A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

A method for multiple attribute decision making with incomplete weight information in linguistic setting

The aim of this paper is to investigate the multiple attribute decision making problems with linguistic information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic variables. We first introduce some approaches to obtaining the weight information of attributes, and then establish an optimization model based on the ideal point of attribute values, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the numerical weighting linguistic average (NWLA) operator to aggregate the linguistic variables corresponding to each alternative, and then rank the alternatives by means of the aggregated linguistic information. Finally, the developed method is applied to the ranking and selection of propulsion/manoeuvring system of a double-ended passenger ferry.     

Customer evaluation for order acceptance using a novel class of fuzzy methods based on TOPSIS

Customer evaluation plays an important role as a part of the order acceptance process of suppliers in optimally allocating resources and prioritizing orders accordingly. In this paper, a new class of fuzzy methods for evaluating customers is applied. Firstly, our approach tackles the issue of uncertainty that is inherent in the problem of customer evaluation that involves qualitative criteria by employing the method proposed by Yong [Yong, D. (2006). Plant location selection based on fuzzy TOPSIS. International Journal of Advanced Manufacturing Technology, 28(7–8), 839–844] in order to efficiently transform linguistic assessments of the weights of criteria and of the ratings of customers into crisp numbers. Secondly, the TOPSIS method is modified in order to integrate the behavioral pattern of the decision maker into its “principle of compromise”. In this context, a new model for the aggregating function of TOPSIS that is based on a fuzzy set representation of the closeness to the ideal and the negative ideal solution is applied. In particular, we use the class of intersection connectives proposed by Yager [Yager, R. R. (1980). On a general class of fuzzy connectives. Fuzzy Sets and Systems, 4(3), 235–242] that enables a formal definition of the relation between the closeness to the ideal solution and the closeness to the negative ideal solution. Thus, a class of methods is formulated whose different instances correspond to different behavioral patterns of the decision makers, e.g. with preference to customers that make as much profit as possible but also avoid as much risk as possible or to customers that are performing well in at least one of the profit and risk criteria. A numerical example, illustrating the application of this class of methods to customer evaluation is given.     

基于云模型的Pythagorean模糊语言多属性决策方法

针对专家给出的属性值为Pythagorean模糊语言且专家权重与属性权重均未知的多属性决策问题进行了研究,提出一种基于云模型的多属性决策方法。首先,根据Pythagorean模糊语言决策信息的距离熵计算得到属性权重;其次,计算决策矩阵间的距离从而得到各决策专家权重;再次,构建Pythagorean模糊云模型决策矩阵并利用专家权重和属性权重进行信息集结;最后,基于TOPSIS方法求取正、负理想解,依据理想解计算各方案贴近度并据此对各备选方案进行排序选择。案例分析表明,该方法优化了复杂环境下的决策,避免了决策信息的丢失,能够较好解决决策信息的不确定性和决策过程的随机性,具有一定的可行性和有效性。     

An objective approach to MADM with interval numbers

In ambiguous decision domain, interval numbers are always employed to model multiple attribute decision making （MADM） problems, in which attribute values of alternatives are expressed in the form of intervals. In this study, a new approach is proposed for the interval MADM problems： The interval decision matrix is transformed into definite one by comparing the interval attribute values with the base intervals of attributes; The attribute weights are determined based on the definite decision matrix; the alternatives are assessed based on TOPSIS. An example of assessing the faculty candidates （alternatives） is used to illustrate the proposed approach.     

A method for group decision making with multi-granularity linguistic assessment information

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.     

Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information

In traditional TOPSIS method, the ideal solutions for alternatives are expressed in vectors. An important step in the process of group decision making is to determine the relative importance of each decision maker. In this paper, the weights of decision makers derived from individual decision are determined by using an extended TOPSIS method with interval numbers. The ideal decisions for all individual decisions are expressed in matrices. The positive ideal decision is the intersection of all individual decisions; the negative ideal decision is the union of all individual decisions. Comparisons with other methods are also made. A numerical example is examined to show the potential applications of the proposed method.     

