单值Neutrosophic sets环境下基于参照系数的VIKOR方法

VIKOR Method Based on the Reference Coefficient under Single-valued Neutrosophic Environment

模糊集的提出极大拓宽了多属性决策理论,但无法处理不一致和不连续信息,单值中智集(single-valued neutrosophic sets)的提出弥补了这一不足。本文把单值中智集的三个参数投影到坐标轴上形成三维空间,并把VIKOR方法拓展到该环境下。为了使得VIKOR方法同时考虑正理想解和负理想解对方案的影响,本文提出参照系数的概念并将其引入到原始VIKOR方法中,并通过参照系数的变动探究不同参照标准对排序及最佳妥协解的影响。通过对比分析验证方法的有效性和可行性。对比结果表明,不同的参照标准下,得到的排序及最佳妥协解不同。最后,把所提方法用到实际问题中。

The proposed single-valued neutrosophic sets make up for the shortcomings of fuzzy sets that cannot handle inconsistent and discontinuous information.The study regards three parameters of singlevalued neutrosophic sets as three coordinates to generate a 3 Ddimension,and extends VIKOR method to single-valued neutrosophic sets environment.The ranking of original VIKOR method is based on the closeness between alternatives and the positive ideal solution(PIS).Namely the optimal compromise solution is the closest to PIS.However,in the 3 Dspace consists of single-valued neutrosophic sets,the closest distance between the alternative and PIS does not mean that it is the farthest from the negative ideal solution(NIS).That is,the ranking and the optimal compromise solution are different when take the closeness between alternatives and PIS as baseline compared with the closeness between alternatives and NIS.Different preference of decision makers for reference standard lead to different results which cause confusion in the decision making.The existing research does not propose some advices to solve the problem.For this reason,the concept of reference coefficient(RC)is proposed and the closeness between alternatives and NIS is introduced into original VIKOR method and the influence of different RC is explored on the ranking and the optimal compromise solution.In order to verify the effectiveness of the improved method,the result of the paper are compared with those of the existing literature.The result shows that the changes of RC have an impact on the ranking and the optimal compromise solution.It is more reasonable for decision makers to consider the results of different RC comprehensively.VIKOR method based on the reference coefficient amends the use of original VIKOR method under the imprecision environment which is an extension of VIKOR method.The research result shows that it is a reasonable ranking method.