Interactive group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a supply chain

With global competition rapidly intensifying and shifting to the supply chain level, the supply chain flexibility has become increasingly important. However, the literature addressing supply chain flexibility remains limited. This study thus builds a group decision-making structure model of flexibility in supply chain management development. This study presents a framework for evaluating supply chain flexibility comprising two parts, an evaluation hierarchy with flexibility dimensions and related metrics, and an evaluation scheme that uses a three-stage process to evaluate supply chain flexibility. This study then proposes an algorithm for determining the degree of supply chain flexibility using a fuzzy linguistic approach. Evaluations of the degree of supply chain flexibility can identify the need to improve supply chain flexibility, and identify specific dimensions of supply chain flexibility as the best directions for improvement. The results of this study are more objective and unbiased for two reasons. First, the results are generated by group decision-making with interactive consensus analysis. Second, the fuzzy linguistic approach used in this study has more advantage to preserve no loss of information than other methods. Additionally, this study presents an example using a case study to illustrate the availability of the proposed methods and compare it with other methods.     

A QFD-based fuzzy MCDM approach for supplier selection

Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study.     

Multi-criteria decision making approaches for supplier evaluation and selection: A literature review

Supplier evaluation and selection problem has been studied extensively. Various decision making approaches have been proposed to tackle the problem. In contemporary supply chain management, the performance of potential suppliers is evaluated against multiple criteria rather than considering a single factor-cost. This paper reviews the literature of the multi-criteria decision making approaches for supplier evaluation and selection. Related articles appearing in the international journals from 2000 to 2008 are gathered and analyzed so that the following three questions can be answered: (i) Which approaches were prevalently applied? (ii) Which evaluating criteria were paid more attention to? (iii) Is there any inadequacy of the approaches? Based on the inadequacy, if any, some improvements and possible future work are recommended. This research not only provides evidence that the multi-criteria decision making approaches are better than the traditional cost-based approach, but also aids the researchers and decision makers in applying the approaches effectively.     

A uniform approach of linguistic truth values in sensor evaluation

During the sensor evaluation procedure, each valuator uses his/her own ordinary linguistic truth values for the same factor because of different preference. That will brings some disadvantages to aggregate the information. For a uniform criterion, the standard linguistic truth value (SLTV) set is proposed. Based on the former hypothesis of transformation models of linguistic truth values, four transformation models are discussed: the model of point to point, the model of fuzzy set to point, the model of point to fuzzy set and the model of fuzzy set to fuzzy set. An example is to analyze it. Using the applicability measure we can choose appropriate SLTV for the different sensory evaluation system.     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

An integrated FCM and fuzzy soft set for supplier selection problem based on risk evaluation

Supplier selection problem, considered as a multi-criteria decision-making (MCDM) problem, is one of the most important issues for firms. Lots of literatures about it have been emitted since 1960s. However, research on supplier selection under operational risks is limited. What’s more, the criteria used by most of them are independent, which usually does not correspond with the real world. Although the analytic network process (ANP) has been proposed to deal with the problems above, several problems make the method impractical. This study first integrates the fuzzy cognitive map (FCM) and fuzzy soft set model for solving the supplier selection problem. This method not only considers the dependent and feedback effect among criteria, but also considers the uncertainties on decision making process. Finally, a case study of supplier selection considering risk factors is given to demonstrate the proposed method’s effectiveness.     

Extension of VIKOR method for multi-criteria group decision making problem with linguistic information

A new method is proposed to solve multi-criteria group decision making problems in which both the criteria values and criteria weights take the form of linguistic information based on the traditional idea of VIKOR method. Firstly, the linguistic criteria weights given by all decision makers are transformed into trapezoidal fuzzy numbers, and then aggregated and defuzzified to crisp values. Secondly, the individual linguistic decision matrix given by each decision maker (DM) is transformed into 2-tuple linguistic decision matrix, and then aggregated into collective 2-tuple linguistic decision matrix by 2-tuple linguistic arithmetic mean operation. Thirdly, the 2-tuple linguistic values (_Si,_αi),$(S_i\text{,}{\alpha }_i)\text{,}$(_Ri,_αi)$(R_i\text{,}{\alpha }_i)$ and (_Qi,_αi)$(Q_i\text{,}{\alpha }_i)$ are calculated by defining the 2-tuple linguistic positive ideal solution (TL-PIS) and 2-tuple linguistic negative ideal solution (TL-NIS). Furthermore, the compromise solution can be obtained. Finally, a numerical example is used to illustrate the application of the proposed approach, and the method is verified by comparing the evaluation result with that of 2-tuple linguistic TOPSIS (TL-TOPSIS) method.     

A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts

Group decision making is a type of decision problem in which multiple experts acting collectively, analyze problems, evaluate alternatives, and select a solution from a collection of alternatives. As the natural language is the standard representation of those concepts that humans use for communication, it seems natural that they use words (linguistic terms) instead of numerical values to provide their opinions. However, while linguistic information is readily available, it is not operational and thus it has to be made usable though expressing it in terms of information granules. To do so, Granular Computing, which has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules, can be used. The aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts, i.e., where the experts have associated importance degrees reflecting their ability to handle the problem. The granulation of the linguistic terms is formulated as an optimization problem, solved by using the particle swarm optimization, in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets. This performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert.     

