A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS

An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers’ opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.     

基于模糊结构元的模糊数直觉模糊多准则决策方法

针对准则权重信息不完全确定的模糊数直觉模糊多准则决策问题,采用模糊结构元方法进行处理.基于模糊数直觉模糊集的模糊结构元表示、模糊数比较和排序的模糊结构元方法以及直觉模糊数的记分函数和距离测度,定义了模糊数直觉模糊数的记分函数和距离测度,进而提出两种准则权重信息不完全确定而准则值为模糊数直觉模糊数的多准则决策方法:记分函数法和逼近理想解排序(TOPSIS)法.实例分析表明了这两种方法的可行性和有效性.     

Integrated group fuzzy multi-criteria model: Case of facilities management strategy selection

Managerial decisions should be made by taking into account the priorities and objectives of different stakeholders' groups. Their preferences are usually expressed in words and are fuzzy concepts. This article analyses the peculiarities of companies’ work and decision - making within a fuzzy market situation. It also presents a developed fuzzy multi-criteria group decision-making model for practical problem solving by taking into account cost-effective management. This case study presents a selection of rational criteria set to use in the weighted cost-effectiveness analysis for facilities management strategies, in which integrated fuzzy multi-criteria decision-making methods are applied. The main findings are: the model is adopted to real- life; the main criteria groups are identified by a three-step Delphi technique; a rational strategy is determined and integrated in one model by the concept of Minkowski distance and fuzzy TOPSIS method, ARAS-F and fuzzy weighted product method. The proposed model is versatile and therefore can be applied for various problems were the experts’ knowledge needed for decision–making.     

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.     

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 peer IF-TOPSIS based decision support system for packaging machine selection

Selecting the appropriate manufacturing machine is a very important and complex problem for firms which usually have to deal with both qualitative and quantitative criteria and involve different decision makers whose knowledge is often vague and imprecise.This paper proposes a peer-based modification to intuitionistic fuzzy multi-criteria group decision making with TOPSIS method (peer IF-TOPSIS) and applies it to a packaging machine selection problem. Intuitionistic fuzzy weighted averaging (IFWA) operator has been selected both to obtain the group opinion on the relevance of the single decision makers and to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives.A case study illustrates the application of the modified IF-TOPSIS method in order to select a Vertical Form Fill and Seal (VFFS) for Double Square Bottom Bag (DSBB) machine in food packaging.     

A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information

The aim of this study is to introduce a novel generalized distance measure for interval valued intuitionistic fuzzy sets and to illustrate the applicability of the proposed distance measure to group decision making problems. Firstly, a generalized distance measure is proposed along with proofs satisfying its axioms. Then, a comparison between the proposed distance measure and well-known distance measures is performed in terms of counter-intuitive cases. Subsequently, the extension of TOPSIS method, in which the proposed distance measure is used to calculate separation measures, to an interval valued intuitionistic fuzzy (IVIF) environment is demonstrated to solve multi-criteria group decision making (MCGDM) problems using optimal criteria weights determined with linear programming model based on the concept of maximizing relative closeness coefficient. Finally, two illustrative examples are provided for proof-of-concept purposes and to demonstrate benefits of using the proposed distance measure over the existing ones in IVIF TOPSIS method for MCGDM problems.     

Investment project evaluation by a decision making methodology based on type-2 fuzzy sets

Although investment projects supported by the state are extremely important in terms of national policy the projects to be transferred from the common public funds brings with it many problems. Highly transparent and comprehensive evaluation model are required to transfer the public resources to the right investment projects. It is necessary to consider many criteria for the evaluation of an investment project. These criteria are generally subjective and extremely difficult to express in numbers. However, using the fuzzy sets provide huge facilities to decision makers in project evaluation process with linguistic variables and measurement challenges. In this study, a new evaluation model for investment projects have been proposed for development agencies operating in Turkey. To address ambiguities and relativities in real world scenarios more conveniently, type-2 fuzzy sets and crisp sets have been simultaneously used. The proposed model for the investment project evaluation problem composed of type-2 fuzzy AHP and type-2 fuzzy TOPSIS methods. The proposed fuzzy MCDM method consists of three phases: (1) identify the criteria to be used in the model, (2) type-2 fuzzy AHP computations, (3) evaluation of investment projects with type-2 fuzzy TOPSIS and determination of the final rank. To perceive proposed model better, an application with real case data have been performed in Middle Black Sea Development Agency in Turkey. As a consequence of this application, it has been observed that the proposed model have proved effective in evaluation of alternatives in multi-criteria group decision making problems in a broader perspective and flexible fashion.     

Robust spatial flood vulnerability assessment for Han River using fuzzy TOPSIS with α-cut level set

This study aims to improve the general flood vulnerability approach using fuzzy TOPSIS based on α-cut level sets which can reduce the uncertainty inherent in even fuzzy multi-criteria decision making process. Since fuzzy TOPSIS leads to a crisp closeness for each alternative, it is frequently argued that fuzzy weights and fuzzy ratings should be in fuzzy relative closeness. Therefore, this study used a modified α-cut level set based fuzzy TOPSIS to develop a spatial flood vulnerability approach for Han River in Korea, considering various uncertainties in weights derivation and crisp data aggregation. Two results from fuzzy TOPSIS and modified fuzzy TOPSIS were compared. Some regions which showed no or small ranking changes have their centro-symmetric distributions, while other regions whose rankings varied dynamically, have biased (anti-symmetric) distributions. It can be concluded that α-cut level set based fuzzy TOPSIS produce more robust prioritization since more uncertainties can be considered. This method can be applied to robust spatial vulnerability or decision making in water resources management.     

