An integrated MCDM method for robot selection under interval-valued Pythagorean uncertain linguistic environment

Robots have received considerable attention in many manufacturing companies due to their great capabilities and characteristics. Selecting an appropriate robot for a specific application can be regarded as a challenging multicriteria decision-making problem. Furthermore, decision makers are inclined to represent their opinions by using linguistic terms owing to their ambiguous thinking. In this regard, we put forward a novel robot selection model by integrating quality function development (QFD) theory and qualitative flexible multiple criteria method (QUALIFLEX) under interval-valued Pythagorean uncertain linguistic context. For the developed model, the evaluations given by decision makers are presented as interval-valued Pythagorean uncertain linguistic sets for dealing with the uncertainty and vagueness of decision makers’ information. An extended QFD method is used for determining criteria weights from the perspective of customers. A modified QUALIFLEX technique based on closeness degree is utilized to generate the ranking order of alternative robots and determine the most suitable one. Finally, an empirical example of an auto manufacturing company is applied to clarify the effectiveness and accuracy of the proposed robot selection approach.     

Deriving the personalized individual semantics of linguistic information from flexible linguistic preference relations

In group decision making, flexible linguistic preference relations (FLPRs) are very useful with the pairwise comparisons taking the form of flexible linguistic expressions (FLEs). Due to the fact that different decision makers have different understandings of words, this paper investigates the personalized individual semantics (PISs) of the linguistic information in FLPRs. Two optimization models are constructed to compute a linguistic distribution which is closest to an incomplete FLE. The FLPRs are transformed into fuzzy preference relations by using optimization models which maximize consistency and consensus of the fuzzy preference relations. The PISs of linguistic terms and subsets of the linguistic term set are obtained in this process. A group decision making model based on FLPRs is presented and a green supplier selection problem in automotive industry is solved by using the proposed model. The comparative analysis is presented to show the feasibility of the group decision making model.     

On group decision making with four formats of incomplete preference relations

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in four formats of incomplete preference relations, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations, incomplete additive linguistic preference relations, incomplete multiplicative linguistic preference relations. In order to make the collective opinion close each decision maker’s opinion as near as possible, an optimization model is constructed to integrate the four different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.     

SNA-based multi-criteria evaluation of multiple construction equipment: A case study of loaders selection

Selecting the proper construction equipment is a challenging task owing to a wide range of available types as well as a host of criteria to be considered during decision making. To deal with this, a heterogeneous group decision-making framework to evaluate multiple purchasing choices of construction equipment is proposed with two data forms, i.e., 2-dimension uncertain linguistic variables (2DULVs) and real numbers. Firstly, a novel way to derive weights of experts by social network analysis (SNA) is applied considering trust degrees among experts in a social trust network. Secondly, after evaluation index system is established, 2DULVs that include both the linguistic evaluations on alternatives and decision makers’ appraisals on the given evaluation results are applied to represent subjective fuzzy evaluation information, while real numbers are used to represent quantitative values. Thirdly, 2-dimension uncertain linguistic power generalized weighted aggregation (2DULPGWA) operator is applied to aggregate evaluation values among experts. Fourthly, analytic hierarchy process (AHP) and entropy method are utilized to derive combined weights of sub-criteria before the rank can be obtained by the evaluation based on distance from average solution (EDAS) method. Finally, a case study to evaluate multiple choices of loaders is proposed and a comparative analysis is conducted to prove the effectiveness of the proposed framework. This study provides a meaningful guidance for the optimal selection among various types of construction equipment.     

Intelligent multi-criteria fuzzy group decision-making for situation assessments

Organizational decisions and situation assessment are often made in groups, and decision and assessment processes involve various uncertain factors. To increase efficiently group decision-making, this study presents a new rational–political model as a systematic means of supporting group decision-making in an uncertain environment. The model takes advantage of both rational and political models and can handle inconsistent assessment, incomplete information and inaccurate opinions in deriving the best solution for the group decision under a sequential framework. The model particularly identifies three uncertain factors involved in a group decision-making process: decision makers’ roles, preferences for alternatives, and judgments for assessment-criteria. Based on this model, an intelligent multi-criteria fuzzy group decision-making method is proposed to deal with the three uncertain factors described by linguistic terms. The proposed method uses general fuzzy numbers and aggregates these factors into a group satisfactory decision that is in a most acceptable degree of the group. Inference rules are particularly introduced into the method for checking the consistence of individual preferences. Finally, a real case-study on a business situation assessment is illustrated by the proposed method.     

