格[0,1]上求解max-product型Fuzzy关系方程的一种算法  

An Algorithm Solving Fuzzy Relational Equation of Max-product Composition on Lattice [0,1]

作　　者：李鸿鹏[1] 王学平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2012年第6期726-729,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671138);四川省青年基金(05ZQ026-003)资助项目

摘　　要：针对max-product型Fuzzy方程的求解具有计算复杂、运算量较大的特点,提出了一种通过计算该方程的极小覆盖来准确求解方程极小解的简便方法.该算法在方程有解的前提下,使方程的求解问题转换为求覆盖的问题,方程的覆盖集可通过求解其最大解得到,化简覆盖集到一个极小覆盖集,即可求出方程的极小解.极小覆盖的求解相对简单,有效减小了算法的复杂性.最后,算法的证明过程和计算实例表明了算法的准确性和有效性.Generaly,solving fuzzy relational equations of max-product composition is lengthy and complicated,a new algorithm is proposed in this paper by calculating the minimal coverage to get exactly minimal solutions of the equations.When the equation has solution,the algorithm converts the problem to calculating the minimal coverage which can be obtained by computing maximum solutions.By comparing with the direct solution of the equation,the calculation of the minimal covering set is relatively simple,so the complexity of the algorithm is effectively reduced.The proof of the algorithm and the present practical example illustrate the accuracy and effectiveness of the new algorithm.

关 键 词：格[0 1] FUZZY关系方程 极小覆盖 极小解 

分 类 号：O159[理学—数学]