Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.

单值中智信息熵及其多属性决策方法

针对评估信息为单值中智数的多属性决策问题,建立了基于单值中智熵的多属性决策方法。首先,针对现有单值中智熵定义的不足,引入了新的单值中智熵的公理化定义;其次,基于三角函数,设计了一种衡量单值中智数不确定性的信息熵公式,并证明其满足单值中智熵的四个公理化条件;然后,运用提出的熵公式,并结合Lagrange乘数法和贴近度,构建了一种新的单值中智多属性决策方法;最后,将提出的决策方法运用于数据产品服务商的选择问题验证该方法的合理性与有效性。

基于单值中智模型的数据产品服务商选择

针对评估信息为单值中智数且属性权重完全未知的多属性决策问题,建立一种基于单值中智熵的多属性决策模型。首先,引入了新的单值中智熵的公理化定义;其次,运用余弦函数,提出了一种衡量单值中智数不确定性的信息熵公式,并证明其满足单值中智熵的4个公理化条件;然后以不确定信息最小化为准则设计最优化模型,确定属性权重,并构建一种属性权重完全未知的单值中智多属性决策方法;最后,将提出的决策方法运用于数据产品服务商的选择问题,并通过对比分析说明了本文方法的合理性与有效性。