Integrating fuzzy DEMATEL and fuzzy hierarchical TOPSIS methods for truck selection

In the present paper, a novel fuzzy Multiple Attribute Decision Making (MADM) model is proposed for modeling and solving truck selection problem of a land transportation company. As truck selection is a very crucial problem for the land transportation companies, a systematic and scientific approach is necessary for its solution. A systematic methodology is proposed in the present study by integrating “fuzzy DEMATEL” and “fuzzy hierarchical TOPSIS”. The proposed method makes use of fuzzy DEMATEL method for evaluating the weights of the criteria and hierarchical fuzzy TOPSIS method for assessing the alternatives according to criteria. The steps of the method are described first then a case study is presented in the paper.     

Supplier selection using a clustering method based on a new distance for interval type-2 fuzzy sets: A case study

Supplier selection is a decision-making process to identify and evaluate suppliers for making contracts. Here, we use interval type-2 fuzzy values to show the decision makers’ preferences and also introduce a new formula to compute the distance between two interval type-2 fuzzy sets. The performance of the proposed distance formula in comparison with the normalized Hamming, normalized Hamming based on the Hausdorff metric, normalized Euclidean and the signed distances is evaluated. The results show that the signed distance has the same trend as our method, but the other three methods are not appropriate for interval type-2 fuzzy sets. Using this approach, we propose a hierarchical clustering-based method to solve a supplier selection problem and find the proximity of the suppliers. To illustrate the applicability of the proposed method, first a case study of supplier selection problem with 8 criteria and 8 suppliers are illustrated and next, an example taken from the literature is worked through. Then, to test the hierarchical clustering-based method and compare with the obtained results by two other methods, a comparative study using experimental analysis is designed. The results show that while the proposed hierarchical clustering algorithm provides acceptable results, it is also conveniently appropriate for using interval type-2 fuzzy sets and obtaining proximity of suppliers.     

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.     

A type 2-hesitation fuzzy logic based multi-criteria group decision making system for intelligent shared environments

Intelligent environments aim to maximize the user comfort and safety while achieving other objectives such as energy minimization. Intelligent shared spaces (such as homes, classrooms, offices, libraries, etc.) need to consider the preferences of users from diverse backgrounds. However, there are high levels of uncertainties faced in intelligent shared spaces. Hence, there is a need to employ intelligent decision making systems which can consider the various users preferences and criteria in order to achieve the convenience of the various users while handling the faced uncertainties. Therefore, we propose a Fuzzy Logic-Multi-Criteria Group Decision Making (FL-MCGDM) system which provides a comprehensive valuation from a group of users/decision makers based on the aggregation of users’ opinions and preferences. The proposed FL-MCGDM system employs an interval type-2 fuzzy logic and hesitation index [from Intuitionistic Fuzzy Sets (IFSs)]. We have carried out experiments in the intelligent apartment (iSpace) located in the University of Essex to evaluate various approaches employing group decision making techniques for illumination selection in an intelligent shared environment. It was found that the Footprint of Uncertainty (of interval type-2 fuzzy sets) and hesitation index (of intuitionistic fuzzy sets (IFSs)) are able to provide a measure of the uncertainties present among the various decision makers. The proposed Type 2-Hesitation FL-MCGDM system better agrees with the users’ decision compared to existing fuzzy MCDM including the Fuzzy Logic based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), type-1 FL-MCGDM and interval type-2 in FL-MCGDM.     

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.     

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.     

基于分式规划的区间直觉梯形模糊数多属性决策方法

针对属性值为区间梯形直觉模糊且属性权重为区间数的多属性决策问题,提出一种基于分式规划的决策方法.定义了区间梯形直觉模糊数的Hamming距离和Euclidean距离,采用优劣解距离法构建了相对贴近度的非线性分式规划模型,并通过Charnes and Cooper变换转化为线性规划模型求解,得到各方案相对贴近度的区间数,进而提出了决策方法.数值算例分析验证了所提出方法的有效性.     

一种基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法

模糊语言决策方法是决策领域的热点研究内容之一.比较现有模糊语言决策方法研究中广泛使用的决策矩阵,提出对象-语言值决策矩阵表示决策专家根据决策属性给出的评价语言信息,分析对象-语言值决策矩阵在区分明晰、部分未知及犹豫的模糊语言决策问题中的优势;借鉴经典TOPSIS决策方法及向量运算,给出基于对象-语言值决策矩阵的正负理想解确定方法以及备选对象与正负理想解的伪距离和贴近度计算方法,分析伪距离和贴近度的相关性质;基于2-元组语言表示模型,提出基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法.通过实例分析,并与已有3种重要的模糊语言决策方法进行比较,比较结果说明所提出的决策方法可以克服已有决策方法的不足, 是一种可选的模糊语言决策方法.     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

Web shopping expert using new interval type-2 fuzzy reasoning

Finding a product with high quality and reasonable price online is a difficult task due to uncertainty of Web data and queries. In order to handle the uncertainty problem, the Web Shopping Expert, a new type-2 fuzzy online decision support system, is proposed. In the Web Shopping Expert, a fast interval type-2 fuzzy method is used to directly use all rules with type-1 fuzzy sets to perform type-2 fuzzy reasoning efficiently. The parameters of type-2 fuzzy sets are optimized by a least square method. The Web Shopping Expert based on the interval type-2 fuzzy inference system provides reasonable decisions for online users.     

