yang et al [19] studied the single-variable term semi-latticized geometric programming subject to maxproduct fuzzy relation equations.…”