一种基于TOPSIS法的单值中智多属性决策新方法  

A Novel Approach to Single-valued Neutrosophic MADM Based OnTOPSIS

作　　者：刘庆 化小会[2] LIU Qing;HUA Xiao-hui(School of Mathematics and Information Science,Xinxiang University,Xinxiang 453003,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]新乡学院数学与信息科学学院,河南新乡453003 [2]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《模糊系统与数学》2020年第1期122-132,共11页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(115010176,11526082)。

摘　　要：单值中智集(SVNS)是中智集(NS)的一种特殊情况,它可以描述现实世界中大量存在的不精确、不确定和不一致信息。由于语言评价的模糊性,传统的模糊评价方法在解决多属性决策(MADM)问题上效果不佳。针对这种情况,提出了一种基于TOPSIS法的单值中智多属性决策新方法。首先介绍了中智集的一些基本概念和运算规则,给出了两个单值中智集之间的广义距离公式;然后构建了聚合专家权重的单值中智决策矩阵,把TOPSIS法推广到单值中智集的环境下;接着通过偏好排序确定了最佳的决策方案。最后通过一个仿真实例,说明了该方案的有效和实用性。A single-valued neutrosophic set(SVNS) is a special case of neutrosophic set(NS), which can describe a large amount of imprecise, indeterminate and inconsistent information in the real world. The conventional fuzzy evaluation method has not much effective for solving multiple attribute decision-making(MADM) problems because of fuzziness nature of the linguistic assessments. In this paper, a novel approach to single-valued neutrosophic MADM is proposed based on TOPSIS. Firstly, Some basic concepts and operation rules of NS are introduced and a generalized distance formula is given between two single-valued neutrosophic sets(SVNSs);Then, the TOPSIS method is extended to SNVS environment by constructing the single-valued neutrosophic decision matrix with expert weights;Next the optimal decision scheme is determined by preference ranking. Finally, an illustrative example is given to verify the effectiveness and practicability of the proposed method.

关 键 词：中智集 单值中智集 决策矩阵 多属性决策 TOPSIS 

分 类 号：O159[理学—数学] C934[理学—基础数学]