Fuzzy multiple attributes and multiple hierarchical decision making

A procedure is proposed to solve the multiple attributes and multiple hierarchical system under fuzzy environment. The approach is based on:

1. (1) fuzzy representation;

2. (2) hierarchical performance evaluation structure,

3. (3) gradient eigenvector method for rating the fuzzy criteria weighting, and

4. (4) using the max-min paired elimination method for aggregation.

To illustrate the approach, an example on the evaluation of teaching performance in higher education is solved.     

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.     

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in [Chen and Lee, 2010a] and [Lee and Chen, 2010b] for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.     

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.     

基于模糊群体多属性的项目融资决策模型*

针对城市群基础设施项目融资决策过程中参与决策主体过多、决策意见模糊复杂而量化困难或决策意见量化结果失真等问题,构建了一个全新的项目融资模糊多属性群体决策模型。该模型综合影响融资决策的各方面因素,采用三角模糊语言变量量化专家群体意见,运用计算机语言来实现专家群体意见的集结与模糊变换。整个过程充分考虑专家意见的权威性与群体意见的一致性,保持决策过程高度客观真实。模型最后运用三角模糊隶属函数期望值概念,对备选方案进行自动排序决策。实例验证表明,该模型能取得较好的决策效果,可为城市群基础设施项目融资提供决策参考。     

Multi-criteria group decision making under uncertainty with application to air traffic safety

There are many methods for solving problems of multi-criteria group decision making under uncertainty conditions. It is quite often that decision makers cannot formulate unequivocally their individual preference relations between variants. Analysing the causes of a serious aircraft incident is an example where a group of experts is required to have a very detailed yet interdisciplinary knowledge. Obviously, each expert has only a fraction of such knowledge. Hence, experts can make fuzzy evaluations when they are not sure about them or it is not possible to gain full knowledge. There is a need for a method that in such a case takes into account the strength of preference expressed in the significance of each criterion. Both the significance of criteria and the scores assigned to variants can be represented using fuzzy expressions.The proposed method reflects the problems of decision making when both objective (represented using non-fuzzy expressions) and subjective (represented using linguistic expressions) criteria, are involved. The proposed method enables to obtain a solution without having to conduct negotiations between decision makers. This is of advantage when there is a risk that some experts will be dominated by others. The method not only helps define a single preferred solution but also create the preference relation within a group. By applying this method, it is possible to reproduce the actual preference relations of individual decision makers. Presenting them to decision makers may induce them to change their evaluation of the weights of criteria or how they score variants.     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.     

A hybrid approach for fuzzy multi-attribute decision making in machine tool selection with consideration of the interactions of attributes

Global economic competition has spurred the manufacturing sector to improve and invest in modern equipment to satisfy the needs of the market. In particular, machine tool selection is the most important problem; it plays a primary role in the improvement of productivity and flexibility in the manufacturing environment and involves the imprecise, vague and uncertain information. This paper presents the hybrid approach of the fuzzy ANP (Analytic Network Process) and COPRAS-G (COmplex PRoportional ASsessment of alternatives with Grey relations) for fuzzy multi-attribute decision-making in evaluating machine tools with consideration of the interactions of the attributes. The fuzzy ANP is used to handle the imprecise, vague and uncertain information from expert judgments and model the interaction, feedback relationships and interdependence among the attributes to determine the weights of the attributes. COPRAS-G is employed to present the preference ratio of the alternatives in interval values with respect to each attribute and calculate the weighted priorities of the machine alternatives. Alternatives are ranked in ascending order by priority. As a demonstration of the proposed model, a numerical example is implemented based on the collected data and the literature. The result is then compared with the rankings provided by other methods such as TOPSIS-G, SAW-G and GRA. Moreover, a sensitivity analysis is conducted to verify the robustness of the ranking. The result highlights that the hybrid approach of the fuzzy ANP and COPRAS-G is a highly flexible tool and reaches an effective decision in machine tool selection.     

