基于双向投影法的概率语言多属性群决策

Probabilistic linguistic multi-attribute group decision-making based on bidirectional projection method

针对概率语言信息下的多属性群决策问题,首先基于概率语言术语集(probabilistic linguistic term sets,PLTS)的调整规则和语言尺度函数,定义了PLTS的新运算,并证明其满足代数运算的基本性质。然后,为解决现有向量模公式在下标对称语言下计算结果与实际不符的问题,提出一种改进的概率语言信息下的向量模公式。在此基础上定义方案与正、负理想解形成的向量表示式,并建立针对概率语言信息的双向投影法,由此提出新的贴近度公式。最后,通过应用算例的对比分析验证了本文所提方法的有效性和可行性。该方法充分考虑了PLTS的数据特征,在简化计算的同时避免了信息损失,为解决概率语言信息中数值差异较小的问题提供了新的方法和思路。

Aiming at the multi-attribute group decision-making problem with the probabilistic linguistic information,a new operation of the probabilistic linguistic term sets(PLTS)is defined based on the adjustment rules and linguistic scale function of the PLTS,which is proved to satisfy the basic properties of algebraic operations.Then,to solve the inconsistency between the calculation results of the existing vector module formula in subscript symmetric language and the actual situation,an improved vector module formula in the probabilistic linguistic information is proposed.On this basis,the vector expressions formed by the scheme,positive and negative ideal solutions are defined,and the bidirectional projection method for the probabilistic linguistic information is established,thus a new closeness degree formula is presented.Finally,the effectiveness and feasibility of the proposed method are verified by the comparative analysis of the application examples.This method fully considers the data characteristics of the PLTS,and avoids the information loss while simplifying the calculation,which provides a new method and idea to solve the problem of small numerical differences in the probabilistic linguistic information.