Supplier selection with different risk preferences and attribute sets: An innovative study based on generalized linguistic term sets

Selecting the optimal supplier is crucial to the management of the company’s supply chain, which has received widespread attention from academia and business circles. Generally, a variety of suppliers and multiple attributes are usually involved in this selection proceeding which can be comparatively regarded as a linguistic multiple attribute group decision making (MAGDM) problem. However, common linguistic MAGDM problems may not take the following characteristics into consideration. Due to the limited knowledge, distinctive interests, and different semantic value expectations of decision makers (DMs), it is necessary for them to consider their diverse risk preferences and use multi-granular linguistic term sets (LTSs) to assess suppliers on individual attribute sets independently. Meanwhile, the complex decision environment may have influences on the integrity of the attribute weight information, such that it is always incompletely known. To deal with the afore-mentioned situations, this paper presents a procedure based on risk preferences and several attribute sets with incomplete weight information for choosing the desirable supplier. Firstly, a new multi-granular fuzzy linguistic transformation model is constructed to normalize linguistic domains of multi-granular generalized linguistic term sets (GLTSs). Multi-granular GLTSs are introduced to describe semantic values of multi-granular LTSs given by DMs with risk preferences. Secondly, according to the maximizing deviation method with incomplete attribute weight information, an optimization model is also established to determine attribute weight vectors of individual attribute sets. Thirdly, a novel method that comprises of the aforesaid models is presented to handle supplier selection problems with risk preferences and several attribute sets. Finally, an illustrative example on supplier selection and comparative analyses are provided to clarify the validity and feasibility of our proposed method. Significantly, the initiation of the proposed method and its application could afford to the theoretical development of linguistic MAGDM, as well as the practical expansion in the domain of supplier selection.     

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.     

Sustainable supplier selection: A ranking model based on fuzzy inference system

In these days, considering the growth of knowledge about sustainability in enterprise, the sustainable supplier selection would be the central component in the management of a sustainable supply chain. In this paper the sustainable supplier selection criteria and sub-criteria are determined and based on those criteria and sub-criteria a methodology is proposed onto evaluation and ranking of a given set of suppliers. In the evaluation process, decision makers’ opinions on the importance of deciding the criteria and sub-criteria, in addition to their preference of the suppliers’ performance with respect to sub-criteria are considered in linguistic terms. To handle the subjectivity of decision makers’ assessments, fuzzy logic has been applied and a new ranking method on the basis of fuzzy inference system (FIS) is proposed for supplier selection problem. Finally, an illustrative example is utilized to show the feasibility of the proposed method.     

An approach to group decision making with heterogeneous incomplete uncertain preference relations

For practical group decision making problems, decision makers tend to provide heterogeneous uncertain preference relations due to the uncertainty of the decision environment and the difference of cultures and education backgrounds. Sometimes, decision makers may not have an in-depth knowledge of the problem to be solved and provide incomplete preference relations. In this paper, we focus on group decision making (GDM) problems with heterogeneous incomplete uncertain preference relations, including uncertain multiplicative preference relations, uncertain fuzzy preference relations, uncertain linguistic preference relations and intuitionistic fuzzy preference relations. To deal with such GDM problems, a decision analysis method is proposed. Based on the multiplicative consistency of uncertain preference relations, a bi-objective optimization model which aims to maximize both the group consensus and the individual consistency of each decision maker is established. By solving the optimization model, the priority weights of alternatives can be obtained. Finally, some illustrative examples are used to show the feasibility and effectiveness of the proposed method.     

AN EXTENDED HIERARCHICAL LINGUISTIC MODEL FOR DECISION‐MAKING PROBLEMS

In multi‐expert decision making (MEDM) problems the experts provide their preferences about the alternatives according to their knowledge. Because they can have different knowledge, educational backgrounds, or experiences, it seems logical that they might use different evaluation scales to express their opinions. In the present article, we focus on decision problems defined in uncertain contexts where such uncertainty is modeled by means of linguistic information, therefore the decision makers would use different linguistic scales to express their evaluations on the alternatives, i.e., multigranular linguistic scales. Several computational approaches have been presented to manage multigranular linguistic scales in decision problems. Although they provide good results in some cases, still present limitations. A new approach, so‐called extended linguistic hierarchies, is presented here for managing multigranular linguistic scales to overcome those limitations, an MEDM case study is given to illustrate the proposed method.     