混合型多属性决策问题的序关系求解方法

研究了包含实数型、区间型和风险型属性的混合型多属性决策问题,提出一种基于优先序关系的决策模型.并给出了具体求解方法和步骤说明,通过比较各属性下方案间的优劣程度,建立模糊互补判断矩阵,以排序向量为基础计算每个方案各属性下的Borda分,根据属性权重向量加权集结得到总排序向量,实现方案总体优劣的排序,该方法直观、概念明确,不需要对决策矩阵进行规范化,易于实际操作.最后以自动目标识别系统性能评估为例,进行了算例分析.     

基于粗糙集的直觉模糊TOPSIS多属性决策方法

针对属性值为直觉模糊信息且属性权重完全未知的多属性决策问题,提出了一种基于粗糙集的直觉模糊TOPSIS多属性决策方法.首先给出了直觉模糊信息的正、负理想点的求法,根据属性值与理想点的贴近度和给定的阈值求得判断矩阵,再根据判断矩阵对属性约简,确定各属性的权重,最后依据TOPSIS思想计算各方案与理想点的加权贴近度,得到方案的排序,并通过算例的分析比较验证了此方法的有效性.     

A novel approach to determine cell formation,intracellular machine layout and cell layout in the CMS problem based on TOPSIS method

This paper deals with the cellular manufacturing system (CMS) that is based on group technology (GT) concepts. CMS is defined as identifying the similar parts that are processed on the same machines and then grouping them as a cell. The most proposed models for solving CMS problems are focused on cell formation and intracellular machine layout problem while cell layout is considered in few papers. In this paper we apply the multiple attribute decision making (MADM) concept and propose a two-stage method that leads to determine cell formation, intracellular machine layout and cell layout as three basic steps in the design of CMS. In this method, an initial solution is obtained from technique for order preference by similarity to the ideal solution (TOPSIS) and then this solution is improved. The results of the proposed method are compared with well-known approaches that are introduced in literature. These comparisons show that the proposed method offers good solutions for the CMS problem. The computational results are also reported.     

A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection

Supplier selection has become a very critical activity to the performance of organizations and supply chains. Studies presented in the literature propose the use of the methods Fuzzy TOPSIS (Fuzzy Technique for Order of Preference by Similarity to Ideal Solution) and Fuzzy AHP (Fuzzy Analytic Hierarchy Process) to aid the supplier selection decision process. However, there are no comparative studies of these two methods when applied to the problem of supplier selection. Thus, this paper presents a comparative analysis of these two methods in the context of supplier selection decision making. The comparison was made based on the factors: adequacy to changes of alternatives or criteria; agility in the decision process; computational complexity; adequacy to support group decision making; the number of alternative suppliers and criteria; and modeling of uncertainty. As an illustrative example, both methods were applied to the selection of suppliers of a company in the automotive production chain. In addition, computational tests were performed considering several scenarios of supplier selection. The results have shown that both methods are suitable for the problem of supplier selection, particularly to supporting group decision making and modeling of uncertainty. However, the comparative analysis has shown that the Fuzzy TOPSIS method is better suited to the problem of supplier selection in regard to changes of alternatives and criteria, agility and number of criteria and alternative suppliers. Thus, this comparative study contributes to helping researchers and practitioners to choose more effective approaches for supplier selection. Suggestions of further work are also proposed so as to make these methods more adequate to the problem of supplier selection.     

Application of TOPSIS Method in Support of Decisions Made in Staff Management Issues

Evaluation model was proposed which refers to fuzzy formalism of the personnel management issues taking account their specific characteristics. Application of TOPSIS （technique for order Performance by similarity to ideal solution） method for evaluation and regulation of alternatives based on hierarchically structured criteria of qualitative character by multiple experts to intellectually support decisions made in staff management issues is reviewed in the article. Candidate selection experiment based on criteria system formed using TOPSIS method for evaluation of candidates during solution of hiring problems reviewed and obtained results were compared with results obtained using Matlab program package.     

