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.     

Improving quality function deployment analysis with the cloud MULTIMOORA method

Quality function deployment (QFD) is a quality guarantee method extensively used in various industries, which can help enterprises shorten the product design period and enhance the manufacturing and managing work. The task of selecting important engineering characteristics (ECs) in QFD is crucial and often involves multiple customer requirements (CRs). In this paper, a modified multi‐objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method based on cloud model theory (called C‐MULTIMOORA) is developed to determine the ranking order of ECs in QFD. First, the linguistic assessments provided by decision makers are transformed into normal clouds and aggregated by the cloud weighted averaging operator. Then, the weights of CRs are determined based on a maximizing deviation method with incomplete weight information. Finally, the importance of ECs is obtained using the C‐MULTIMOORA method. An empirical case conducted in an electric vehicle manufacturing organization is provided together with a comparative analysis to validate the advantages of our proposed QFD model.     

Fuzzy group decision-making for multi-format and multi-granularity linguistic judgments in quality function deployment

As a customer-driven tool, quality function deployment (QFD) is widely used in product planning or improvement to achieve higher product performance and customer satisfaction. QFD uses a matrix called the house of quality (HoQ) to translate customer requirements (CRs) into engineering characteristics (ECs). Constructing the HoQ, which includes determining the importance weights of CRs, the correlation matrix among ECs and the relationship matrix between CRs and ECs, is an important issue in the application of QFD. However, decision-makers (DMs) participating the construction of HoQ tend to give their individual judgments in multi-format or multi-granularity depending on their different knowledge, experience, culture and circumstance. Furthermore, these judgments are more difficult to assess with the precise quantitative forms due to the vagueness and uncertainty existed in the early stage of new product development. In this paper, a group decision-making approach incorporating with two optimization models (i.e. logarithmic least squares model and weighted least squares model) is proposed to aggregate these multi-format and multi-granularity linguistic judgments. Fuzzy set theory is utilized to address the uncertainty in the decision-making process. The proposed method is illustrated with a real-world case of horizontal directional drilling machine. The application indicates that the group decision-making method may be a promising tool for constructing the HoQ.     

Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

Construction of house of quality for new product planning: A 2-tuple fuzzy linguistic approach

A house of quality (HOQ) diagram is used to analyze the critical factors involved in the quality function deployment (QFD) processes for the new product planning (NPP). The principal tasks of the QFD acting process comprise describing and scoring customer requirements (CRs); determining design requirements (DRs), the relationship between CRs and DRs, the correlations among CRs, and the correlations among DRs. Finally, the DRs can be scored by these assessments in NPP. This study proposes various methods of scoring the requirements of current and potential customers to reflect the knowledge and preference differences among different customers regarding CRs. The CR scores provided by different customers can be assessed by using linguistic, numerical, and interval values, or can be assessed using linguistic label sets with different granularity. A 2-tuple fuzzy linguistic computational approach is adopted to aggregate the CR importance scores obtained from customers by using various methods. In addition, to accurately rate the DRs, a modified relationship between CRs and DRs is proposed. The proposed HOQ construction model is practical because it prevents the loss of information during the QFD process for NPP. An example is used to demonstrate the applicability of the proposed model.     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

An objective and interactive-information-based feedback mechanism for the consensus-reaching process considering a non-support degree for minority opinions

The consensus-reaching process (CRP) to achieve higher unanimity and ensure common agreement before deriving a final decision has become an important procedure in group decision-making problems. The demand for high-quality decision results has motivated the development of large-scale group decision-making (LGDM). In such cases, the issue of minority opinion has gained awareness due to the related effects on enhancing consensus and decision quality. A minority opinion cannot exert an effect unless the majority attach importance to whether that opinion is supported or not. To reflect the effect of minority opinions on consensus, this paper establishes a LGDM framework with an objective and interactive-information-based feedback mechanism for the CRP. Given the natural forms of human expression, multi-granular linguistic information and a 2-tuple linguistic model are used. First, initial weights are objectively assigned to decision-makers (DMs) to weaken the impact of the majority. Subsequently, a non-support degree function is newly defined to reflect the extent to which other DMs dissent from a minority opinion. More importantly, feedback rules are constructed to make corresponding adjustments to the powers of discourse among all DMs in the attempt to reach consensus. Finally, the proposed three-phase LGDM framework is applied to new product development (NPD), and simulation experiments are conducted based on two algorithms to verify the framework's applicability and feasibility.     

Algorithm for improving additive consistency of linguistic preference relations with an integer optimization model

Linguistic preference relation (LPR) composed by linguistic terms can well express decision makers’ (DMs’) qualitative preference opinion by comparing alternatives with each other. The investigation of its consistency becomes an important issue to guarantee the rationality of the decision making solutions. Therefore, it is significant to investigate the consistency measure and the consistency improving approach for LPRs. In this paper we present a new method for group decision making (GDM) with LPRs. First, an additive consistency index is introduced on the basis of the information of the original LPR to check whether a LPR is acceptably additive consistency. For unacceptably additively consistent LPR, an integer optimization model is further developed to obtain the acceptably additively consistent LPR. Moreover, the optimization model can guarantee the integrity of the information of the LPR with acceptably additive consistency. Then, with respect to GDM with LPRs, an entropy weight method is proposed to determine the weights of DMs. Finally, the proposed methods are implemented in two numerical examples including a GDM problem. Meanwhile, the comparative analysis with existing methods are discussed in detail to demonstrate the validity of the proposed methods.     