一种基于二元语义信息处理的多属性群决策方法

为了解决评价信息为语言信息的多属性群决策问题,结合VIKOR方法,提出一种基于二元语义信息处理的多属性群决策方法．该方法使用二元语义信息集结算子获得决策群组的决策信息,通过最大化群效用和最小化个体遗憾来获得决策者满意的折衷方案．该方法计算简单,便于理解,可有效避免信息的丢失和扭曲,并可克服理想解方法不能反映出各方案与正负理想解的接近程度的不足．最后,算例计算结果表明了该方法的有效性．     

A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection

A more scientific decision making process for radio frequency identification (RFID) technology selection is important to increase success rate of RFID technology application. RFID technology selection can be formulated as a kind of group decision making (GDM) problem with intuitionistic fuzzy preference relations (IFPRs). This paper develops a novel method for solving such problems. First, A technique for order preference by similarity to ideal solution (TOPSIS) based method is presented to rank intuitionistic fuzzy values (IFVs). To achieve higher group consensus as well as possible, we construct an intuitionistic fuzzy linear programming model to derive experts’ weights. Depending on the construction of membership and non-membership functions, the constructed intuitionistic fuzzy linear programming model is solved by three kinds of approaches: optimistic approach, pessimistic approach and mixed approach. Then to derive the ranking order of alternatives from the collective IFPR, we extend quantifier guided non-dominance degree (QGNDD) and quantifier guided dominance degree (QGDD) to intuitionistic fuzzy environment. A new two-phase ranking approach is designed to generate the ordering of alternatives based on QGNDD and QGDD. Thereby, the corresponding method is proposed for the GDM problems with IFPRs. Some generalizations on the constructed intuitionistic fuzzy linear programming model are further discussed. At length, the validity of the proposed method is illustrated with a real-world RFID technology selection example.     

A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach

This study presents a strategy-aligned fuzzy simple multiattribute rating technique (SMART) approach for solving the supplier/vendor selection problem from the perspective of strategic management of the supply chain (SC). The majority of supplier rating systems obtained their optimal solutions without considering firm operations management (OM)/SC strategy. The proposed system utilizes OM/SC strategy to identify supplier selection criteria. A fuzzy SMART is applied to evaluate the alternative suppliers, and deals with the ratings of both qualitative and quantitative criteria. The final decision-maker incorporates the supply risks of individual suppliers into final decision making. Finally, an empirical study is conducted to demonstrate the procedure of the proposed system and identify the suitable supplier(s).     

The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach

Technological forecasting is a tool for organizations to develop their technology strategies. The quality of forecasting is extremely important for the accuracy of the results and in turn company future. Therefore a proper selection methodology of forecasting technique that considers the characteristics of technology and resources needed such as cost, time is essential. On the other hand, although many forecasting techniques are available, there is a high uncertainty in choosing the most appropriate technique among a set of available techniques. In this paper interval valued intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method is proposed for the solution of technological forecasting technique selection problem. The proposed method includes seven selection criteria and twelve forecasting technique alternatives. The methodology is applied for 3D TV technology. The results revealed that Fisher Pry method is found as the most appropriate method for forecasting since it has the highest closeness coefficient.     

Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information

With respect to multi-criteria group decision making (MCGDM) problems under trapezoidal intuitionistic fuzzy environment, a new MCGDM method is investigated. The proposed method can effectively avoid the failure caused by the use of inconsistent decision information and provides a decision-making idea for the case of “the truth be held in minority”. It consists of three interrelated modules: weight determining mechanism, group consistency analysis, and ranking and selection procedure. For the first module, distance measures, expected values and arithmetic averaging operator for trapezoidal intuitionistic fuzzy numbers are used to determine the weight values of criteria and decision makers. For the second module, a consistency analysis and correction procedure based on trapezoidal intuitionistic fuzzy weighted averaging operator and OWA operator is developed to reduce the influence of conflicting opinions prior to the ranking process. For the third module, a trapezoidal intuitionistic fuzzy TOPSIS is used for ranking and selection. Then a procedure for the proposed MCGDM method is developed. Finally, a numerical example further illustrates the practicality and efficiency 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.     

