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.     

Multiperiod multiattribute decision‐making method based on trend incentive coefficient

In this paper, we develop a method for multiperiod multiattribute decision‐making (MP‐MADM) problems, in which the decision information, including attribute weights and attribute values, is given at different periods. First, using the variation in attribute values of the various alternatives for unit time, we can obtain the trend incentive coefficient of variation that represents reward or punishment for the development tendency of alternatives. This paper proposes a method based on maximum entropy ordered weighted averaging (MEOWA) to determine the trend incentive coefficient. Second, considering the differences development tendency of the alternatives, we propose an approach that integrates the trend incentive coefficient and the original decision information to solve the MP‐MADM problems. Finally, two MP‐MADM cases are used to illustrate the effectiveness and practicability of the proposed method. Comparisons with previous research are also discussed.     

The use of ordered weighted averaging method for decision making under uncertainty

A decision making under uncertainty (DMUU) prevails at the outset and often evolves into a decision making under partial uncertainty as information on the states of nature, for example, a probability distribution, is advanced. Many methods have emerged for solving the DMUU problems, which includes the classical decision criteria and the domain criterion. Yager (1988) introduced a new approach, the so‐called ordered weighted averaging (OWA) as a viable method for solving the DMUU problems. The OWA weights to be used in the aggregation are generated under the degree of optimism provided by a decision maker and then combined with the reordered payoffs to produce aggregated payoffs for each strategy. The reordering process, one of the characterizing features of the OWA method, enables us to perform various types of aggregations including maximax, maximin, and Hurwicz‐α index in conjunction with the generated weights. The OWA method obviously extends the Hurwicz approach by taking into account the tradeoffs among the entire payoffs while the Hurwicz approach considers a tradeoff only between the two extremes, the maximum and the minimum payoffs. In this paper, we examine the features of the OWA method in light of Milnor's set of requirements for reasonable decision criteria, thus providing a solid methodological foundation for the DMUU. The OWA method can also be used to solve a group DMUU problem by exploiting individual decision results in the situation when the use of a fuzzy majority is advocated.     

Prioritized multi-criteria decision making based on preference relations

There may exist priority relationships among criteria in multi-criteria decision making (MCDM) problems. This kind of problems, which we focus on in this paper, are called prioritized MCDM ones. In order to aggregate the evaluation values of criteria for an alternative, we first develop some weighted prioritized aggregation operators based on triangular norms (t-norms) together with the weights of criteria by extending the prioritized aggregation operators proposed by Yager (Yager, R. R. (2004). Modeling prioritized multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 34, 2396–2404). After discussing the influence of the concentration degrees of the evaluation values with respect to each criterion to the priority relationships, we further develop a method for handling the prioritized MCDM problems. Through a simple example, we validate that this method can be used in more wide situations than the existing prioritized MCDM methods. At length, the relationships between the weights associated with criteria and the preference relations among alternatives are explored, and then two quadratic programming models for determining weights based on multiplicative and fuzzy preference relations are developed.     

基于云模型的不确定性大群体多属性决策方法

针对传统不确定性大群体多属性决策方法中只考虑决策信息的模糊性,没有考虑信息的随机性这一问题,提出了一种基于云模型的多属性决策方法,从而用于解决由多个小群体组成的不确定性大群体决策问题。首先将不确定语言评价值转化为一维正态云;其次采用决策者主观确定和一致性分析相结合的方法确定针对不同决策对象的小群体权重,进而生成综合云;然后提出了一种改进的云相似度算法作为云模型距离的度量,通过比较各方案综合云与最优云的相似度对方案排序。最后通过实例验证了所提方法的可行性和有效性。     

Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers

This paper puts forward a new ranking method for multiple attribute decision‐making problems based on interval‐valued intuitionistic fuzzy set (IIFS) theory. First, the composed ordered weighted arithmetic averaging operator and composed ordered weighted geometric averaging operator are extended to the IIFSs in which they are, respectively, named interval‐valued intuitionistic fuzzy composed ordered weighted arithmetic averaging (IIFCOWA) operator and interval‐valued intuitionistic composed ordered weighted geometric averaging (IIFCOWG) operator. Afterwards, to compare interval‐valued intuitionistic fuzzy numbers, we define the concepts of the maximum, the minimum, and ranking function. Some properties associated with the concepts are investigated. Using the IIFCOWA or IIFCOWG operator, we establish the detailed steps of ranking alternatives (or attributes) in multiple attribute decision making. Finally, an illustrative example is provided to show that the proposed ranking method is feasible in multiple attribute decision making.     

Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making

Hamacher product is a t‐norm and Hamacher sum is a t‐conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average (PHFHWA) operator, Pythagorean hesitant fuzzy Hamacher weighted geometric (PHFHWG) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average (PHFHOWA) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric (PHFHOWG) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted average (PHFHIOWA) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted geometric (PHFHIOWG) operator, Pythagorean hesitant fuzzy Hamacher induced correlated aggregation operators, Pythagorean hesitant fuzzy Hamacher prioritized aggregation operators, and Pythagorean hesitant fuzzy Hamacher power aggregation operators. The special cases of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for green supplier selections in green supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

TOPSIS with belief structure for group belief multiple criteria decision making

The technique for order performance by similarity to ideal solution(TOPSIS)is one of the major techniques in dealing with multiple criteria decision making(MCDM)problems, and the belief structure(BS)model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.     

属性权重不确定条件下的区间直觉模糊多属性决策

在区间直觉模糊集(Interval-valued intuitionistic fuzzy set, IVIFS)的框架内,重点研究了属性权重在一定约束条件下和属性权重完全未知的 多属性群决策问题.首先利用区间直觉模糊集成算子获得方案在属性上的综合区间直觉模糊决策矩阵,进一步依据逼近理想解排序法(Technique for order preference by similarity to an ideal solution, TOPSIS) 的思想计算候选方案和理想方案的加权距离,最后确定方案排序.其中针对属性权重在一定约束条件下的决策问题,提出了基于 区间直觉模糊集精确度函数的线性规划方法,用以解决属性权重求解问题.针对属性权重完全未知的决策问题,首先定义了区间直觉 模糊熵,其次通过熵衡量每一属性所含的信息量来求解属性权重.实验结果验证了决策方法的有效性和可行性.     

On Pythagorean fuzzy decision making using soft likelihood functions

Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)-based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA-based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.     

基于云综合方法的三支群决策模型

在三支决策问题中，领域专家群决策是一种确定损失函数的最直接方法。相较于体现单一不确定性的语言变量模型和模糊集模型，云模型描述的专家评价更能够反映认知过程中复杂的不确定性形式，并能通过云综合的方法获得综合评价函数。但当前的云综合方法仅对数字特征进行简单的线性组合，缺乏对概念语义差异上的描述，难以获得令人信服的结果。因此首先证明了在云模型的距离空间中赋权距离和是一个凸函数，并将综合云模型定义为此函数的最小值点。然后，将该定义推广到多个云模型的场景下，提出了一种新的云综合方法——基于密度中心的云综合方法。群决策过程中，该方法在保证综合评价与基础评价之间的相似度最高的同时获得最精确的综合评价，为损失函数的确定提供了一种新的语义解释。实验结果表明，在与简单线性组合和合理粒度方法对比中，该方法所确定的损失函数使得三支决策中的误分类率最低。     

Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem

Evaluating and selecting a suitable supplier is a complex problem which involves a number of different criteria. In literature, there are various multi-criteria decision making (MCDM) methods available with their own characteristic features. The focus of this study is intuitionistic fuzzy (IF) MCDM methods which have attracted much attention from academics and practitioners in recent years. IF sets are widely used to tackle imprecise and uncertain decision information in decision making due to their capability of accommodating the hesitation in human decision processes. This study proposes a new integrated methodology that is used for the first time in the literature. This approach consists of intuitionistic fuzzy analytic hierarchy process (IFAHP), an MCDM technique, for determining the weights of supplier evaluation criteria, and the concept of intuitionistic fuzzy axiomatic design (IFAD) principles for ranking competing supplier alternatives with respect to their overall performance. Decision makers’ assessments and opinions are extended to the IF environment in this approach and furthermore, the group decision making (GDM) approach is utilized in order to overcome uncertainties and vagueness, minimize the partiality of decision process and to avoid bias. This study contributes to supplier selection and IF sets literature by providing a combined framework based on IFAHP and IFAD methodology for the first time. To assess the validity of the proposed integrated IF MCDM approach, a case study from Turkey is provided. This study can be useful to researchers in better understanding the supplier selection problem theoretically, as well as to organizations in designing better satisfying supplier evaluation systems.     

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.     