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation (IFPR) is a suitable technique to express fuzzy preference information by decision makers (DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR, by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly, a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.      

犹豫不确定离散语言Z-numbers及其基于离散T模的多准则群决策问题的应用

介绍基于Z-numbers和语言模型的犹豫不确定离散语言Z-numbers(HUDLZNs).HUDLZNs能够有效地描述决策信息的复杂性和不确定性,并能较好地反映出决策者的犹豫性.在此基础上,提出一种基于离散T模融合和正理想方案的多准则群决策方法.首先,借助语言尺度函数来处理语言信息,并定义HUDLZNs间的距离、$\lambda$ 截集和$C^λ截集;其次,提出基于HUDLZNs的离散T模融合;再次,结合离散T模融合和语言尺度函数的优点提出一种HUDLZNs的多准则群决策方法;最后,用ERP系统选型的实例进行阐明,并通过灵敏度分析和已有方法的比较进一步表明所提出方法的有效性和可行性.     

An integrated fuzzy MCDM approach for supplier evaluation and selection

A fuzzy multi-criteria group decision making approach that makes use of quality function deployment (QFD), fusion of fuzzy information and 2-tuple linguistic representation model is developed for supplier selection. The proposed methodology seeks to establish the relevant supplier assessment criteria while also considering the impacts of inner dependence among them. Two interrelated house of quality matrices are constructed, and fusion of fuzzy information and 2-tuple linguistic representation model are employed to compute the weights of supplier selection criteria and subsequently the ratings of suppliers. The proposed method is apt to manage non-homogeneous information in a decision setting with multiple information sources. The decision framework presented in this paper employs ordered weighted averaging (OWA) operator, and the aggregation process is based on combining information by means of fuzzy sets on a basic linguistic term set. The proposed framework is illustrated through a case study conducted in a private hospital in Istanbul.     

A new method for probabilistic linguistic multi-attribute group decision making: Application to the selection of financial technologies

“No technology, no finance” has been the consensus in banking industry. Under the background of financial technology (Fintech), how to select an appropriate technology company to cooperate for the banks has become a key. The technology company selection can be regarded as a kind of multi-attribute group decision making (MAGDM) problems. The probabilistic linguistic term set (PLTS) is a useful tool to express decision makers’ (DMs’) evaluations in the technology company selection. This paper develops a new method for MAGDM with PLTSs. Firstly, the possibility degree and range value of PLTSs are defined. Then a possibility degree algorithm is designed for ranking PLTSs. An Euclidean distance measure between PLTSs is presented and extended to probabilistic linguistic matrices. Based on Archimedean t-norm and s-norm, some new operational laws for PLTSs are defined and some desirable properties are discussed. Then, a generalized probabilistic linguistic Hamacher weighted averaging (GPLHWA) operator and a generalized probabilistic linguistic Hamacher ordered weighted averaging (GPLHOWA) operator are developed. Some useful properties for these operators are investigated in detail. Combined with the subjective weights of DMs, the DMs’ weights are determined by the adjusted coefficients. Using the GPLHWA operator, the collective decision matrix is obtained by aggregating all the individual decision matrices. By maximizing the total weighted square possibility degree, a multi-objective program is constructed to derive the attribute weights. The ranking order of alternatives is generated by integrating ELECTRE and TOPSIS. Thereby, a new method is put forward for MAGDM with PLTSs. A Fintech example is analyzed to show the effectiveness of the proposed method. The sensitivity analysis and comparative analyses are conducted to illustrate its advantages.     

A new integrated approach for engineering characteristic prioritization in quality function deployment

As a customer-driven quality improvement tool, quality function deployment (QFD) can convert customer requirements (CRs) into appropriate engineering characteristics (ECs) in product design and development. However, the conventional QFD method has been criticized for a variety of drawbacks, which limit its efficiency and potential applications. In this study, a new QFD approach integrating picture fuzzy linguistic sets (PFLSs) and the evaluation based on distance from average solution (EDAS) method is proposed for the determination of ranking order of ECs. The PFLSs are utilized to express the judgements of experts on the relationships among CRs and ECs. Then, the EDAS method is extended under picture fuzzy linguistic environment for the prioritization of the ECs identified in QFD. Moreover, a combined weighing method based on technique for order of preference by similarity to ideal solution (TOPSIS) and maximum entropy theory is established to calculate the weights of experts objectively. Finally, a product-service system design is provided to illustrate the effectiveness of the proposed QFD approach. The result shows that the manufacturer should pay more attention to “Meantime before failure”, “Warning feature” and “Quality of product manual”. Feedback from domain experts indicates that the integrated approach being proposed in this paper is more suitable for assessing and prioritizing ECs in QFD.     