Attribute selection with fuzzy decision reducts

Rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems. It revolves around the notion of discernibility: the ability to distinguish between objects, based on their attribute values. It allows to infer data dependencies that are useful in the fields of feature selection and decision model construction. In many cases, however, it is more natural, and more effective, to consider a gradual notion of discernibility. Therefore, within the context of fuzzy rough set theory, we present a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations. The paper unifies existing work in this direction, and introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure. Experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets, leading to decision models with a better coverage and with comparable, or even higher accuracy.     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

On the fusion of multi-granularity linguistic label sets in group decision making

Group decision-making problem is a common and crucial human activity. Many times due to inherent uncertainty, exact numbers can be either costly or unnecessary to be applied to express experts’ opinions or preferences. The use of linguistic labels makes expert judgment more reliable and informative for decision-making.     

A new approach for multiple attribute group decision making with interval-valued intuitionistic fuzzy information

This paper proposes a novel method for multiple attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy information. The interval-valued intuitionistic fuzzy numbers of each expert preference matrix are first mapped into two dimensions. Thus, the values of each membership degree and non-membership degree are considered as points in the two-dimensional representation. Moreover, the distance between the points represents the variance among the different experts preferences. The preference points of the same character are considered as a point set. We employ the plant growth simulation algorithm (PGSA) to calculate the optimal rally points of every point set, the sum of whose Euclidean distances to other given points is minimal, and these optimal rally points reflect the preferences of the entire expert group. These points are used to establish an expert preference aggregation matrix. Suitable points from the matrix are chosen to constitute an ideal point matrix, a projection method is employed to calculate the sum of its Euclidean distance to the expert preference aggregation matrix, and the score of each alternative is evaluated. Finally, the overall ranking of alternatives is obtained. In addition, this study develops a process to evaluate the pros and cons of different aggregation methods. Two typical examples are presented to illustrate the feasibility and effectiveness of the proposed approach.     

Leveraging technological knowledge transfer by using fuzzy linear programming technique for multiattribute group decision making with fuzzy decision variables

Despite the importance of knowledge transfer for firms involved in foreign direct investment activities, this area has not received appropriate attention from the perspectives of both the knowledge transferor (i.e., MNC parent) and the knowledge recipient. To fill in the gap in the current literature we propose a model to understand the links between criteria complicating the transfer of knowledge and preferences that the company has to focus. This model is based on both the existing literature as well as views of company representatives and provides a useful methodology for identifying decision making problems on the transfer of knowledge. In this paper, we investigate the fuzzy linear programming technique (FLP) to analyze these links and for multiple attribute group decision making (MAGDM) problems with preference information on criteria. To reflect the decision maker’s subjective preference information and to determine the weight vector of attributes, the technique for order preference by similarity to ideal solution (TOPSIS) developed by Hwang and Yoon (1995) and the linear programming technique for multidimensional analysis of preference (LINMAP) developed by Sirinivasan and Shocker (Psychometrica 38:337–369, 1973) are used.     

An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers

This article proposes an approach to resolve multiple attribute group decision making (MAGDM) problems with interval-valued intuitionistic trapezoidal fuzzy numbers (IVITFNs). We first introduce the cut set of IVITFNs and investigate the attitudinal score and accuracy expected functions for IVITFNs. Their novelty is that they allow the comparison of IVITFNs by taking into accounting of the experts’ risk attitude. Based on these expected functions, a ranking method for IVITFNs is proposed and a ranking sensitivity analysis method with respect to the risk attitude is developed. To aggregate the information with IVITFNs, we study the desirable properties of the interval-valued intuitionistic trapezoidal fuzzy weighted geometric (IVITFWG) operator, the interval-valued intuitionistic trapezoidal fuzzy ordered weighted geometric (IVITFOWG) operator, and the interval-valued intuitionistic trapezoidal fuzzy hybrid geometric (IVITFHG) operator. It is worth noting that the aggregated value by using these operators is also an interval-valued intuitionistic trapezoidal fuzzy value. Then, based on these expected functions and aggregating operators, an approach is proposed to solve MAGDM problems in which the attribute values take the form of interval-valued intuitionistic fuzzy numbers and the expert weights take the form of real numbers. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.