Linear Searching Method for Solving Approximate Solution to System of Max-Min Fuzzy Relation Equations With Application in the Instructional Information Resources Allocation
Gang Xiao, Zhu Tianxiang, Yanhua Chen, Xiaopeng Yang · IEEE Access · 2019
Max-min fuzzy relation equations are introduced to describe the peer-to-peer (P2P) data transmission mechanism in 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 a 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 the 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.