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.     

Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers

In this paper, we investigate the fuzzy multi-attribute group decision making (FMAGDM) problems in which all the information provided by the decision makers (DMs) is expressed as the trapezoidal interval type-2 fuzzy sets (IT2 FS). We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two trapezoidal IT2 FS. Then, we develop two aggregation techniques called the trapezoidal interval type-2 fuzzy geometric Bonferroni mean (TIT2FGBM) operator and the trapezoidal interval type-2 fuzzy weighted geometric Bonferroni mean (TIT2FWGBM) operator. We study its properties and discuss its special cases. Based on the TIT2FWGBM operator and the possibility degree, the method of FMAGDM with trapezoidal interval type-2 fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.     

A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set

Interval type-2 fuzzy sets are associated with greater imprecision and more ambiguities than ordinary fuzzy sets. This paper presents a signed-distance-based method for determining the objective importance of criteria and handling fuzzy, multiple criteria group decision-making problems in a flexible and intelligent way. These advantages arise from the method’s use of interval type-2 trapezoidal fuzzy numbers to represent alternative ratings and the importance of various criteria. An integrated approach to determine the overall importance of the criteria is also developed using the subjective information provided by decision-makers and the objective information delivered by the decision matrix. In addition, a linear programming model is developed to estimate criterion weights and to extend the proposed multiple criteria decision analysis method. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a group decision-making problem of patient-centered medicine in basilar artery occlusion.     

FLM-TOPSIS: The fuzzy linguistic multiset TOPSIS method and its application in linguistic decision making

Linguistic decision making is an important subject in decision making, many interesting and important linguistic decision making methods have been proposed, in which, alternatives-criteria decision matrix are uniformly used to express linguistic assessments of alternatives provided by decision makers with respect to criteria. Alternatives-criteria decision matrixes have some limitations when we use them to distinguish distinct, partial unknown or hesitant linguistic decision making or carry out linguistic decision making in the huge amounts of decision information and alternatives. In this paper, we propose alternatives-linguistic terms decision matrix to represent linguistic assessments of alternatives, analyze advantages of the decision matrix in representing linguistic assessments and distinguishing distinct, partial unknown or hesitant linguistic decision making. To simple and fast fuse alternatives-linguistic terms decision matrixes, we further provide linguistic multiset or fuzzy linguistic multiset to represent linguistic assessments in alternatives-linguistic terms decision matrixes, analyze the function properties of the fuzzy linguistic multiset. Motivated by fuzzy multiset and the TOPSIS method, we develop the fuzzy linguistic multiset TOPSIS method for linguistic decision making, the method is mainly consisted of transformation, aggregation and exploitation phases. In transformation phase, linguistic assessments of alternatives are transformed into fuzzy linguistic multisets by using alternatives-linguistic terms decision matrixes. In aggregation phase, we use Union, Intersection and Sum operations of multisets to obtain the positive and negative ideal solutions of linguistic decision making, which are different with the positive and negative ideal solutions of the traditional TOPSIS method, in addition, we provide a pseudo-distance between two fuzzy linguistic multisets to fast fuse linguistic assessments of alternatives. In exploitation phase, we define a new closeness degree of alternative by using pseudo-distances between the alternative and the positive and negative ideal solutions, which can be used to obtain the set of most satisfying alternatives. We also design an algorithm to carry out linguistic decision making based on the proposed method. In cases study, we use two practical examples to illustrate the practicality of the proposed method and compare it with the symbolic aggregation-based method, the hesitant fuzzy linguistic TOPSIS method, the hesitant fuzzy linguistic VIKOR method and the probabilistic linguistic term sets TOPSIS method, results indicate that alternatives-linguistic terms decision matrix and fuzzy linguistic multiset are alternative, useful and flexible tools for linguistic decision method and the fuzzy linguistic multiset TOPSIS method is suitable to deal with partial unknown or hesitant linguistic decision making.     

