Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment

The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.     

基于单值中智集的投资决策方案优选模型

为了优化投资决策方案优选模型,提出一个基于单值中智环境下的多属性决策问题的新方法。首先给出一个基于单值中智集的广义距离公式,然后通过语言变量确定了决策专家和属性指标的权重,接着构建了加权的综合决策矩阵,进一步得到各备选方案与正负理想方案的距离,利用相对贴近度系数对各备选方案就进行综合排序,得到最优决策方案。最后通过一个投资决策的实例,验证了该模型的有效性和实用性。     

基于GRA-GCRITIC和改进加权双向投影的区间Fermatean模糊多属性群决策方法

针对司法案件决策环境的复杂性及评价信息的模糊性,提出一种基于GRA-GCRITIC（grey relational analysis-group criteria importance through intercriteria correlation）和改进加权双向投影的区间Fermatean模糊Hamacher-TODIM多属性群决策方法。首先考虑到各位专家对各评价方案下各指标评价信息的差异性,提出一种GRA-GCRITIC方法,该方法将灰色关联融入到CRITIC中,以确定指标综合权重比单一获取的指标权重更加客观可靠。其次,结合信任关系对加权双向投影法进行改进,兼顾主客观关系,利用专家个体与群体评价信息的隶属度及非隶属度矩阵间的相似度得到专家权重。最后,考虑到决策者的损失规避心理,将融合了Hamacher算子的TODIM方法拓展至区间Fermatean模糊环境中,通过具体算例可得到其综合优势度及排序,验证了所提方法的可行性及灵活性。     

Similarity and Pythagorean reliability measures of multivalued neutrosophic cubic set and its application to multiple-criteria decision-making

Considering the limitations of interval neutrosophic set (INS), multivalued neutrosophic set (MVNS), and neutrosophic cubic set (NCS) in describing uncertainty, respectively, this study proposes a multivalue neutrosophic cubic set (MVNCS). Originating from the combination of INS and MVNS, MVNCS is regarded as the general form of NCS. First, some basic operations of MVNCS and the similarity measures of MVNCS are defined. Second, considering the complexity of actual decision-making problems, the Pythagorean reliability measure of MVNCS is further developed to process the evaluation indicators and attribute weights given by decision-makers more accurately. Third, a multicriteria decision-making approach under the multivalue neutrosophic cubic environment is proposed based on the above measures. Finally, an example of investment options that follow sensitivity and comparative analysis provided to justify the advantages of our method is given.     

On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision-making

In this paper, we develop a new and flexible method for Pythagorean fuzzy decision-making using some trigonometric similarity measures. We first introduce two new generalized similarity measures between Pythagorean fuzzy sets based on cosine and cotangent functions and prove their validity. These similarity measures include some well-known Pythagorean fuzzy similarity measures as their particular and limiting cases. The measures are demonstrated to satisfy some very elegant properties which prepare the ground for applications in different areas. Further, the work defines a generalized hybrid trigonometric Pythagorean fuzzy similarity measure and discuss its properties with particular cases. Then, based on the generalized hybrid trigonometric Pythagorean fuzzy similarity measure, a method for dealing with multiple attribute decision-making problems under Pythagorean fuzzy environment is developed. Finally, a numerical example is given to demonstrate the flexibility and effectiveness of the developed approach in solving real-life problems.     

区间值模糊软集的信息测度及其聚类算法

针对区间值模糊软集信息测度难以精确定义的问题,提出了区间值模糊软集的距离测度、相似度、熵、包含度、子集度的公理化定义,给出了区间值模糊软集的信息测度公式,并讨论了它们的转换关系。然后提出了一个基于相似度的聚类算法,该算法结合区间值模糊软集的特性,着重对给出评价对象的具有相似知识水平的专家进行聚类,同时讨论了算法的计算复杂度。最后通过实例说明该算法能有效地处理专家聚类问题。     

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction

The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness.     

