Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

Method for multi-attribute group decision-making based on the compromise weights

Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Ranking environmental projects model based on multicriteria decision-making and the weight sensitivity analysis

With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental quality and economic benefits is an important problem for the decision makers. The purpose of this paper is to develop a decision-making model to rank a finite number of alternatives with several and sometimes conflicting criteria. A model for ranking the projects of municipal sewage treatment plants is proposed by using exports＇ information and the data of the real projects. And, the ranking result is given based on the PROMETHEE method. Furthermore, by means of the concept of the weight stability intervals （WSI）, the sensitivity of the ranking results to the size of criteria values and the change of weights value of criteria are discussed. The result shows that some criteria, such as “proportion of benefit to project cost”, will influence the ranking result of alternatives very strong while others not. The influence are not only from the value of criterion but also from the changing the weight of criterion. So, some criteria such as “proportion of benefit to project cost” are key critera for ranking the projects. Decision makers must be cautious to them.

Assessing Criteria Weights by the Symmetry Point of Criterion (Novel SPC Method)–Application in the Efficiency Evaluation of the Mineral Deposit Multi-Criteria Partitioning Algorithm

Information about the relative importance of each criterion or theweights of criteria can have a significant influence on the ultimate rank of alternatives.Accordingly,assessing the weights of criteria is a very important task in solving multi-criteria decision-making problems.Three methods are commonly used for assessing the weights of criteria:objective,subjective,and integrated methods.In this study,an objective approach is proposed to assess the weights of criteria,called SPCmethod(Symmetry Point of Criterion).This point enriches the criterion so that it is balanced and easy to implement in the process of the evaluation of its influence on decision-making.The SPC methodology is systematically presented and supported by detailed calculations related to an artificial example.To validate the developed method,we used our numerical example and calculated the weights of criteria by CRITIC,Entropy,Standard Deviation and MEREC methods.Comparative analysis between these methods and the SPC method reveals that the developedmethod is a very reliable objective way to determine the weights of criteria.Additionally,in this study,we proposed the application of SPCmethod to evaluate the efficiency of themulti-criteria partitioning algorithm.The main idea of the evaluation is based on the following fact:the greater the uniformity of the weights of criteria,the higher the efficiency of the partitioning algorithm.The research demonstrates that the SPC method can be applied to solving different multi-criteria problems.

Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

Consensus intuitionistic fuzzy group decision-making method for aircraft cockpit display and control system evaluation

A novel group decision-making （GDM） method based on intuitionistic fuzzy sets （IFSs） is developed to evaluate the ergonomics of aircraft cockpit display and control system （ACDCS）. The GDM process with four steps is discussed. Firstly, approaches are proposed to transform four types of common judgement representations into a unified expression by the form of the IFS, and the features of unifications are analyzed. Then, the aggregation operator called the IFSs weighted averaging （IFSWA） operator is taken to synthesize decision-makers’ （DMs’） preferences by the form of the IFS. In this operator, the DM’s reliability weights factors are determined based on the distance measure between their preferences. Finally, an improved score function is used to rank alternatives and to get the best one. An illustrative example proves the proposed method is effective to valuate the ergonomics of the ACDCS.

Method for Risky Multiobjective Group Decision-Making and Its Application

The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.

Application of Interval Multi-attribute Decision-Making Method to Aeroengine Performance Ranking

In view of the uncertainty of the monitored performance parameters of aeroengines, the fluctuating scope of the monitored infurmation during a period is taken as interval numbers, and the interval multi-attribute decision-making method is employed to predict the performance of aeroengine, The synthetic weights of interval numbers are obtained by calculating deviation degree and possibility degree. As an example of application, 5 performance parameters monitored on 10 CF6 aeroengines of China Eastern Airlines Co., Ltd are adopted as decision attributes to verify the algorithm. The obtained synthetic ranking result shows the effectiveness and rationality of the proposed method in reflecting the performance stares of aeroengins.

Synergizing Wind,Solar,and Biomass Power:Ranking Analysis of Off-Grid System for Different Weather Conditions of Iran

Nowadays,the use of renewable energies,especially wind,solar,and biomass,is essential as an effective solution to address global environmental and economic challenges.Therefore,the current study examines the energy-economic-environmental analysis of off-grid electricity generation systems using solar panels,wind turbines,and biomass generators in various weather conditions in Iran.Simulations over 25 years were conducted using HOMER v2.81 software,aiming to determine the potential of each region and find the lowest cost of electricity production per kWh.In the end,to identify the most suitable location,the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method was employed to rank different stations based on simulation output parameters and some other influential factors.Considering the evaluation of various parameters,the stations in Yazd,Marand,and Dezful achieved the best results,while the stations in Ramsar,Shahrekord,and Gonbad presented the least favorable outcomes.In Yazd,the wind turbine is an economic priority,and a 100 kW wind turbine is utilized in the optimal system.In Yazd,where the simultaneous use of renewable energies is most prominent,the lowest pollutant production occurred with a quantity of 1174 kg/year.Annual energy losses are highest in Jask station and lowest in Yazd.

Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species

The weighted Gini-Simpson quadratic index is the simplest measure of biodiversity which takes into account the relative abundance of species and some weights assigned to the species. These weights could be assigned based on factors such as the phylogenetic distance between species, or their relative conservation values, or even the species richness or vulnerability of the habitats where these species live. In the vast majority of cases where the biodiversity is measured the species are supposed to be independent, which means that the relative proportion of a pair of species is the product of the relative proportions of the component species making up the respective pair. In the first section of the paper, the main versions of the weighted Gini-Simpson index of biodiversity for the pairs and triads of independent species are presented. In the second section of the paper, the weighted Gini-Simpson quadratic index is calculated for the general case when the species are interdependent. In this instance, the weights reflect the conservation values of the species and the distribution pattern variability of the subsets of species in the respective habitat induced by the inter-dependence between species. The third section contains a numerical example.

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.

科技金融生态对区域经济韧性的空间效应及影响机制

从“宏观环境子系统”和“微观群落子系统”两个维度构建科技金融生态评价体系,运用时空极差熵权法测算2008—2020年31个省份(不包括港澳台地区)科技金融生态水平,并采用动态空间杜宾模型全面考察科技金融生态对经济韧性的直接效应和间接效应及其影响机制。结果表明:我国科技金融生态水平存在明显的空间非均衡性,呈现“东高西低”的特征,由于省、自治区、直辖市间存在示范效应及经济关联效应,经济韧性表现出显著的正向空间溢出效应,科技金融生态产生的技术创新、产业协同集聚效应均从总体上提升本地及空间关联地区的经济韧性。基于以上研究结论,进一步提出提高科技金融生态水平的政策供决策参考。

基本农田指标分解的熵权系数法研究

针对基本农田指标分解的问题,应用熵权系数法的基本原理,综合考虑评价对象的多种指标,提出对基本农田指标分解的多指标综合评价的熵权系数方法,克服了以往基本农田指标分解的只注重几个简单指标而造成结果的偏差。以济南市基本农田指标分解为例,进行了具体的评价计算。

基于未确知测度理论的煤矿井下“六大系统”安全评价模型

通过分析"六大系统"的构成,给出了"六大系统"评价指标体系,构造了基于未确知测度理论的单指标测度函数评价模型,并通过信息熵确立指标的分类权重。结果表明,采用该方法得到的评价结果能够准确、客观、全面地反映安全评价的等级情况。

灰度-梯度共生矩阵模型的加权条件熵阈值法

基于二维灰度直方图的最大熵阈值法是依据"灰度-灰度均值"构成直方图的图像分割方法,该方法着重于图像的内部信息,忽略了边界区域的信息。应用图像的梯度信息建立"灰度-梯度共生矩阵",构造图像的二维灰度直方图,结合最大条件熵法进行阈值选取。为了充分提取图像内部和边缘信息,提出了二维加权最大熵阈值法。结果表明,该方法一方面能够保留更多的图像边缘信息,另一方面能够根据实际需要调节权值大小,得到兼顾图像内部和边缘信息的分割结果。

以利润和熵为性能指标的车间生产调度

为解决以往研究中车间调度指标考虑因素不全面的问题,将时间、质量、成本、能耗和环境5个因素统一为利润指标、提出了以利润作为调度指标、熵作为调度方案有效性的评估指标、基于遗传算法的柔性制造车间调度方法.该方法以利润指标作为遗传算法的染色体适应值,经多次寻优,求解出一组次优调度方案,对次优调度方案集进行利润与熵为指标的基于熵权的多目标决策,决定最终的最优调度方案.应用实例和程序进行验证,结果表明,与传统调度方法相比,所提出的方法在指标的全面性及实用性上有一定优势.

基于熵权理论的传动比优化配置

将机械传动系统划分为若干组传动副,利用各级传动副的传动比参考范围对其进行分级,并建立相应的传动比评判指标分级矩阵,随后借助信息工程中的熵权理论,根据分级矩阵中各评价指标的差异程度来修正各级传动副间的传动比权重,从而建立了一种新的传动比分配模型———传动比熵权优化配置模型,这在一定程度上弥补了传统人为分配传动比所带来的一些缺陷。

一种组合齿轮传动系统的设计及仿真

设计了一种组合式齿轮传动系统。该系统首先根据输入输出转速计算出系统总的传动比,其次基于熵权理论对系统各级传动比进行优化,确定相应标准传动件的各项参数,最后利用Pro/E零件与组件模块,对各标准传动件进行参数化三维实体造型与组件装配,通过限制组件局部自由度来对传动方案进行动态仿真,仿真结果为某型号样机研制提供理论参考。

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.