模糊一致矩阵的权重计算方法研究  

Research on Weight Calculation Method of Fuzzy Consistent Matrix

作　　者：赵治华[1] 腾腾[1,2] ZHAO Zhi-hua;TENG Teng(National Key Laboratory of Science and Technology on Vessel Integrated Power System,Naval Univ,of Engineering,Wuhan 430033,China;Naval Research Academy,Beijing 100161,China)

机构地区：[1]海军工程大学舰船综合电力技术国防科技重点实验室,湖北武汉430033 [2]海军研究院,北京100161

出　　处：《模糊系统与数学》2019年第2期139-146,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(51507184);国家重点基础研究发展计划(973计划)项目(2015CB251004)

摘　　要：针对模糊一致判断矩阵与权重的线性关系,深入分析了其转换系数的取值范围和含义,并给出了更具一般特性的幂函数关系形式。针对模糊层次分析法中模糊一致判断矩阵权重计算的不确定问题,提出了分别以最小权值或最大比值为附加信息的权重优化计算方法,获得了最优的线性转换系数。通过算例验证了权重优化计算方法的有效性。权重优化计算方法可避免转换系数取值的盲目性,获得更接近真实的权重值,且具有较好的适应性和较强的鲁棒性。Aiming at the linear relationship between fuzzy consistent judgment matrix and its weight, the value range and meaning of its conversion coefficient are deeply analyzed, and the power function as the general form is given. In order to solve the problem of the uncertainty of calculation of the fuzzy consistent judgment matrix's weight in fuzzy analytic hierarchy process (FAHP), the optimal weight calculation method based on the minimum weight or the maximum ratio as additional information is proposed and the optimal linear conversion coefficient is obtained. The optimal weight calculation methods are verified by examples. The optimal weight calculation methods can avoid the blindness of choosing the value of conversion coefficient, get the calculated weight closer to the real weight, and has good adaptability and strong robustness.

关 键 词：模糊层次分析法 模糊一致矩阵 权重计算 最优线性转换系数 

分 类 号：O159[理学—数学]