A normal wiggly hesitant fuzzy linguistic projection-based multiattributive border approximation area comparison method

As a useful information representation tool, hesitant fuzzy linguistic term set (HFLTS) allows decision makers (DMs) to express their cognitive preferences in terms of several ordered and continuous linguistic terms. Considering the fact that much valuable information related to the cognitive behavior of DMs is hidden in the original evaluation information, this paper studies how to comprehensively mine uncertain information from original hesitant fuzzy linguistic evaluation information given by DMs. To address this objective, we present a new representation tool, normal wiggly hesitant fuzzy linguistic term set (NWHFLTS), which not only retains the original evaluation information, but also delivers and quantifies potential uncertain information, and can also help DMs express their evaluation information in a more complete manner. First, we develop the basic operations, score function, and comparison rule of NWHFLTS based on linguistic scale functions (LSFs), and propose the projection measure, the normal projection measure, and the normalized projection-based distance measure to describe the degree of deviation between two NWHFLTSs. Furthermore, for the case when the attribute weight is completely unknown, we combine the multiattributive border approximation area comparison (MABAC) method and develop a new method called as normal wiggly hesitant fuzzy linguistic projection-based MABAC to solve the multiattribute decision-making problems where attribute values are expressed in the form of NWHFLTS. Finally, through a practical example of marine ecological security situation, the specific calculation steps of this method are exemplified, the feasibility and advancement of the proposed method are demonstrated via a comprehensive comparative study.     

Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators.     

Quality function deployment implementation based on Fuzzy Kano model: An application in PLM system

Product lifecycle management (PLM), a strategic business system allows more effective communication among different groups at dispersed locations to share ideas and access information needed for developing new products and executing innovative processes. The main function of PLM is to develop an attractive system which ensures customer satisfaction. Therefore, one of the important topics of the PLM system developments is to take customer requirements into consideration. Quality function deployment (QFD) has been widely used for numerous years; it is one of the structured methodologies that are used to translate customer needs into specific quality development. However, in the traditional QFD approach, each element’s interdependence and customer requirements are usually not systematically treated. Additionally, the Kano model can effectively classify customer demand attributes, but to make Kano model more objective in the course of weighing, we have also included Fuzzy mode in our discussion. This study presents an integrative approach by incorporating the Kano model with Fuzzy mode into the matrix of QFD and adjusting customer requirement weights. This approach can fulfill two objectives, First, through the Kano model with the Fuzzy mode, it will not only discriminate out options for the required attributes in much more breadth but also simultaneously render the discretions on the linguistic implications much more accurate with the aid of the ambiguous questionnaire response method. Second, combining the Kano model and QFD, can not only provide a new way to optimize the product design but can also enhance customer satisfaction and loyalty, and minimize dissatisfaction. The proposed methods can be useful to both practitioners and researchers. To illustrate our findings, we have incorporated an example which suggests that the proposed approach can contribute to the creation of attractive PLM attributes and PLM innovation.     

Consensus reaching process for group decision-making based on trust network and ordinal consensus measure

Due to the urgent nature of emergency decision making, it is necessary to reach the consensus requirement quickly. Ordinal consensus measure explores the relation between the rankings and helps to intuitively know which alternative needs to be adjusted to accelerate the improvement of consensus. Moreover, decision makers (DMs) in the decision making problem are often connected through trust relationships which affect the DMs’ judgments in the process of DMs’ interaction. Therefore, this paper explores trust network-based group decision-making in which the consensus level is estimated by an ordinal consensus measure. We first focus on the supplementation of an incomplete trust network. One of the most common methods is to design the trust propagation operator, whereas the intensity of information propagation may be different in various scenarios. Therefore, considering the different numerical scale of the linguistic term set, a trust propagation operator with different intensity of trust propagation is designed to obtain the indirect trust relationship. In the process of supplementing the incomplete trust network, the contribution of DMs to propagating information is concerned, which can be described by the betweenness centrality, and the importance weights of DMs are determined by combining the betweenness centrality and trust in-degree. In the consensus reaching process, we first propose an improved ordinal consensus measure, which takes into account the consistency of orders of the same alternative in different rankings as well as the importance of positions of alternatives. Then, we design the identification rule and the feedback mechanism for those with low consensus levels. The identification rule is used to select the DMs which first few alternatives in the ranking are different with those in the ranking of group. And in the feedback mechanism, the referenced preference relation (FPR) obtained by the trust network is provided for the identified DMs. Afterwards, combining the referenced FPR, an optimization model is designed to give the adjustment opinion. Finally, a numerical example elaborates on the feasibility of the trust propagation operator and consensus model. The comparative analysis demonstrates the rationality and effectiveness of the proposed model.     

Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision‐making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.