基于直觉模糊数的信息不完全的多准则规划方法

定义了直觉模糊数和直觉梯形模糊数及其期望值.针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出了信息不完全确定的直觉梯形模糊多准则决策的规划方法.该方法利用权系数的不完全信息构造方案集综合期望值的最优线性规划模型,求解该模型得到各准则的最优权系数,进而得到各方案综合期望值的区间数.利用区间数可能度法对其进行比较,得到整个方案集的排序.实例分析说明了该方法的有效性和可行性.     

Novel approach to group multi-criteria decision making based on interval rough numbers: Hybrid DEMATEL-ANP-MAIRCA model

This paper presents a novel approach for treating uncertainty in the multi-criteria decision making process by introducing interval rough numbers (IRN). The IRN approach enables decision making using only the internal knowledge incorporated in the data provided by the decision maker. A hybrid multi-criteria model was developed based on IRN, and demonstrated using the example of the bidder selection process in the state administration public procurement procedure. The first segment of the hybrid model deals with the rough interval DEMATEL-ANP (IR'DANP) model, which enables more objective expert evaluation of criteria in a subjective environment than the traditional/crisp approach. In the second segment, the evaluation is enabled by applying the new rough interval MAIRCA method, which introduces mathematical tools and shows high stability concerning changes in the nature and characteristics of the criteria. The results of the hybrid IR'DANP-MAIRCA model were analyzed using 36 scenarios of sensitivity analysis, which showed high stability of the results. The results of the interval rough method were compared with the fuzzy extensions of the TOPSIS, VIKOR, MABAC, TODIM, ELECTRE I and DEMATEL-ANP models.     

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.     

基于区间梯形二型犹豫模糊数的多准则决策方法

针对准则权重不完全的犹豫模糊多准则决策问题,提出基于区间梯形二型犹豫模糊数的决策方法.首先,给出区间梯形二型犹豫模糊数,根据几何面积法定义区间梯形二型犹豫模糊数的可能度和差异度;然后,利用差异度和离差最大化模型得到各准则权重,基于TOPSIS思想得到各方案的综合贴近度,并对方案进行排序;最后,通过算例分析和对比分析验证了所提出方法的可行性和有效性.     

基于前景理论的信息不完全的模糊多准则决策方法

针对准则权重不完全确定且方案的准则值为梯形模糊数的多准则决策问题,提出一种基于前景理论的模糊多准则决策方法.该方法将决策者的风险心理因素引入多准则决策,根据前景理论及模糊数距离公式,定义梯形模糊数的前景价值函数,并以此构建方案综合前景值最大化的非线性规划模型,求解模型得出最优权向量,最终确定出方案的排序.最后通过实例说明了该方法的有效性和可行性.     

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。     

The evaluation of financial performance for Taiwan container shipping companies by fuzzy TOPSIS

In this paper, financial performance of Taiwan container shipping companies are evaluated by fuzzy multi-criteria decision-making (FMCDM). In the evaluating problem, we first apply grey relation analysis to partition financial ratios into several clusters and find representative indices from the clusters. Then the representative indices are considered as evaluation criteria on financial performance assessment of Taiwan container shipping companies, and an FMCDM method called fuzzy technique for order preference by similarity to ideal solution (fuzzy TOPSIS) is utilized to evaluate financial performance. By fuzzy TOPSIS, financial performances of container shipping companies are ranked, and thus a container shipping company can realize its finance competitive strength and weakness between container shipping companies.     

基于二型三角诱导OWA算子的多准则决策方法

定义了二型三角模糊数的相关概念、运算规则和可能度公式,并针对隶属度难以用精确数进行衡量的多准则决策问题,提出了基于二型三角诱导OWA算子的多准则决策方法。该方法通过二型三角诱导OWA算子确定方案的综合准则值,并由二型三角模糊数的可能度公式计算出综合准则值的排序,进而得到方案的排序。最后通过实例分析验证了所提出方法的有效性和可行性。     

基于直觉梯形模糊数的信息不完全确定的多准则决策方法

针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出一种基于直觉梯形模糊的信息不完全确定的多准则决策方法.该方法利用权系数的不完全确定信息,建立关于各方案综合直觉梯形模糊数与理想解和负理想解的Hamming距离的优化模型.通过求解优化模型可得到各准则的最优权系数,进而得到各方案与相对理想解的贴近度,再根据贴近度得到方案集的一个排序.实例分析表明了该方法的有效性和可行性.     

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision maker’s knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.     

Fuzzy performance evaluation in Turkish Banking Sector using Analytic Hierarchy Process and TOPSIS

The performance evaluation of banks has important results for creditors, investors and stakeholders since it determines banks’ capabilities to compete in the sector and has a critical importance for the development of the sector. The aim of this study is to propose a fuzzy multi-criteria decision model to evaluate the performances of banks.The largest five commercial banks of Turkish Banking Sector are examined and these banks are evaluated in terms of several financial and non-financial indicators. Fuzzy Analytic Hierarchy Process (FAHP) and Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) methods are integrated in the proposed model. After the weights for a number of criteria are determined based on the opinions of experts using the FAHP method, these weights are input to the TOPSIS method to rank the banks. The results show that not only financial performance but also non-financial performance should be taken into account in a competitive environment.