An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application,it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them.Multi-valued neutrosophic set,as an extension of neutrosophic set,can more effectively and accurately describe incomplete,uncertain or inconsistent information.TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods,each of which has its advantages and disadvantages.This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic environment.After introducing the related theory of multi-valued neutrosophic set and the traditional TODIM and TOPSIS methods,the new method based on a combination of TODIM and TOPSIS methods is described.And then,two illustrative examples proved the feasibility and validity of the proposed method.Finally,the result has been compared with some existing methods under the same examples and the proposed method’s superiority has been proved.This paper studies this kind of decision-making problem from algorithm idea,algorithm steps and decision-making influencing factors.

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.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.

基于概率多值中智统计距离的灰色妥协关联双向投影决策法

文章针对已有灰色关联投影决策法尚存在适用性差的技术缺陷,提出一种新型灰色妥协关联双向投影决策法。运用描述统计中的集中趋势测量与离散趋势测量,并引入概率多值中智数的表达优势,构造概率多值中智统计距离公式;在此基础上,结合妥协思想与双向投影技术,提出基于概率多值中智统计距离的灰色妥协双向投影决策法;通过算例分析,直接验证了概率多值中智灰色妥协关联双向投影决策法的实用性,间接验证了概率多值中智统计距离和灰色妥协关联双向投影法的有效性。

基于概率多值中智集和GIS的大型环境类邻避设施两阶段规划选址

考虑邻避设施选址影响因素之间的关联性和居民对邻避设施在空间距离上的排斥,基于地理信息系统(GIS)和多目标决策理论,构建两阶段优化选址模型。第1阶段,建立包含地理信息因素的综合评价指标体系,采用决策试行与评价实验室法(DEMATEL)确定指标间的影响关系进而计算指标权重,之后使用GIS技术对地理图层叠加处理得到备选区域。第2阶段,引入概率多值中智集的概念对备选区域进行评价,提出基于偏差测度的专家权重计算方法。将基于前景理论的交互式多准则决策方法(TODIM)拓展到概率多值中智集群决策环境中,对备选区域进行排序。最后,以北京市某垃圾焚烧发电项目为例,验证模型的可行性和稳定性,从而为城市规划布局大型环境类邻避设施的选址提供了有力的决策参考。