不确定语言信息下的大规模群体DEMATEL决策方法

针对现有不确定语言决策试验和评价实验(DEMATEL)方法大多仅适用于中小规模群体,且未考虑不确定语言变量采用非均匀标度的情况,探讨一种新的不确定语言信息下的大规模群体DEMATEL决策方法.首先,给出一种群体不确定语言DEMATEL矩阵的聚类方法,并对大规模群体DEMATEL意见进行合理分组;然后,定义三维不确定语言密度算子,并对大规模群体DEMATEL意见进行有效集结;最后,提出一种改进的基于不确定语言DEMATEL的指标权重确定方法,并在此基础上进行多属性决策.算例分析验证了所提方法的可行性与有效性,该方法采用非均匀标度来表征和呈现不确定语言变量,而且考虑了大规模群体决策的共识度,使得决策结果更为客观合理且更为可靠.     

An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management

This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socio-economic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, co-operative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.     

Personnel Selection Using Interval 2‐Tuple Linguistic VIKOR Method

Personnel selection is a very important activity in the human resource management of an organization. However, in many practical circumstances, due to time pressure and lack of information about candidates, decision makers generally tend to provide linguistic assessments and use different linguistic term sets to express their opinions during the personnel selection process. In this article, the VIKOR method combined with interval 2‐tuple linguistic variables is proposed to choose appropriate individuals among candidates in a group decision‐making environment. The interval 2‐tuple linguistic variable, which comprises two linguistic terms and two real numbers, is more flexible and precise to deal with linguistic information in solving personnel selection problems. To demonstrate the applicability and effectiveness of the proposed interval 2‐tuple linguistic VIKOR method, a numerical example of personnel selection in a tertiary care hospital is provided.     

q-Rung orthopair uncertain linguistic partitioned Bonferroni mean operators and its application to multiple attribute decision-making method

A q-rung orthopair uncertain linguistic set can be served as an extension of an uncertain linguistic set (ULS) and a q-rung orthopair fuzzy set, which can also be treated as a generalized form of the existing intuitionistic ULS and Pythagorean ULS. The new linguistic set uses the uncertain linguistic variable to express the qualitative evaluation information and allows decision makers to provide their true views freely in a larger membership grade space. In this paper, we investigate the Bonferroni mean under the q-rung orthopair uncertain linguistic environment, then we propose the q-rung orthopair uncertain linguistic Bonferroni mean and its weighted form. Furthermore, considering the specific partition pattern among the attributes, the q-rung orthopair uncertain linguistic partitioned Bonferroni mean and its weighted form are developed. Meanwhile, we discuss several representative cases and attractive properties of our proposed operators in depth. Subsequently, a novel multi-attribute decision-making method is developed based on the above-mentioned aggregation operators. In the end, a comprehensible case is performed to analyze the superiority of the developed method by comparing with other typical studies.     

A fuzzy-logic-based approach for new product Go/NoGo decision at the front end

New product development (NPD) is both a complex process and a substantial business risk. It still requires 6.6 ideas to generate a successful product. Thus, researchers claim that inferior new products should be eliminated at the front end. Limited by both the nature and the timing of NPD, managers often perform screening in uncertain environments and based on incomplete information. Furthermore, the conventional evaluation approaches, which encapsulate or merely discard the ambiguity and multiplicity of possible concerns, make a screening economically sound but dysfunctional as well. Since most assessments are described subjectively by linguistic terms, a comprehensive method for new product screening using fuzzy logic is proposed, in which the criteria ratings and their corresponding importance are assessed in linguistic terms described by fuzzy numbers, and fuzzy weighted average is employed to aggregate these fuzzy numbers into a fuzzy-possible-success rating (FPSR) of the product. Finally, the FPSR is translated back into linguistic terms to derive at a new product screening decision. Furthermore, a case study is cited to illustrate the performance within an actual decision process. The result shows that this approach can efficiently aid managers dealing with ambiguity and complex environments in achieving relatively realistic and informative results, as well as give managers a high degree of flexibility in decision-making. In addition, the variations in linguistic values and levels of linguistic variables have an effect on the ranges of the FPSR which ultimately, affect the selection of the NPD project.     

Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the assessment values of attributes take the form of interval-valued hesitant uncertain linguistic elements, a novel MAGDM method is proposed in this paper. Firstly, the concept, operational laws and score function of interval-valued hesitant uncertain linguistic elements (IVHULEs) are introduced. Then, based on the operational laws of IVHULEs, some generalized aggregation operators are proposed for aggregating the interval-valued hesitant uncertain linguistic information, including the generalized interval-valued hesitant uncertain linguistic weighted aggregation operators, the generalized interval-valued hesitant uncertain linguistic ordered weighted aggregation operators and the generalized interval-valued hesitant uncertain linguistic hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed. Based on the proposed operators, an approach to multiple attribute group decision making with unknown weight information is developed under interval-valued hesitant uncertain linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.     

A goal programming approach to group decision-making with three formats of incomplete preference relations

This paper proposes a goal programming approach to solve the group decision-making problem where the preference information about alternatives provided by decision makers can be represented in three formats, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations and incomplete linguistic preference relations. In the approach, a transformation function is introduced to transform the incomplete linguistic preference relation into an incomplete fuzzy preference relation. To narrow the gap between the collective opinion and each decision maker’s opinion, a liner goal programming model is constructed to integrate the three different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. Thus, the ranking order of alternatives or selection of the most desirable alternative(s) is obtained directly according to the computed collective ranking values. A numerical example is also used to illustrate the feasibility and the applicability of the proposed approach.     

A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets

Multiple criteria decision making (MCDM) approach plays an important role in life, since it is always necessary to make decisions through various alternatives based on specific criteria. In this paper, interval type-2 fuzzy sets (IT2FSs) are used because in most cases in the real-world the information is incomplete and ambiguous. A new group decision approach with linear assignment method (LAM) is proposed. In addition, weight of each evaluation factor according to subjective and objective data is constructed based on a new developed version of linear programming technique for multidimensional analysis of preference (LINMAP) method. In the proposed method, weights of decision makers (DMs) are computed based on a novel approach that applies a new modified method based on the concept of ideal solutions. Furthermore, a new IT2F-ranking method is introduced. To display the applicability of the presented soft computing method, firstly, a real case study of green supplier selection problem is adopted from the literature and solved. Moreover, the method is applied in a second case study of project evaluation and selection problem. Two applications show that the introduced method presents a proper soft computing framework that can handle real-world uncertain environments. Moreover, the method can consider importance of the DMs and evaluation criteria.     

Group decision making with linguistic preference relations with application to supplier selection

Linguistic preference relation is a useful tool for expressing preferences of decision makers in group decision making according to linguistic scales. But in the real decision problems, there usually exist interactive phenomena among the preference of decision makers, which makes it difficult to aggregate preference information by conventional additive aggregation operators. Thus, to approximate the human subjective preference evaluation process, it would be more suitable to apply non-additive measures tool without assuming additivity and independence. In this paper, based on λ-fuzzy measure, we consider dependence among subjective preference of decision makers to develop some new linguistic aggregation operators such as linguistic ordered geometric averaging operator and extended linguistic Choquet integral operator to aggregate the multiplicative linguistic preference relations and additive linguistic preference relations, respectively. Further, the procedure and algorithm of group decision making based on these new linguistic aggregation operators and linguistic preference relations are given. Finally, a supplier selection example is provided to illustrate the developed approaches.     

基于相对熵的残缺语言判断矩阵群排序方法

针对残缺语言判断矩阵的群决策问题,提出一种基于相对熵的群排序方法。首先,定义一种用于识别残缺语言判断矩阵可接受的残缺度指标;其次,将残缺语言型偏好转化成残缺数值型偏好,根据相对熵与加性一致性算法,构建决策者对方案排序向量的最优模型;再次,通过构建接近度熵权与相似度熵权指标,对决策者权重进行动态调整,得到稳定的决策者权重,进而得出群体排序向量;最后,通过应用算例进行验证,以表明所提出的方法是可行的。