1、华北电力大学 2013 届本科毕业设计 （ 论文 ） 1 摘 要 目前 ,关于模糊关系方程的理论研究已越来越多的应用于解决实际问题当中 ,如系统分析 ,决策理论 ,模糊推理 ,模糊控制等等。作为模糊关系方程的推广 ,区间值模糊关系方程在反映日常推理的模糊性和不确定性中更有优势。随着在模糊环境下的优化问题在日常经济生活中的广泛应用 ,如何用简捷有效的方法解决模糊优化问题 ,尤其是近年出现的模糊关系约束的优化问题已成为广大学者关注的热点之一 ,但是 应用 PSO 算法求解极大极小模糊关系方程 约束的最优化问题 还是空白 。 本文详细叙述了极大极小模糊关系方程的一些基本概念，介绍 PSO 算法的 主
2、要思想及算法步骤 ,研究如何应用 PSO 算法来求解极大极小模糊关系方程约束的最优化问题，给出一个解决的算法。最后，结合一个具体例子，检验此方法。 关键词 ： 模糊关系方程 , PSO 算法 , 最优解 华北电力大学 2013 届本科毕业设计 （ 论文 ） 2 Abstract At present, the theoretical research for the fuzzy relational equations has more and more applied in solving practical problems, such as system analysis, decisi
3、on theory, fuzzy reasoning, and fuzzy control and so on. As the promotion of the fuzzy relational equations, interval valued fuzzy relational equations has more advantages in the fuzziness and uncertainty of reflecting the daily inferences. As the optimization problem under fuzzy environment is wide
4、ly used in daily economic life, the simple and effective method of solving fuzzy optimization problems has become one of the hot spot of many scholars, especially the optimization problem of the fuzzy relation constraint in recent years, but PSO algorithm has not been applied to solve max-min fuzzy
5、relational equations constrained optimization problems. The paper describes in detail some basic concepts of max-min fuzzy relational equations, introduces the main ideas and algorithm steps of the PSO algorithm, study how to apply the PSO algorithm to solve the constrained optimization problem of max-min fuzzy relational equations and offers a solution algorithm. Finally, the paper combines with a concrete example to test this method. KEY WORDS： Fuzzy relational equations, Particle swarm optimization, The optimal solution
