單值Neutrosophic sets環(huán)境下基于參照系數(shù)的VIKOR方法

摘要： 模糊集的提出極大拓寬了多屬性決策理論,但無法處理不一致和不連續(xù)信息,單值中智集(single-valued neutrosophic sets)的提出彌補(bǔ)了這一不足。本文把單值中智集的三個(gè)參數(shù)投影到坐標(biāo)軸上形成三維空間,并把VIKOR方法拓展到該環(huán)境下。為了使得VIKOR方法同時(shí)考慮正理想解和負(fù)理想解對(duì)方案的影響,本文提出參照系數(shù)的概念并將其引入到原始VIKOR方法中,并通過參照系數(shù)的變動(dòng)探究不同參照標(biāo)準(zhǔn)對(duì)排序及最佳妥協(xié)解的影響。通過對(duì)比分析驗(yàn)證方法的有效性和可行性。對(duì)比結(jié)果表明,不同的參照標(biāo)準(zhǔn)下,得到的排序及最佳妥協(xié)解不同。最后,把所提方法用到實(shí)際問題中。
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.