基于2可加模糊测度的多线性效用函数建模和求解

构建合适的多属性效用函数是多属性效用分析的关键。针对不同偏好假设,文献从可加独立、效用独立、效用依赖等分别进行了多属性效用函数构建的研究。然而,由于求解的复杂性,多属性效用理论的应用绝大部分限于可加效用函数和多乘效用函数。提出一种基于2可加模糊测度的多线性效用函数建模和求解方法。首先,证明多线性效用函数和基于模糊测度的多线性模型之间的等价性,提出利用基于模糊测度的多线性模型对多线性效用函数进行表示。其次,针对多线性模型的特点和模糊测度识别的复杂性,利用Banzhaf交互指数和2可加模糊测度对多线性模型进行表示,并利用最小方法差进行模糊测度和Banzhaf交互指数识别,进而实现多线性效用函数的求解。最后,将方法用于某可穿戴医疗设备基于顾客需求的多属性效用函数构建,确认了可行性。方法为多线性效用函数的求解提供了一种新思路。

Modeling and Solving Multilinear Utility Function Based on 2-additive Fuzzy Measures

It is critically important to build appropriate multi-attribute utility functions(MAUT)for multi-attribute utility analysis. Multiple types of MAUT are developed in terms of different preference assumptions, such as additive independence, utility independence and utility dependence. However, in view of complexity in solving MAUT, most applications of MAUT focus on additive function form and multiplicative function form. A novel method based on 2-additive fuzzy measures is proposed to model and solve multilinear utility function in this paper. Firstly, the equivalence between multilinear utility function in a special condition and fuzzy measure-based multilinear model is proved, which can transform multilinear utility function into fuzzy measure-based multilinear model. Then, considering the characteristic of multilinear model and complexity of identifying fuzzy measures, Banzhaf interaction index and 2-additive fuzzy measures are introduced to model fuzzy measure-based multilinear model. 2-additive fuzzy measures and Banzhaf interaction indices are then identified through minimum variance method, which are substituted into multilinear utility function. The method is finally applied to building a multilinear utility function based on customer requirements for a wearable medical equipment. It provides an alternative and effective method to solve multilinear utility functions.