基于极端积算子的 LL 型模糊数的最小一乘回归

摘要

针对模糊输入和模糊输出数据系统中的回归分析问题，考虑到系统中依赖关系不确定性特点以及模型稳健性和求解准确性等需求，建立一个模糊最小一乘优化模型。首先利用能诱导出LL型模糊数乘法保形运算的唯一T-模，即极端积算子，结合扩张原理，给出LL型模糊数间加法和乘法的运算规则。其次，基于LL型模糊数间的完备距离，得到模糊线性回归模型的参数估计，由此给出考虑清晰参数或清晰输入的两个简约模型及相应参数估计。通过计算Kim＆Bishu测度、贴近测度和输出展形差异测度，比较与其他7种回归方法的优劣，并由模型的敏感性分析，充分说明本文算法的有效性和稳健性。%Fuzzy least-absolutes regression is developed by considering uncertain dependence ,model robustness and exact solutions in the system with fuzzy inputs and fuzzy output .Firstly,Tw based addition and multiplication properties for LL type of fuzzy number are derived using the extension principle , where TW is also called drastic product ,which is the only T norm inducing a shape preserving multiplication of LL type of fuzzy number .Second-ly, fuzzy parameters are determined based on a complete metric on LL type of fuzzy number and then two particu -lar cases of the general model are discussed .Finally,the potential of the proposed model with regard to other re-gression approaches is illustrated by some experiments and sensitivity analysis by adopting several measures , which turns out that the proposed model has good prediction accuracy and resistant power against outliers .