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.

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

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.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

A Method of Job Scheduling on SMEs' Key Equipments Based on Hybrid Multi-attribute Decision Making

An analysis of the key factors affecting on the single production process job scheduling of the parts waiting for be- ing processed on the key equipments for SMEs (Small Manufacturing Enterprises) is given in this paper,which include interval number,real number and uncertain linguistic value.A kind of hybrid multi-attribute decision making method for the single pro- duction process job scheduling is presented in this paper,that the parts are firstly sorted about each factor,and then the total evalu- ative attributive value of each part is calculated with the method of weighted arithmetic average,and thus the part with the highest total evaluative attributive value is chosen for being processed firstly.The mathematic model corresponding to the method is set up in this paper.An example is studied in this paper,and the results of the example testify the correctness of this model.

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set(SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging(SNNPWA) operator, simplified neutrosophic number power weighted geometric(SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging(SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric(SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multiattribute group decision making(MAGDM) within the framework of SNSs is developed by the above aggregation operators.Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.

A Comprehensive Overview of the ELECTRE Method in Multi-Criteria Decision-Making

The ELECTRE(ELimination Et Choix Traduisant la REalite)method has gained widespread recognition as one of the most effective multi-criteria decision-making(MCDM)methods.Its versatility allows it to be applied in a wide range of areas such as engineering,economics,business,environmental management and many others.This paper aims to provide an overview of the ELECTRE method,including its fundamental concepts,applications,advantages,and limitations.At its core,the ELECTRE method is an outranking family of MCDM techniques,which allows for the direct comparison of alternatives based on a set of criteria.The method takes into account the preferences and importance of decision-makers and generates a ranking of the alternatives based on their relative strengths and weaknesses.The ELECTRE method is a powerful tool for decision-making,and its applicability to a wide range of fields demonstrates its versatility and adaptability.By understanding its concepts,applications,merits,and demerits,decision-makers can use the ELECTRE method to make informed and effective decisions in a variety of contexts.

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Understanding Applications and Best Practices of DEMATEL:A Method for Prioritizing Key Factors in Multi-Criteria Decision-Making

Decision Making Trial and Evaluation Laboratory(DEMATEL)method is a powerful tool for understanding and visualizing the causal relationships among factors in complex decision-making problems.The method uses diagrams and matrixes to map out the causal relationships and interdependencies among factors,allowing decision-makers to identify key drivers and potential solutions to the problem.DEMATEL has a wide range of application areas,including supply chain management,environmental planning,healthcare,finance,and engineering,among others.The DEMATEL method is a valuable tool for decision-makers who need to understand the complex causal relationships among factors in order to make informed decisions.The method provides a structured approach for analyzing and prioritizing factors and for identifying potential solutions to complex problems.This paper describes the main features of this method,its application areas as well as the main process steps in the DEMATEL method.

Multi-attribute decision-making approach dealing with uncertain linguistic assessment information

An approach is presented to deal with a multi-attribute decision-making problem in which the attribute weights are unknown and the attribute values take the form of uncertain linguistic variables. First, a linguistic assessment standard is set up to deal with the uncertain linguistic attributes, and the operation laws of uncertain linguistic variables and the uncertain linguistic weighting average(ULWA)operator are introduced. Then a ranking formula of uncertain linguistic variables based on expectation-variance is proposed. As for the case without weight information, a goal program based on a warp function is constructed to determine the attribute weights, and the ULWA operator is utilized to aggregate the assessment information of uncertain linguistic variables, and the corresponding alternatives are ranked by a formula based on expectation-variance. Finally, a numerical example is given, and the results demonstrate that it is much easier and faster for the ranking method based on expectation-variance when compared to the existing methods.

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.

Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

VIKOR Method-An Effective Compromising Ranking Technique for Decision Making

The VIKOR(VlseKriterijumska Optimizacija I Kompromisno Resenje)method,which is a multi-criteria decision-making method,is examined in this paper.The VIKOR method,like other MCDM techniques such as the Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS),is widely used to solve complex decision-making problems in various fields such as engineering,management,and finance.This paper provides an overview of the VIKOR method,including its application areas,advantages,and disadvantages.Besides,in this survey paper,the process steps of the VIKOR method are described,including determining the decision matrix,normalizing the matrix,determining the weights of the criteria,calculating the utility and regret values,calculating the VIKOR index,and finally ranking the alternatives.By providing an overview of the VIKOR method and its process steps,this paper aims to provide a better understanding of the method and its potential application in different decision-making contexts.

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。

计及群体压力和群体极化的PDHFSs-TODIM多属性群体决策算法

在概率对偶犹豫模糊环境下的多属性决策中,针对决策过程一般未考虑决策专家在讨论中所受的群体压力和群体极化的问题,提出了一种计及群体压力和群体极化的概率对偶犹豫模糊集-拓扑判别目标间方法(probabilistic discriminative heterogeneous fuzzy sets-topological discriminative inter-objective method,PDHFSsTODIM)的多属性群体决策算法。首先,定义了考虑群体压力的决策信息修正公式,有效削弱群体压力对专家决策信息的影响;然后,搭建了一种考虑群体极化现象的决策模型,该模型充分考虑了专家的主观性,为专家讨论和修正决策提供了机会,通过分配动态决策权重提高决策的置信度,并通过群体极化阈值约束群体的极化效应;进一步,将计算得到的决策数据输入改进的TODIM算法,得到最终决策结果。将算法运用于储能电池综合性能评估分析,通过与其他先进决策算法做对比,验证了所提算法的可靠性与准确性。

基于NSGA-Ⅲ算法的长距离调水泵站多目标优化调度研究

针对长距离调水泵站运行过程中水泵运行效率低、安全隐患较大等问题,以调水泵站运行电费最小、水泵平均效率最大、水泵流量平均偏离度最小、水泵平均启停频次最小为目标建立优化模型。以华东某沿海城市调水工程为例,采用第三代非支配排序遗传算法(NSGA-Ⅲ)求解优化模型,运用层次分析法与CRITIC法进行组合赋权,结合逼近理想解排序法(TOPSIS)进行方案优选。结果表明,相较于常规调度方案,优化调度方案中两泵站的运行电费和水泵流量平均偏离度均显著降低,水泵平均效率均显著提高,水泵平均启停频次均有所减少。表明在综合考虑泵站运行经济性的情况下,所建优化模型能够有效降低安全隐患。

Using Mathematical Models in Decision Making Methodologies to Find Key Nodes in the Noordin Dark Network

A Dark Network is a network that cannot be accessed through tradition means. Once uncovered, to any degree, dark network analysis can be accomplished using the SNA software. The output of SNA software includes many measures and metrics. For each of these measures and metric, the output in ORA additionally provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning best methods to disrupt or deceive a given dark network. In the Noordin Dark network, different nodes were identified as key nodes based upon the metric used. Our goal in this paper is to use methodologies to identify the key players or nodes in a Dark Network in a similar manner as we previously proposed in social networks. We apply two multi-attribute decision making methods, a hybrid AHP & TOPSIS and an average weighted ranks scheme, to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We compare these methods by illustration using the Noordin Dark Network with seventy-nine nodes. We discuss sensitivity analysis that is applied to the criteria weights in order to measure the change in the ranking of the nodes.