Aggregating linguistic expert knowledge in type-2 fuzzy ontologies

In many industrial contexts, knowledge and data provided by experts are imprecise as there seems to be an understanding that “experts do not need precise details as they understand anyway what is meant”. The imprecision inherent in the knowledge that experts acquire in their practice require decision support tools that can be tailored to the specific application contexts to aid complex decisions. As a specific example, expert knowledge expressed in linguistic terms is not precisely structured and concepts are not defined specifically enough in order to be easy to use and process. If we want to represent and use expert knowledge for knowledge-based systems on a general level, that is easily adaptable, we need to find ways to represent and process knowledge elements; our approach is to use interval-valued fuzzy sets, fuzzy ontology and aggregation operators. We show that these instruments will offer us a novel approach for aggregation of imprecise data to obtain actionable knowledge to aid complex decisions. The framework is described and the approach is shown through the context of a fuzzy wine ontology; the problem formulation resembles many features of important and complex decision making problems found in different industries. We describe the potential application of the framework in the case of paper machine maintenance. A web-based application is introduced to better demonstrate the benefits decision-makers can receive from the proposed framework. Additionally, we present an approach to utilize the framework in finding consensual solutions in situations involving several experts.     

The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets

Pythagorean fuzzy sets (PFSs) as a new generalization of fuzzy sets (FSs) can handle uncertain information more flexibly in the process of decision making. In our real life, we also may encounter a hesitant fuzzy environment. In view of the effective tool of hesitant fuzzy sets (HFSs) for expressing the hesitant situation, we introduce HFSs into PFSs and extend the existing research work of PFSs. Concretely speaking, this paper considers that the membership degree and the non-membership degree of PFSs are expressed as hesitant fuzzy elements. First, we propose a new concept of hesitant Pythagorean fuzzy sets (HPFSs) by combining PFSs with HFSs. It provides a new semantic interpretation for our evaluation. Meanwhile, the properties and the operators of HPFSs are studied in detail. For the sake of application, we focus on investigating the normalization method and the distance measures of HPFSs in advance. Then, we explore the application of HPFSs to multi-criteria decision making (MCDM) by employing the technique for order preference by similarity to ideal solution (TOPSIS) method. A new extension of TOPSIS method is further designed in the context of MCDM with HPFSs. Finally, an example of the energy project selection is presented to elaborate on the performance of our approach.     

信息对抗中多属性决策模型的研究

在分析信息对抗重要作用的基础上,针对各种决策理论在信息对抗中的应用,利用不确定性理论,建立基于理想点的多属性决策模型,给出决策结论的可靠性分析。     

基于CBR和MADM的多Agent推荐系统

为解决目前基于CBR的推荐系统只考虑属性值全部为精确或全部为非精确数据的情况,提出一种基于MADM的多Agent推荐系统框架。在考虑了属性分类的基础上设计了基于距离的混合数据类型的相似性度量算法及TOPSIS多属性决策方法,设计了该系统各组成部分功能、结构和流程。模拟算例演示了案例推理及多属性决策在本系统的应用过程,结果表明该系统有较好的实用性。     

New aggregation operators based on the Choquet integral and 2-tuple linguistic information

Considered in this paper is the group decision making problem with inter-dependent or interactive attributes, where evaluation values of decision makers are in linguistic arguments. By using the Choquet integral, some new aggregation operators are introduced, including the 2-tuple correlated averaging operator, the 2-tuple correlated geometric operator and the generalized 2-tuple correlated averaging operator. The proposed operators can better reflect the correlations among the elements. After investigating properties of these operators, a new multiple attribute decision making method based on the new operators is proposed. Finally, a numerical example is provided to illustrate the feasibility and efficiency of the proposed method.     

基于新型语言评估标度的二元语义改进模型

为了有效地求解基于语言评价信息的多属性决策问题,针对目前常用的二元语义分析方法中存在的标度转换问题,提出一种处理语言评价信息的新型复合标度(该标度综合了指数标度和-n～n标度的优点),建立了基于新型复合标度的二元语义改进模型.算例验证结果表明,新型复合标度为处理定性的语言评价信息提供了科学依据,所提出的改进模型可以有效提高决策结果的精度和可信度.     

直觉梯形模糊数MADM问题的灰色关联分析法

针对属性权重信息完全已知且属性值以直觉梯形模糊数形式给出的多属性决策问题,提出了一种灰色关联分析方法。首先给出了直觉梯形模糊数的定义、距离和性质,然后依据传统的灰色关联分析法的基本思想建立了直觉梯形模糊数多属性决策问题的决策步骤。最后给出了一个实例分析,其结果表明了该方法的实用性和有效性。     

The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making

The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.