Linear Searching Method for Solving Approximate Solution to System of Max-Min Fuzzy Relation Equations With Application in the Instructional Information Resources Allocation

• Published in: IEEE access Vol. 7; pp. 65019 - 65028
• Main Authors: Xiao, Gang, Zhu, Tianxiang, Chen, Yanhua, Yang, Xiaopeng
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: approximate solution; Approximation; Approximation algorithms; Data transmission; dissatisfaction degree; Fuzzy relation equation; Hamming distance; inconsistent system; Indexes; Information resources; Information services; Information sources; linear searching; Peer-to-peer computing; Resource allocation; Resource management; Search algorithms; Search methods; Search problems
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2912217

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.