【作者】 史丽华；

【导师】 兰继斌；

【作者基本信息】 广西大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 模糊数排序是模糊优化中的一个重要问题,从模糊集的定义及性质中可知,模糊数之间的序关系不是通常意义下的全序关系,而是格结构下的半序关系,这使得模糊数的比较和判别成为模糊决策中既重要又艰难的任务之一。近年来许多模糊数排序方法涌现出来。对这些排序方法进行分析的基础上,本文提出了一种基于左、右拟优于度的区间数排序公式。通过构造一致性正互反判断矩阵得到的排序指标,满足模糊排序合理性的五个公理:序关系的完全性、不相交模糊量的性质、不相关模糊量的独立性、序关系的传递性和对加的相容性。接下来将三角模糊数转换为α截集,利用新提出的区间数排序公式确定各个三角模糊数在α水平下的排序,再通过加权积分最终确定三角模糊数的序关系。这种排序方法考虑到了模糊数的各截集水平对排序结果的影响,还可以通过调整悲观系数λ的取值,使排序问题更加灵活,排序结果更加科学。作为模糊决策最常见的一种决策方法,层次分析法,其关键是获取决策者完备的偏好信息,构造判断矩阵,再运用适当的技术确定优先权重。在AHP分析方法中,具有一致性是判断矩阵应用的前提。本文提出一种确定正互反判断矩阵优先权重的方法,揭示了一致性正互反判断矩阵元素与优先权重新的逻辑关系。新的逻辑关系不仅能充分利用已知的判断信息,也能很大程度上利用决策者的信息偏好,所确定的优先权重含有参数,决策者可通过参数的选择,达到对优先权重分辨率的要求。更多还原

【Abstract】 Ranking fuzzy number is an important issue in the process of fuzzy optimization. Considering the definition and quality of fuzzy sets, the sequence of fuzzy numbers is not the entire-sequence but semi-sequence under lattice structures, which makes both the comparison and discrimination of fuzzy numbers become important and hardship tasks in the decision-makers.In recent years, various methods of ranking fuzzy number have been proposed. A sequence formula of interval numbers which is based on left and right imitated preceding degrees of fuzzy numbers is provided in this paper. This new index, which is obtained by constructing consistent positive reciprocal judgment matrix, satisfies five axioms of reasonable ranking fuzzy number, including the completeness of sequence, the property of uncross fuzzy quantity, the independence of misrelated fuzzy quantity, the transitivity of sequence and the compatibility to addition. Subsequently, triangle fuzzy numbers are converted toα-cut sets, and the sequence of triangle fuzzy numbers underα-level is determined by the new sequence formula of interval numbers. Finally, the sequence of triangle fuzzy numbers is determined by weighted integral. This sort of approach takes account of the impact of fuzzy-numbers’ cut-set levels on the outcome of the sequence, and adjusts the value of pessimistic coefficientλto make the sequence more flexible and the outcome more scientific.The Analytic Hierarchy Process (AHP) is the most common method of decision-making. The key of AHP is to construct the judgment matrices by obtaining decision-makers’ complete favorable information, and determine priority vectors with appropriate method. In the AHP method, the consistency of the judgment matrices is the precondition of their application. In this paper, a new approach to determine priority vectors of consistent positive reciprocal judgment matrix is provided. After that, the logic relationship between elements of consistent positive reciprocal judgment matrix with the parameter and the priority is revealed. It could not only take full advantage of the judgment of known information, but also take use of information preference of decision-makers to a large extent. The priority determined by this new logic relationship contains parameters can help the decision-makers choose parameters and meet the requirement of priority resolution.更多还原