In order to cope with the complex features of ambiguity, randomness and uncertainty in multi-attribute decision-making problems, this paper introduces the Dempster-Shafer evidence theory in the framework of cloud modeling. First, a cloud model is used to calculate the affiliation of each evaluation metric, which was subsequently converted to a basic confidence assignment function. Second, the game theory idea is borrowed to combine the dynamic and static weights of the evidence in the game, to improve the traditional evidence theory and realize the effective integration of information. The idea of average fit is identified again, and a comprehensive evaluation conclusion is drawn by comparing the closeness of the evaluation object to the optimal and worst solutions. The new electric power system investment project is illustrated, and the applicability of the algorithm is verified.

The aim of this study is to address the multi-criteria group decision-making problems, where decision information is expressed by experts using single-valued or interval-valued fuzzy linguistic terms, with both expert weights and criteria weights being unknown. This paper proposes a novel method that combines the merits of distance entropy and the interval rough number cloud model, for handling uncertain information. Firstly, criteria weights are determined using distance entropy applied to interval rough numbers, which are derived from a fuzzy linguistic decision matrix containing single-valued or interval-valued. Secondly, expert weights are determined by measuring deviations between each expert’s individual decision matrix and those of other experts. Thirdly, construct an interval rough number cloud model based decision matrix to aggregate decision information via the determined expert weights and criteria weights. Finally, alternatives are ranked based on cloud closeness degrees, which are calculated via the TOPSIS method. To validate the method’s effectiveness, this paper presents a case study on failure mode and effects analysis, for the single-point mooring system of a floating production storage and offloading vessel in the South China Sea. The proposed method yields the following advantages: (1) it enhances decision-making accuracy in complex and uncertain environments; (2) it minimizes information loss; (3) it effectively handles both the inherent uncertainty of decision data and the randomness of the decision-making process.

The multi-dimensional cloud model is proposed as the expansion of the one-dimensional cloud model. The features of ambiguity and stochasticity in complex information situations are considered; thus, this optimized model can be utilized upon multiple value classifications and ordering via which the objects' attributes of physical and social can be reflected. Therefore, this promoted model is wildly used. This paper provides a knowledge graph by reviewing the theoretical research of the multi-dimensional cloud model and its related bibliographies, and Cite Space is applied here to give a visualization conclusion. In recent years, a multitude of theories and methods have emerged to address the challenges posed by fuzzy and stochastic uncertainty in various domains, such as image segmentation, data mining, prediction techniques, and comprehensive evaluation of multiple metrics and dimensions using uncertain linguistic variables.

The Aczel Alsina MacLaurin symmetric mean (AAMSM) operator using the Aczel Alsina norm is constructed in the interval-valued Pythagorean fuzzy (IVPF). Its advantage is that decision-makers can make decisions based on risk preferences which is suitable for handling complex data in uncertain environments. The definitions of the Aczel-Alsina norm and MacLaurin symmetric mean operator are given; then, it is of importance to analyse the properties of the interval-valued Pythagorean fuzzy Aczel-Alsina MacLaurin symmetric mean (IVPFAAMSM) operator, propose the IVPFAAMSM multi-attribute decision-making method, and perform sensitivity analysis. Finally, a scenario is illustrated to show that the approach is feasible and effective.

文章结合云模型与Bonferroni几何均值算子给出一种决策方法,根据直觉模糊云的概念及其代数运算,采用直觉模糊云逆向云生成算法,构建直觉模糊规范加权Bonferroni云模型集成算子;最后,算例分析结果表明本文方法的有效性和可行性.

There are implications for important sectors of the U.S. economy as well. For example, if the opioid crisis spreads to all cross-sections of the U.S. population (including the college-educated and those with advanced degrees), businesses requiring precision labor skills, high technology component assembly, and sensitive trust or security relationships with clients and customers might have difficulty filling these positions. Further, if the percentage of people with opioid addiction increases within the elderly, health care costs and assisted living facility staffing will also be affected. Based on the Gradient Boosting Decision Tree (GBDT) model, this paper analyzes the correlation analysis with support vector machine algorithm, geographic information marker and so on, and puts forward some relevant strategy suggestions. Firstly, the parameters of the model are constantly adjusted so that the model adapts to the parameters, and the accuracy of the model is finally 0.8438. Secondly, combined with analysis and related literature, this paper enumerates the reasons for the growth of opioid use and addiction in three points and the reasons for two growth. The number of different drugs is calculated according to the model, and the threshold for drug identification in each county reached 5501 of the county's total drug identification, and Philadelphia was the most likely to exceed the drug identification threshold level. With the support vector machine algorithm to process the data, it is concluded that the function of the support vector machine regression model is proposed. Finally, three strategies are proposed against the opioid crisis. The remaining variables of this model still have an effect on synthetic opioids. In order to make the results universal, this article fills in the remaining variables and calculates the corresponding amount of synthetic opioids. The results show that the propagation characteristics of the use of synthetic opioids and heroin events are increasing with the increase of time. And the use of multiple regions of opioid drugs has a certain radiation influence on the surrounding area which has a piece-wise structure. It can be concluded from the characteristic graph that the problem of aging in the social economic structure has the greatest influence on synthetic opioids. And the problem of social aging has a certain impact on the opioid crisis.