Extension of the DEMATEL method in an uncertain linguistic environment

The decision making trial and evaluation laboratory (DEMATEL) method is a useful tool for analyzing correlations among factors using crisp values. However, the crisp values are inadequate to model real-life situations due to the fuzziness and uncertainty that are frequently involved in judgments of experts. The aim of this paper is to extend the DEMATEL method to an uncertain linguistic environment. In this paper, the correlation information among factors provided by experts is in the form of uncertain linguistic terms. A formula is first presented to transform correlation information from uncertain linguistic terms to trapezoidal fuzzy numbers. Then, we aggregate the transformed correlation information of each expert into group information using the operations of trapezoidal fuzzy numbers. The importance and classification of factors are determined via fuzzy matrix operations. Furthermore, a causal diagram is constructed to vividly show the different roles of factors. Finally, an example is used to illustrate the procedure of the proposed method.     

Interval type 2-based hybrid fuzzy evaluation of financial services in E7 economies with DEMATEL-ANP and MOORA methods

The financial services are key instrument for the right evolution of economy, mainly in the emerging countries. Therefore, the evaluation of the financial services is crucial for the economic development of such a type of countries. Different methods have been applied to accomplish this service evaluation, but its complexity greatly involves uncertain information. Therefore, this paper aims at considering in a more comprehensive way the managing of such uncertainty by the use of interval type-2 fuzzy sets. Hence, it will be proposed a novel evaluation methodology based on a hybrid multi-criteria decision method integrating DEMATEL-ANP (DANP) and MOORA able to deal with interval type-2 fuzzy sets. For the robustness check, the TOPSIS and VIKOR based on interval type-2 fuzzy sets are compared with the MOORA method and the sensitivity analysis is also applied to analyze the consistency of decision makers’ priorities. This novel hybrid methodology will be used to evaluate the financial service performance in the emerging seven (E7) economies to conclude what kind of strategic actions should be taken by governments to improve their financial systems as well as to identify a ranking regarding the financial service quality of the E7 economies.     

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.     

Local consistency adjustment strategy and DEA – driven interval type-2 trapezoidal fuzzy decision-making model and its application for fog-haze factor assessment problem

This paper aims to develop a novel decision-making method with interval type-2 trapezoidal fuzzy preference (IT2TrFPR), which can deal with the complex decision information presented in the form of interval type-2 trapezoidal fuzzy numbers. In this paper, we mainly propose a novel interval type-2 trapezoidal fuzzy decision-making method with local consistency adjustment strategy and data envelopment analysis (DEA). Considering the harm of fog-haze pollution to the environment and human life, we apply the decision-making method to the problem about influence factors of for-haze weather. Firstly, we introduce the definition of IT2TrFPR that sufficiently expresses the uncertainty of original decision-making information. After that, we show the definition of the order consistency and additive consistency for IT2TrFPR. Considering that the original IT2TrFPR given by decision-makers usually does not satisfy the characteristic of consistency, to transform the unacceptable additive consistent IT2TrFPRs into acceptable ones, we design a consistency-improving algorithm that uses the local adjustment approach to preserve the original decision-making information as much as possible and avoids the original information loss. Then, an output-oriented interval type-2 trapezoidal fuzzy DEA model and the concept for quasi interval type-2 trapezoidal fuzzy priority weight are developed to derive the interval type-2 trapezoidal fuzzy priority weight vector (IT2TrFPW) and obtain the final ranking result of alternatives. Finally, the effectiveness of the proposed decision-making method is demonstrated by a numerical example of selecting the most crucial fog-haze influence factor. Meanwhile, we also conduct a comparative analysis by comparing our method with the existing methods to show some merits of the proposed method.

     

Fuzzy decision maps: a generalization of the DEMATEL methods

The Decision making trial and evaluation laboratory (DEMATEL) method is used to build and analyze a structural model with causal relationships between different criteria. In this paper, it shows that DEMATEL is the specific case of fuzzy decision maps (FDM) when the threshold function is linear. Both FDM and DEMATEL have the same direct and indirect influence matrix. FDM incorporates the eigenvalue method, the fuzzy cognitive maps, and the weighting equation. In addition two numerical examples are illustrated to demonstrate the proposed results. On the basis of the mathematical proof and numerical results, we can conclude that FDM is a generalization of DEMATEL method.     

Multiple-attribute decision making methods for plant layout design problem

The layout design problem is a strategic issue and has a significant impact on the efficiency of a manufacturing system. Much of the existing layout design literature that uses a surrogate function for flow distance or for simplified objectives may be entrapped into local optimum; and subsequently lead to a poor layout design due to the multiple-attribute decision making (MADM) nature of a layout design decision. The present study explores the use of MADM approaches in solving a layout design problem. The proposed methodology is illustrated through a practical application from an IC packaging company. Two methods are proposed in solving the case study problem: Technique for order preference by similarity to ideal solution (TOPSIS) and fuzzy TOPSIS. Empirical results showed that the proposed methods are viable approaches in solving a layout design problem. TOPSIS is a viable approach for the case study problem and is suitable for precise value performance ratings. When the performance ratings are vague and imprecise, the fuzzy TOPSIS is a preferred solution method.