基于商空间的语言型Z-number多准则决策方法

针对Z-number多准则决策中计算复杂度高，计算量大等问题，提出了一种较为简单且行之有效的基于粒度的多准则决策方法；将语言型Z-number决策信息转化为经典模糊数，用提出的可能度公式来两两比较方案的优劣程度，并且根据定义的模糊度公式计算出各准则的权重，继而得到最终的决策矩阵；然后，基于商空间的基本理论对QUALIFLEX排序方法进行改进，根据方案间的优势关系以及保假原理，可以将问题的最优解确定在较小的粒度空间内，在这个较小的粒度空间内搜索出综合一致性最大的最优排列，得到问题的最优解；最后通过实例分析可验证提出方法的可行性和有效性，且方法有效降低了计算的复杂度。

Linguistic Z number Multiple Criteria Decision making Method Based on Quotient Space

In order to solve the problems of high computational complexity and a large amount of computation in Z-number multiple criterion decision making, a simple and effective multi criterion decision making method based on granularity is proposed.The linguistic Z number decision information is transformed into the classical fuzzy number,and the proposed likelihood degree formula is used to compare the pros and cons of the scheme in pairs,the weight of each criterion is calculated according to the defined fuzzy degree formula, and then the final decision matrix is obtained. Finally, based on the basic theory of quotient space, the QUALIFLEX sorting method is improved, according to the falsity preserving principle and the degree of dominance between schemes,the optimal solution of the problem can be determined in a small granularity space,and the optimal solution with the largest comprehensive consistency is obtained by searching in this smaller granularity space.Finally,the feasibility and validity of the proposed method can be verified by an example,and the computational complexity can be reduced effectively.