Optimal management model in BitTorrent-like peer-to-peer (P2P) file sharing system can be reduced into a min-max programming problem subject to addition-min fuzzy relation inequality. To deal with such problem, we introduce the concept of optimal vector. Besides, a novel optimal-vector-based (OVB) algorithm is developed to find a minimal optimal solution. Based on practical application consideration, solution obtained by the OVB algorithm is theoretically demonstrated to be better than or equal to that obtained by the existing method. Advantage of our proposed OVB algorithm is illustrated by detailed numerical examples.

In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods.

Multi-level linear programming problem subject to addition-min fuzzy relation inequalities is introduced to characterize a kind of optimization models in BitTorrent-like Peer-to-Peer file sharing systems. Based on some theorems, which contribute to the resolution of the proposed problem, we develop a novel algorithm to find the unique optimal solution. A practical application example is presented to illustrate the feasibility and efficiency of the algorithm.

Max-min fuzzy relation equations are introduced to describe the Peer-to-Peer (P2P) data transmission mechanism in an instructional information resources sharing system. In some cases it is not able to satisfy the download requirements of the terminals completely. Hence the max-min fuzzy relation equations system might be inconsistent. In order to avoid the unbalance of the dissatisfaction degree, we introduce new definition of approximate solution for the inconsistent max-min fuzzy relation equations system. Our defined approximate solution could minimize the biggest dissatisfaction degree among the equations. Based on an auxiliary system with parameter, we propose a linear searching algorithm to find an approximate solution of an inconsistent max-min system. A detailed numerical example is provided to show the resolution processes and the validity of our proposed algorithm.