基于极端积算子的具有直觉模糊输入–直觉模糊输出的回归模型研究
Research on Regression Model for Intuitionistic Fuzzy Input-Intuitionistic Fuzzy Output System Based on Drastic Product Operator
摘要: 本文首先基于极端积算子，结合扩张原理，给出LL-型直觉模糊数间除法运算的结果。通过举例来说明基于极端积算子的除法不能保证直觉模糊数的形状不变性。其次基于直觉模糊数的截集提出了直觉模糊数之间距离测量并进行性质分析，利用距离将直觉模糊回归模型等价于整合回归分析，极端积算子的LL-型直觉模糊数间的运算，以及最小一乘估计的最小优化问题，考虑当直觉模糊数退化成模糊数时的模型。最后将模型应用到对称的三角直觉模糊数据和对称的模糊数据，利用三个拟合优度准则，与其他方法进行对比验证了该方法的适用性。
Abstract: This paper uses the drastic product operator, combines with extension principle, division between LL-type intuitionistic fuzzy numbers is given by. An example is given to illustrate that the division based on drastic product operator cannot guarantee the shape invariance of intuitionistic fuzzy numbers. Secondly, based on the level set of intuitionistic fuzzy numbers, the distance measurements between intuitionistic fuzzy numbers are obtained and properties are discussed. The intuitionistic fuzzy regression model is explained as the equivalent minimum optimization problem integrating regression analysis, drastic product operator based arithmetic operations on LL-type intuitionistic fuzzy numbers and least absolutes estimates by distance view together to derive the intuitionistic fuzzy dependency relationship, and the model is considered when intuitionistic fuzzy numbers degenerates into fuzzy numbers. Finally, the model is applied to symmetric triangular intuitionistic fuzzy data and symmetric fuzzy data, and three goodness of fit criteria are used to verify the applicability of this method compared with other methods.
文章引用：陈良凤, 陆秋君. 基于极端积算子的具有直觉模糊输入–直觉模糊输出的回归模型研究[J]. 运筹与模糊学, 2022, 12(2): 141-156. https://doi.org/10.12677/ORF.2022.122014

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