不确定多属性群决策中混合信息的集结

在不确定多属性群决策中,研究专家给出的评价信息为语言和三角模糊数混合型的决策问题.提出一种转化方法,先将模糊数转化为语言短语集上的模糊集,然后,再将此模糊集转化为二元语义.同时在信息集结过程中,也均以二元语义的形式,以防止信息的过分丢失.最后,给出一个算例来说明此种处理方法的有效性和实用性.     

Aggregating crisp values into intuitionistic fuzzy number for group decision making

This paper presents a multiple attribute group decision making model based on aggregating crisp values into intuitionistic fuzzy numbers. First, each alternative is evaluated with respect to their attributes, whose values are provided by decision maker as crisp numbers. Second, to make a reasonable normalization of attribute values in the group decision making environment, a maximum grade and a minimum grade are added to the attribute values. These normalized attribute values are then aggregated (per attribute) into an induced intuitionistic fuzzy number. Each alternative is then evaluated according to the induced intuitionistic fuzzy number. To show the major technical advances in this paper, comparisons with other methods are also made. Finally, an experimental analysis for supplier selection is given to illustrate the reasonableness and efficiency of the introduced method.     

Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations

In [R.R. Yager, D.P. Filev, Operations for granular computing: Mixing words and numbers, in: Proceedings of the FUZZ-IEEE World Congress on Computational Intelligence, Anchorage, 1998, pp. 123–128] Yager and Filev introduced the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we provide some IOWA operators to aggregate fuzzy preference relations in group decision-making (GDM) problems. These IOWA operators when guided by fuzzy linguistic quantifiers allow the introduction of some semantics or meaning in the aggregation, and therefore allow for a better control over the aggregation stage developed in the resolution process of the GDM problems. In particular, we present the Importance IOWA (I-IOWA) operator, which applies the ordering of the argument values based upon the importance of the information sources; the Consistency IOWA (C-IOWA) operator, which applies the ordering of the argument values based upon the consistency of the information sources; and the Preference IOWA (P-IOWA) operator, which applies the ordering of the argument values based upon the relative preference values associated to each one of them. We provide a procedure to deal with ‘ties’ in respect to the ordering induced by the application of one of these IOWA operators; it consists of a sequential application of the above IOWA operators. We also present a selection process for GDM problems based on the concept of fuzzy majority and the above three IOWA operators. Finally, we analyse the reciprocity and consistency properties of the collective fuzzy preference relations obtained using IOWA operators.     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

A fuzzy approach to cooperative n-person games

The object of this paper is to provide a systematic treatment of bargaining procedures as a basis for negotiation. An innovative fuzzy logic approach to analyze n-person cooperative games is developed. A couple of indices, the Good Deal Index and the Counterpart Convenience Index are proposed to characterize the heuristic of bargaining and to provide a solution concept. The indices are examined theoretically and experimentally by analyzing three case studies. The results verify the validity of the approach.     

Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles

An interactive DSS for consensus reaching is presented. Experts provide their testimonies as fuzzy preference relations. The consensus reaching process is supervised by a moderator (super-expert). A degree of consensus, based on the concept of a fuzzy majority given as a linguistic quantifier is employed. Algorithms of cluster analysis are used to find groups of experts having similar preferences.     

An intuitionistic fuzzy projection-based approach for partner selection

The partner selection is an important decision problem in the formation of a new virtual enterprise. Using the projection technique, this study introduces an approach to partner selection with linguistic values and intuitionistic fuzzy information under a group decision-making environment. To avoid information loss, there is no aggregations of decision information in this model except ideal decisions as auxiliary decision tools. Comparisons of the suggested methodology with other methods are also made. A numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.     

基于二元语义信息处理的项目群决策方法

项目群的决策是项目群管理的一个重要组成部分,是一个涉及众多不确定性因素的系统工程。本文给出项目群中子项目的评价依据,在此基础上,将二元语义信息处理的方法应用于项目群决策,给出了基于二元语义信息处理的项目群决策的算法步骤,最后通过一个算例,说明该方法的有效性和实用性。     

A consensus-based probabilistic linguistic gained and lost dominance score method

This paper proposes a comprehensive Multiple Criteria Group Decision Making (MCGDM) method with probabilistic linguistic information based on a new consensus measure and a novel outranking method, Gained and Lost Dominance Score (GLDS). Firstly, new operations of the probabilistic linguistic term sets are introduced based on the adjusted rules of probabilistic linguistic term sets and the linguistic scale functions for semantics of linguistic terms. After defining a new consensus measure based on the correlation degree between probabilistic linguistic term sets, we develop a consensus reaching method to improve the consensus degree of a group. To rank alternatives reasonably, we further propose the GLDS method which considers both the “group utility” and the “individual regret” values. The core of the GLDS is to calculate the gained and lost dominance scores that the optimal solution dominates all other alternatives in terms of the net gained dominance flow and the net lost dominance flow. Then, we integrate the GLDS ranking method with the consensus reaching process and develop a consensus-based PL-GLDS method to solve the MCGDM problems with probabilistic linguistic information. Finally, the proposed method is validated by a case study of selecting optimal green enterprises. Some comparative analyses are given to show the efficiency of the proposed method.     

A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets

Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.