判断矩阵一致性是群体综合评价的重要内容.一致性可以反映专家群体就所有可能的替代方案达成完全一致的意见,利用一致性测度可以衡量评价者之间的差异,也是共识判断的基础.文章针对加权幂平均复合判断矩阵中存在的一致性问题进行研究,从幂平均次数对复合判断矩阵影响的角度,分析幂平均次数对一致性比率的影响程度,揭示两者之间的变化规律;研究专家判断矩阵的阶数对一致性比率的作用;从群体专家权重的角度,研究权重对复合判断矩阵一致性比率的敏感性.结果表明:(1)幂平均的次数会影响复合判断矩阵的一致性,幂平均的次数在有限区间内保证复合判断矩阵的满意一致性,有限区间长度同时依赖于判断矩阵的阶数与幂平均的次数,且一致性比率是关于幂平均次数的凹函数;(2)判断矩阵的阶数越高,专家给出判断矩阵的难度加大,然而随着判断矩阵阶数的升高,一致性比率会呈递减趋势;(3)专家的权数对于一致性比率影响较小,即专家权数的灵敏度较低,给定权数的扰动后不会影响复合判断矩阵的满意一致性.

This article addresses the issue of selecting Financial Strategies in Multi-National companies (F.S.M.). The F.S.M. typically has to consider multiple factors involving multiple stakeholders and, hence, can be handled by applying an appropriate Multi-Criteria Group Decision-Making (M.C.G.D.M.) approach. To address this issue, we develop an M.C.G.D.M. framework to tackle the F.S.M. problem. To handle inherent uncertainty in business decisions as reflected by linguistic reasoning, we embark on constructing a Linguistic Pythagorean Fuzzy (L.P.F.) M.C.G.D.M. framework that is capable of tackling both uncertain decision information and linguistic variables. The proposed approach extends the combinative distance-based assessment (C.O.D.A.S.) method into the L.P.F. environment, and processes decision input expressed as Pythagorean fuzzy sets (P.F.S.) and pure linguistic variables (rather than converting linguistic information into fuzzy numbers). The developed L.P.F.-C.O.D.A.S. technique aggregates the L.P.F. information and is applied to the F.S.M. problem with uncertain linguistic information. A comparative analysis is carried out to compare the results obtained from the proposed L.P.F.-C.O.D.A.S. approach with those from other extensions of C.O.D.A.S. Furthermore, a sensitivity analysis is conducted to check the impact of changes in a distance threshold parameter on the ranking results.

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

针对当前统计信息质量评估方法存在的问题,本文给出一种基于云理论的统计数据质量评估方法.首先,确定云模型的评价等级语言粒度,对其进行软划分,并根据统计数据质量的评价指标体系从八个维度刻画数据质量评估云模型,利用云模型加权算术平均集成技术构造评价综合云;然后,结合云模型相似性的测度方法,根据综合云与评价等级云模型的相似度判断统计数据质量评估综合云的隶属等级.最后,通过实例表明本文方法的可行性和有效性,该方法可以作为统计数据质量评估和监管的一个参考.

针对群组评价过程具有模糊性,不确定性和复杂性以及群组内专家之间的判断能力存在差异等问题.以群组评价一致性分析为视角探讨如何有效解决专家之间意见的冲突,提出基于直觉模糊距离的测度方法,对群组评价结果达成共识进行分析;其次,对指标权重和专家权重修正并进行下一轮评价,直至达到满意的一致性;最后,通过实例表明方法的合理性与有效性.

