考虑QoS偏好的多属性群决策服务选择策略

面对多个功能相同或相似的服务,服务的Qo S是服务选择中重要的考虑因素.将Qo S属性分为精确数型、区间数型和三角模糊数型.在此基础上,利用TOPSIS（technique for order preference by similarity to an ideal solution）条件下的多属性群决策模型给出了服务选择过程,该过程考虑了多个决策者在决策过程中所占的权重,以及多个决策者不同的Qo S偏好权重.通过一个实例验证了该方法的有效性.     

Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

Entropy-based weights on decision makers in group decision-making setting with hybrid preference representations

The weights of decision makers play an important role in group decision-making problems. Entropy is a very important measure in information science. This work models an approach to determine the weights of decision makers by using an entropy measure. A new normalized projection as a separation measure, along with TOPSIS (technique for order preference by similarity to ideal solution) technique, is used for current decision model. The attribute values in current model are characterized by exact values and intervals. A comparison and experimental analysis show the applicability, feasibility, effectiveness and advantages of the proposed method.     

Group decision-making based on pythagorean fuzzy TOPSIS method

Group decision-making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well-known method for multiple-criteria decision-making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision-making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF-TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF-TOPSIS are solved.     

Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment

This paper develops an evaluation approach based on the Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), to help the Air Force Academy in Taiwan choose optimal initial training aircraft in a fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterised by triangular fuzzy numbers. This study applies the fuzzy multi-criteria decision-making (MCDM) method to determine the importance weights of evaluation criteria and to synthesize the ratings of candidate aircraft. Aggregated the evaluators’ attitude toward preference; then TOPSIS is employed to obtain a crisp overall performance value for each alternative to make a final decision. This approach is demonstrated with a real case study involving 16 evaluation criteria, seven initial propeller-driven training aircraft assessed by 15 evaluators from the Taiwan Air Force Academy.     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

An integrated fuzzy multi criteria group decision making approach for ERP system selection

This paper aims to ease group decision-making by using an integration of fuzzy AHP (analytic hierarchy process) and fuzzy TOPSIS (technique for order preference by similarity to ideal solution) and its application to software selection of an electronic firm. Firstly, priority values of criteria in software selection problem have been determined by using fuzzy extension of AHP method. Fuzzy extension of AHP is suggested in this paper because of little computation time and much simpler than other fuzzy AHP procedures. Then, the result of the fuzzy TOPSIS model can be employed to define the most appropriate alternative with regard to this firm's goals in uncertain environment. Fuzzy numbers are presented in all phases in order to overcome any vagueness in decision making process. The final decision depends on the degree of importance of each decision maker so that wrong degree of importance causes the mistaken result. The researchers generally determine the degrees of importance of each decision maker according to special characteristics of each decision maker as subjectivity. In order to overcome this subjectivity in this paper, the judgments of decision makers are degraded to unique decision by using an attribute based aggregation technique. There is no study about software selection using integrated fuzzy AHP-fuzzy TOPSIS approach with group decision-making based on an attribute based aggregation technique. The results of the proposed approach and the other approaches are compared. Results indicate that our methodology allows decreasing the uncertainty and the information loss in group decision making and thus, ensures a robust solution to the firm.     

基于语言偏好序的多属性群决策方法及其在废旧物资循环利用中的应用

循环经济作为应对资源短缺威胁和绿色低碳转型需求的新型经济发展模式,正受到越来越广泛的关注.为了推动这一计划的实践进程,众多举措被提出并付诸行动,废旧物资循环利用体系建设是其中之一.考虑到与此类问题相关的决策过程中通常涉及多方面的制约因素且需要平衡各方意见,提出一种基于语言偏好序和拓展TOPSIS的多属性群决策方法.首先,利用数据挖掘和自然语言处理等技术,对相关新闻网站进行爬虫并获得大量的公共数据,再通过关键词提取和聚类确定决策属性及其权重;然后,采用基于多准则相互评估矩阵的专家互评方式,对参与决策的专家完成赋权;接着,运用语言偏好序、拓展的TOPSIS方法以及最小-最大优化模型依次实现决策信息表征、个体排序和集体排序的完整决策过程;最后,为了验证所提出方法的适用性,将其应用于废旧物资回收站点设置方案选择的实例,并进一步通过比较分析对其优势和特点展开具体说明.     

