AHP多路径排序度量转换中的非线性问题

发布时间：2018-11-26 17:42

【摘要】：由于不同测量条件下的测量结果不是线性可加,AHP用矩阵乘法实现多路径序转换值得商榷.自隶属度从只取"1或0"两个值扩展到可取[0,1]区间上一切实数,可表征界于"是"与"不是"之间所有可能"部分是"模糊状态时起,对二值逻辑的研究已拓展到研究近似推理的模糊逻辑.这是逻辑的一个新的研究方向,目的是在隶属度转换过程中,通过对人类近似推理本领进行规范,使得到的目标值是"真值"在当前条件下的最优近似.模糊逻辑的量化方法是数值计算;推理依据是区分权滤波的冗余理论;实质性计算是由冗余理论导出的、实现隶属度转换的非线性去冗算法;所建的隶属度转换模型也是不同测量条件下高维状态空间上测量结果的非线性可加模型.将一维测量数据映射到高维状态空间上表为隶属度向量,可借助隶属度转换模型解决AHP多路径序转换的非线性计算.
[Abstract]:Because the measurement results under different measurement conditions are not linear additive, it is debatable that AHP uses matrix multiplication to realize multipath order conversion. Since the membership degree extends from "1" or "0" to all real numbers on the desirable [0] interval, it can be characterized by the fact that all possible parts between "yes" and "no" are "fuzzy", The study of binary logic has been extended to study fuzzy logic of approximate reasoning. This is a new research direction of logic. The aim is to normalize the approximate reasoning ability of human beings in the process of conversion of membership degree, so that the target value obtained is the optimal approximation of "true value" under current conditions. The quantitative method of fuzzy logic is numerical calculation, the inference is based on the redundancy theory of discriminant weight filtering, the substantive calculation is derived from redundancy theory, and the nonlinear de-redundancy algorithm is realized. The membership conversion model is also a nonlinear additive model for the measurement results in high dimensional state space under different measurement conditions. The one-dimensional measurement data are mapped to the high dimensional state space table as membership vector, and the nonlinear calculation of AHP multipath sequence conversion can be solved by using membership conversion model.
【作者单位】：河北工程大学不确定信息研究所;河北工程大学信息与电气工程学院;
【基金】：国家自然科学基金(61375002,61375003)
【分类号】：O223

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