Pythagorean fuzzy sets are highly appealing in dealing with uncertainty as they allow for greater flexibility in regards to the membership and non-membership degrees by extending the set of possible values. In this paper, we propose a multi-criteria group decision-making approach based on the Pythagorean normal cloud. Some cloud aggregation operators are presented in this paper to facilitate the appraisal of the underlying utilities of the alternatives under consideration. The concept and properties of the Pythagorean normal cloud and its backward generation algorithm, aggregation operators and distance measurement are outlined. The proposed approach resembles the TOPSIS technique, which, indeed, considers the symmetry of the distances to the positive and negative ideal solutions. Furthermore, an example from e-commerce is presented to demonstrate and validate the proposed decision-making approach. Finally, the comparative analysis is implemented to check the robustness of the results when the aggregation rules are changed.

在综合评价过程中,Radar图既可以进行可视化定性分析,同时也具有定量分析的能力.针对传统的Radar图综合评价方法进行缺陷分析,并提出三条改进思路:(1)采用Radar图各指标轴之间的夹角大小表示指标的重要程度;(2)简化综合评价函数为特征值分量的几何均值法;(3)采用有序加权的Radar图综合评价方法.改进后的Radar图法评价结果不再受评价者主观取向的影响,评价结果具有唯一性.实例表明Radar图综合评价方法具有可操作性和有效性.

Background: Multiple attribute group decision making (MAGDM) is the common phenomenon in modern life, which is to select the optimal alternative(s) from several alternatives or to discover their ranking by aggregating the performances of each alternative under several attributes, in which the aggregation techniques play an important role, also described in various patents. Keywords: Bonferroni harmonic mean, intuitionistic fuzzy set, ordered weighted, multiple attribute group decision making, trapezoidal fuzzy number, TrIFBHE.

The evaluation index system of ecological civilization construction in China is analyzed .With the methods of analytic hierarchy process (AHP) ,grey comprehensive evaluation and fuzzy compre-hensive evaluation based on grey relational degree ,the comprehensive evaluation model is established in view of ecological development ,environmental development ,economic development and coordina-tion degree .Ten provinces ,autonomous regions and municipalities are selected as samples based on the regional and economic differences such as Jiangsu Province ,Inner Mongolia Autonomous Region , Hainan Province and so on .The comprehensive evaluation on the degree of ecological civilization is made and the results are drawn .The recommendations are also given .

The measurement and evaluation of information security level in big data age is very important to the construction of enterprise information security system and the improvement of enterprise informatization level. According to the analysis and research of the enterprise information security management system under the big data environment, it is found that the domestic enterprises still have shortcomings in the big data security management. The article aims to explore the construction of information security water system, study the evaluation of big data security management system and information security risk countermeasures. Taking NH Company as an example, the evaluation model is analyzed and constructed, and then the final evaluation result is obtained by solving the model. The effectiveness and feasibility of the method are illustrated by an example.

The cloud model, which mainly reflects the uncertainty in the real life and the concepts in human knowledge: fuzziness and randomness. Actually, many practical problems occur in uncertain environments, especially in the situations where the information about all the criteria weights, criteria values and expert weights are uncertain linguistic variables called uncertain pure linguistic problems. For this purpose, In this paper, we present an approach to multi-criteria group decision-making with uncertain pure linguistic information based on the cloud model. To do so, firstly, the uncertain linguistic values are converted into integrated cloud and interval integrated cloud, respectively, and the cloud decision-making information are converted into generating floating cloud and generating floating interval cloud by the cloud operational laws. Secondly, by means of the Hamming distance and closeness degree, the ranking of all alternatives is determined. Finally, a numerical example and comparative analysis with related decision-making methods are provided to illustrate the practicality and feasibility of the proposed method.

针对伴语言变量的区间数多属性决策问题,给出了一种基于云模型的决策方法.方法将云模型和区间数相结合对方案进行模糊综合决策,由语言变量生成对应的云模型,决策者无须给定每朵云的特征.通过云规则进行区间数云转换,结合云模型转化后的区间数进行可能度分析,得到决策方案的排序.通过空袭目标威胁评估实例说明了方法的合理性和有效性.

The kernel and the parameters of Support Vector Machine(SVM)have a significant impact on precision. In view of better learning capability of local kernels and better generalization capability of global kernels, the mixed kernel is constructed by a typical local kernel-Radial Basis Function(RBF)and a typical global kernel-polynomial kernel. By use of Fruit Fly Optimization Algorithm(FOA), a novel FOA-LSSVM model with mixed kernels is set up in this paper. Results demonstrate that the new model has great accuracy than traditional methods and has real application value in forecasting.

数值分析是一门与实际紧密结合的课程.在教学过程中,既要注重介绍课程的思想和方法,更要通过实际问题阐述方法的应用.探讨了将数学建模引入数值分析教学中的必要性和可行性,并通过实例说明方法的有效性.