Multiple attribute decision-making methods for the dynamic operator allocation problem

This study explores two multiple attribute decision-making (MADM) methods to solve a dynamic operator allocation problem. Both methods use an analytic hierarchy process (AHP) to determine attribute weights a priori. The first method uses a technique for order preference by similarity to ideal solution (TOPSIS). The second method incorporates a fuzzy-based logic that uses linguistic variable representation, fuzzy operation, and fuzzy defuzzification. The TOPSIS uses deterministic performance ratings and attribute weights, whilst the fuzzy-based is a linguistic method. An applied case study drawn from existing literature is used to demonstrate and test findings. The proposed methods systematically evaluate alternative scenarios, with the result indicating promise for solving an operator allocation decision problem.     

Group decision making with multi-attribute interval data

The aim of this paper is to present a group decision making methodology, in which the decision information, including the attribute values, attribute weights and weights of decision makers, is expressed in interval data. An extended TOPSIS technique is twice used in the proposed method, which is first used to determine the weights of decision makers, and second used to rank the preference order of alternatives. There is no aggregation of decision information in decision process, except that the ideal decisions as auxiliary decision tools are used in decision process. We give a comparison with another method for group decision making to show the technical advance of reported method. Additionally, we also give a real life application for supplier selection and a discussion to test the effectiveness and practical implications of the proposed method.     

A consensus based group decision making methodology for strategic selection problems of supply chain coordination

In a supply chain (SC), the partners often make collective decisions to solve a number of problems which are characterized by various quantitative and qualitative criteria. This article presents a fuzzy TOPSIS and soft consensus based group decision making methodology to solve the multi-criteria decision making (MCDM) problems in supply chain coordination, i.e., selection problems. This methodology is proposed to improve the coordination in decentralized supply chains, i.e., supply chains that comprise several independent, legally separated entities with their own decision authorities. In order to address the imprecision of supply chain partners in formulating the preference value of various criteria, a fuzzy TOPSIS based methodology is proposed. Moreover, a soft consensus based group decision making approach is used for consensus forming among the supply chain partners, regarding the preference values of various criteria for different alternatives. Correlation coefficient and standard deviation (CCSD) based objective weight determination method is also used for enumeration of the weights of the criterion for fuzzy TOPSIS. To demonstrate the applicability of proposed methodology, an illustrative example has been presented.     

A simulated annealing-based permutation method and experimental analysis for multiple criteria decision analysis with interval type-2 fuzzy sets

The aim of this paper is to develop a simulated annealing-based permutation method for multiple criteria decision analysis within the environment of interval type-2 fuzzy sets. The outranking methodology constitutes one of the most fruitful approaches in multiple criteria decision making and has been applied in numerous real-world problems. The permutation method is a classical outranking model, which generalizes Jacquet–Lagreze's permutation method and is based on a pairwise criterion comparison of the alternatives. Because modeling of the uncertainty in the decision-making process becomes increasingly important, an extension to the interval type-2 fuzzy environment is a useful generalization of the permutation method and is appropriate for handling uncertain and imprecise information in practical decision-making situations. This paper produces a signed-distance-based comparison among the comprehensive rankings of alternatives for concordance and discordance analyses. An integrated nonlinear programming model is constructed for estimation of the criterion weights and the optimal ranking order of the alternatives under incomplete preference information. To enhance the implementation efficiency, a simulated annealing-based permutation method and its meta-heuristic algorithm are developed to produce a polynomial time solution for the total completion time problem. Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result.     

An integrated fuzzy multi-criteria approach for the performance evaluation of multiple manufacturing plants

The performance evaluation is regarded as a multiple criteria decision making (MCDM) problem and has a significant impact on the operations of the enterprise. This paper develops an integrated MCDM approach that combines the voting method and the fuzzy TOPSIS (technique for order preference by similarity to ideal solution) method to evaluate the performance of multiple manufacturing plants in a fuzzy environment. Fuzzy TOPSIS helps decision-makers carry out analysis and comparisons in ranking their preference of the alternatives with vague or imprecise data. Since the evaluation result is often greatly affected by the weights used in the evaluation process, the voting method is used in this study to determine the appropriate criteria weights. A case study demonstrating the applicability of the proposed model is presented. The case company is the world’s largest manufacturer of power supplies. It has three primary manufacturing bases located in Wujiang, Dongguan, and Tianjin, China. The proposed approach is used to evaluate the performance of the company’s five manufacturing plants in Wujiang, which produce switch power, telecom power, DC/DC converters, uninterruptible power systems (UPS) and AC/DC adapters.     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.     

Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method

Evaluation of the competitiveness of high-tech industry is a technical decision-making issue involving multiple criteria. It is also a practical path to promote a country’s competitiveness. However, the competitiveness indicators in high-tech industry often act and react upon one another. Moreover, different dimensions and indicator weights also affect the evaluation results. In this paper, the Mahalanobis distance is used to improve the traditional technique for order preference by similarity to ideal solution (TOPSIS). The improved TOPSIS method has the following properties: (1) an improved relative closeness which is invariant after non-singular linear transformation, and (2) the weighted Mahalanobis distance is the same as the weighted Euclidean distance when the indicators are uncorrelated. The new method is applied to evaluate the competitiveness of the Chinese high-tech industry using data from 2011. Consideration of the correlation between indicators improves the evaluation results (in terms of sorting and closeness) to a certain extent compared to the traditional TOPSIS method. The top five provinces are: Guangdong, Jiangsu, Shanghai, Beijing, and Shandong. This finding reflects the practical linkage among provinces and softens the closeness value, consistent with reality.     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.     

Logistics tool selection with two-phase fuzzy multi criteria decision making: A case study for personal digital assistant selection

Efficient logistics and supply chain management are enabled through the use of efficient information technologies (IT). The mobile logistics tools represent the IT interface in the supply chain. This paper aims to aid decision makers to identify the most appropriate mobile logistics tools and to achieve this aim, several evaluation criteria are identified to evaluate logistics tools, and a fuzzy axiomatic design (FAD) based group decision-making method is adopted to perform the evaluation in two phases. In the first phase of pre-assessment, alternatives that cannot meet basic requirements and the defined threshold are eliminated. In the second phase of selection, the remaining alternatives are more meticulously evaluated. Criteria weights are determined using fuzzy analytic hierarchy process (AHP) and another fuzzy multi-criteria decision-making (MCDM) technique, namely fuzzy technique for order preference by similarity to ideal solution (TOPSIS), is applied in the second phase to compare the outcome of FAD. A case study is provided in order to demonstrate the potential of the proposed methodology. Personal digital assistants (PDAs) with integrated barcode scanner that are available in the Turkish market are evaluated.     

A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets

This paper develops new methods based on the preference ranking organization method for enrichment evaluations (PROMETHEE) that use a signed distance-based approach within the environment of interval type-2 fuzzy sets for multiple criteria decision analysis. The theory of interval type-2 fuzzy sets provides an intuitive and computationally feasible way of addressing uncertain and ambiguous information in decision-making fields. Many studies have developed multiple criteria decision analysis methods in the context of interval type-2 fuzzy sets; most of these methods can be characterized as scoring or compromising models. Nevertheless, the extended versions of outranking methods have not been thoroughly investigated. This paper establishes interval type-2 fuzzy PROMETHEE methods for ranking alternative actions among multiple criteria based on the concepts of signed distance-based generalized criteria and comprehensive preference indices. We develop interval type-2 fuzzy PROMETHEE I and interval type-2 fuzzy PROMETHEE II procedures for partial and complete ranking, respectively, of the alternatives. Finally, the feasibility and applicability of the proposed methods are illustrated by a practical problem of landfill site selection. A comparative analysis is also performed with ordinary fuzzy PROMETHEE methods to validate the effectiveness of the proposed methodology.     

Multicriteria decision making in energy planning using a modified fuzzy TOPSIS methodology

Energy planning is a complex issue which takes technical, economic, environmental and social attributes into account. Selection of the best energy technology requires the consideration of conflicting quantitative and qualitative evaluation criteria. When decision-makers’ judgments are under uncertainty, it is relatively difficult for them to provide exact numerical values. The fuzzy set theory is a strong tool which can deal with the uncertainty in case of subjective, incomplete, and vague information. It is easier for an energy planning expert to make an evaluation by using linguistic terms. In this paper, a modified fuzzy TOPSIS methodology is proposed for the selection of the best energy technology alternative. TOPSIS is a multicriteria decision making (MCDM) technique which determines the best alternative by calculating the distances from the positive and negative ideal solutions according to the evaluation scores of the experts. In the proposed methodology, the weights of the selection criteria are determined by fuzzy pairwise comparison matrices. The methodology is applied to an energy planning decision-making problem.