Multi-variable-term Latticized Linear Programming with Addition-Min Fuzzy Relation Inequalities Constraint

• Published in: Quantitative Logic and Soft Computing 2016 Vol. 510; pp. 515 - 525
• Main Authors: Lin, Hai-Tao, Yang, Xiao-Peng
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2016; Springer International Publishing
• Series: Advances in Intelligent Systems and Computing
• Subjects: Addition-min composition; Artificial intelligence; Fuzzy relation inequality; Latticized linear programming; Minimal interval
• ISBN: 3319462059; 9783319462059
• ISSN: 2194-5357; 2194-5365
• DOI: 10.1007/978-3-319-46206-6_48

P2P network can be reduced into a system of fuzzy relation inequalities with addition-min composition. In this paper we introduce multi-variable-term latticized linear programming subject to this system. Firstly, we introduce some properties on the minimal solution of the system. Next we define the minimal intervals of the system. Meanwhile, We prove that the optimal solution of the programming is the minimal solution of the system. Finally, we get algorithm for the programming by translating it into some linear programming problems with minimal intervals constraint. An example is given to show the efficiency and feasibility of the algorithm.