當綜合評價之多種屬性間,具有潛在交互作用時,傳統可加性測度方法表現欠佳,可考慮採用模糊測度與模糊積分。進行模糊積分前,須先選擇適當之模糊測度,眾所周知Sugeno之λ測度與Zadeh之P測度均只有唯一解,劉湘川先後提出逐次改進之三種多值模糊測度;「μ測度」、「v測度」及「L測度」,上述三種多值模糊測度均可有無限多模糊測度之解可供選擇。本文在L測度之定義式中添加「平方指標」以增進靈敏度,提出進一步改進之「二階L測度」,同時亦提出「基於二階L測度之Choquet 積分迴歸模式」,將更有利於具潛在交互作用資料之綜合評價與預測分析。
When interactions among criteria exist in multiple decision-making problems or forecasting problems, the performance of the traditional additive scale method is poor. Non-additive fuzzy measures and fuzzy integral can be applied to improve this situation. The λ-measure proposed by Sugeno and the P-measure proposed by Zadeh, are the most often used fuzzy measures, but the above two measures both have only one solution of fuzzy measure. Hsiang-Chuan Liu has proposed three polyvalent fuzzy measures: μ-measure, v-measure and L-measure. All of the three improved measures have infinite many solutions of fuzzy measures. In this paper, A square index is adding to two terms in formula of the L-measure for being more sensitive then L-measure, and get an improved fuzzy measures, called ”second-order L-measure”, and a new Choquet integral regression model based on this second-order L-measure is also proposed.