融合贝叶斯网络与前景理论的产品工业设计多阶段决策方法#br#

针对产品工业设计决策中的不确定性与单一设计决策阶段难以准确描述全局决策结果的问题,引入三参数区间灰数对决策者的意见进行描述,构建贝叶斯网络(BN)模型学习用户群体对市场上现有成熟产品的决策信息,获得目标产品工业设计方案在各决策属性上的状态分布概率。为反映决策者对设计方案感知相对收益和损失的心理行为,融合前景理论(PT)与 BN 构建不同决策阶段产品工业设计方案的前景价值函数,以认知递进假设建立优化模型计算产品工业设计决策多阶段权重,通过综合前景价值计算判断设计方案优劣。以数控磨床工业设计方案决策的多阶段融合为例验证了方法的有效性,结果表明该方法能够引入用户群体的多阶段意见偏好估计设计决策属性的概率分布,以前景价值实现产品工业设计多阶段决策信息的有效集结,提高设计决策的全局性和科学性。     

Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the Economic Zone of Chengdu Plain

The probabilistic linguistic term set is a powerful tool to express and characterize people’s cognitive complex information and thus has obtained a great development in the last several years. To better use the probabilistic linguistic term sets in decision making, information measures such as the distance measure, similarity measure, entropy measure and correlation measure should be defined. However, as an important kind of information measure, the inclusion measure has not been defined by scholars. This study aims to propose the inclusion measure for probabilistic linguistic term sets. Formulas to calculate the inclusion degrees are put forward Then, we introduce the normalized axiomatic definitions of the distance, similarity and entropy measures of probabilistic linguistic term sets to construct a unified framework of information measures for probabilistic linguistic term sets. Based on these definitions, we present the relationships and transformation functions among the distance, similarity, entropy and inclusion measures. We believe that more formulas to calculate the distance, similarity, inclusion degree and entropy can be induced based on these transformation functions. Finally, we put forward an orthogonal clustering algorithm based on the inclusion measure and use it in classifying cities in the Economic Zone of Chengdu Plain, China.     

A class of projection and contraction methods for asymmetric linear variational inequalities and their relations to Fukushima's descent method

For solving asymmetric linear variational inequalities, we present a class of projection and contraction methods under the general G-norm. The search direction of our methods is just a convex combination of two descent directions of Fukushima's merit function. However, we use the direction to reduce the distance function (1/2)u − u*²_G, where μ* is a solution point of the problem. Finally, we report some numerical results for spatial price equilibrium problems by using the presented methods.     

基于多层次灰色综合评价法的工业设计方案优选决策模型及其应用

为辅助企业在产品设计方案评估阶段进行合理地决策,减少设计的盲目性和主观性,基于多层次灰色综合评价法构建了工业产品设计方案优选决策模型.在评价流程中,首先依据层次分析法(AHP)与熵权法通过定性、定量分析,合理地进行评价指标权重系数的确定.其次,采用灰色关联度分析法对各设计方案进行灰色加权关联度的计算,确定其排序,并依据...     

A decision-making framework model for design and manufacturing of mechanical transmission system development

Knowledge-based systems are proving to be a powerful tool with great potential for developing intelligent design support environments to improve quality of products and reduce product development costs by eliminating or minimizing many of the trial-and-error iterations involved in product development. This article describes an approach towards the development of intelligent design support environments for mechanical transmission systems, along with implementation details of a distributed knowledge-based gearing design and manufacturing system that is deployed over the Internet. The system embodies the various tasks of the design process, with modules that address: performance evaluation, process optimization, manufacturability analysis, and provides reasoning and decision-making capabilities for reducing the time between gear tooth creation, detailed design and final production. This methodology is highly desirable in that it is able to simulate real working conditions, evaluate and optimize the design effectively, prevent designers from time-consuming iterations and reduce long and expensive test phases.     

Information structuring for use and reuse of mechanical analysis models in engineering design

Nowadays, in an industrial context, cost and delay reduction, as well as quality improvement are of major interest in engineering design. Therefore, in order to make a decision as early as possible and according to the product specifications, mechanical analysis is used more and more, and earlier and earlier in the engineering process. Then, a multitude of mechanical models are elaborated during engineering design, and management difficulties appear with engineering changes or evolution of specifications. Moreover, when the designer is faced with design or modelling options, previous analysis could answer the choice of options for decision making. Then, the reuse of a previous analysis must be envisaged. The paper presented deals with the aim and the different use of mechanical analysis in embodiment design. Afterwards, different levels of models handled by the designer during the engineering process are proposed. A particular type of analysis, namely instructional' is identif ied in a further step and its interest in a reuse context is emphasized. Finally, information structuring is proposed in order to allow mechanical analysis reuse during engineering design.