An extended GRA method for MCDM with interval-valued triangular fuzzy assessments and unknown weights

Multiple criteria decision making (MCDM) is the process of ranking the feasible alternatives and selecting the best one by considering multiple criteria. Owing to the complexity, fuzziness and uncertainties of the objective things, the criterion values often take the form of linguistic variables, which can be expressed in interval-valued triangular fuzzy numbers. The purpose of this paper is to develop an extended grey relational analysis (GRA) method for solving MCDM problems with interval-valued triangular fuzzy numbers and unknown information on criterion weights. In order to determine the criterion weights, some optimization models based on the basic idea of traditional GRA method are established. Then, calculation steps of extended GRA method for MCDM are given. Finally, a numerical example is shown to verify the developed method and to demonstrate its practicality and feasibility.     

Comparative study of multiple criteria decision making methods for building design

In this paper, multiple criteria decision making methods are studied in the context of building design. The approach is to compare the functionality and the results provided by different methods on three test problems that represent various design situations. The number of criteria in the test problems are two, three and four. Multicriteria optimization is applied to generate the alternatives, among which a preferred solution is to be searched by the decision making methods. Six methods have been selected for comparison: the weighted sum method, the weighted product method, VIKOR, TOPSIS, PROMETHEE II, and a procedure based on the PEG-theorem. The numerical study on the test problems indicate that in most cases, the methods provide different solutions. The PEG-procedure tends to find a well-balanced solution, where none of the criteria is emphasized. While the “best” MCDM method is not discovered in the study, information about the performance of the methods in building design problems is presented.     

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches.     

基于后悔理论的具有期望水平的直觉语言多准则决策方法

针对准则具有期望水平的直觉语言多准则决策问题, 考虑决策者后悔规避的心理行为特征, 提出一种基于后悔理论的决策方法. 该方法利用期望效用函数构建各准则值的效用值矩阵; 利用后悔-欣喜函数构建各准则值相对于准则期望水平的后悔-欣喜值矩阵; 在此基础上, 依据后悔理论构建各准则值相对于准则期望水平的感知价值矩阵; 进一步, 利用线性加权法计算各方案的综合感知价值, 并确定方案排序. 最后通过实例分析表明了所提出方法的可行性和有效性.

     

Hybrid assessment method for software engineering decisions

During software development, many decisions need to be made to guarantee the satisfaction of the stakeholders' requirements and goals. The full satisfaction of all of these requirements and goals may not be possible, requiring decisions over conflicting human interests as well as technological alternatives, with an impact on the quality and cost of the final solution. This work aims at assessing the suitability of multi-criteria decision making (MCDM) methods to support software engineers' decisions. To fulfil this aim, a HAM (Hybrid Assessment Method) is proposed, which gives its user the ability to perceive the influence different decisions may have on the final result. HAM is a simple and efficient method that combines one single pairwise comparison decision matrix (to determine the weights of criteria) with one classical weighted decision matrix (to prioritize the alternatives). To avoid consistency problems regarding the scale and the prioritization method, HAM uses a geometric scale for assessing the criteria and the geometric mean for determining the alternative ratings.     

Extension of Fuzzy ELECTRE based on VIKOR method

Many decision problems in real-world deal with conflicting criteria, uncertainty and imprecise information. Some also allow a group of decision makers (DMs) to make their opinions independently. Multi-criteria decision making (MCDM) is a well known decision method that can make the quality of group multiple criteria decisions better by creating a more explicit, rational and efficient process. A group of MCDM models known as “outranking methods” have been used to rank a set of alternatives. ELECTRE I is an outranking method which is simple, but provides partial ranking. So we consider VIKOR and try to mitigate this problem with regard to relations between VIKOR and ELECTRE. The objective of this paper is to extend ELECTRE I method based on VIKOR to rank a set of alternatives versus a set of criteria to show the decision maker’s preferences.     

A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making

The ranking of interval-valued intuitionistic fuzzy sets (IVIFSs) is very important for the interval-valued intuitionistic fuzzy decision making. From the probability viewpoint, the possibility degree of comparison between two interval-valued intuitionistic fuzzy numbers (IVIFNs) is defined by using the notion of 2-dimensional random vector, and a new method is then developed to rank IVIFNs. Hereby the ordered weighted average operator and hybrid weighted average operator for IVIFNs are defined based on the Karnik–Mendel algorithms and employed to solve multi-attribute group decision making problems with IVIFNs. The individual overall attribute values of alternatives are obtained by using the weighted average operator for IVIFNs. By using the hybrid weighted average operator for IVIFNs, we can obtain the collective overall attribute values of alternatives, which are used to rank the alternatives. A numerical example is examined to illustrate the effectiveness and flexibility of the proposed method in this paper.