AHP多路径排序度量转换中的非线性问题

The Nonlinear Problem of AHP Multi Path Conversion

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.

As the measurement results under different measurement conditions are not lin- ear addictive, it is worth discussing how to realize multi path conversion by using matrix multiplication in AHP. The research of the binary logic has been extended to the fuzzy logic of approximate reasoning, since the concept of the membership degree was extended from the binary logic of ＂1 or 0＂ to the [0,1] interval, which stands for all the possible ＂partly yes＂ fuzzy state between yes and no. This is a new research direction of logic. The purpose of it is to make the target value is the optimal approximation of the true value under the current condition through making the human approximate reasoning ability standard, in the process of the membership conversion. The quantization method is the numerical calculation not the ＂big or small＂. The reasoning basis is the redundancy logic of the discrimination power filter. The nonlinear redundancy algorithm derived by the redundancy theory and realized by the membership conversion can solve the problem of the nonlinear addictive calculation for high dimensional data through the realization of the membership conversion.The mem- bership conversion model is a nonlinear addictive model which can be used to measure the high dimensional state space under different measurement conditions. The one dimensional data can be mapped to a high dimensional state space as the membership degree vector, then the nonlinear addictive problem of which can be solved by the addictive for high dimensional data.