区间Pythagorean模糊交互式多准则决策模型

研究了权重信息部分已知,评价信息为区间Pythagorean模糊数的交互式多准则决策问题。利用区间Pythagorean模糊数得分函数,计算各方案的加权得分向量在Pythagorean模糊正理想点和Pythagorean模糊负理想点上的投影,构建基于方案满意度最大的非线性规划准则权重确定模型。根据决策者的主观偏好并结合现有客观信息建立单目标规划模型,通过对方案满意度的给定与修正来实现交互决策。通过算例说明模型及方法的可行性和有效性。     

Hesitant interval-valued Pythagorean fuzzy VIKOR method

In this article, we investigate multiple attribute decision-making problems with hesitant interval-valued Pythagorean fuzzy information. First, the concepts of hesitant interval-valued Pythagorean fuzzy set are defined, and the operation laws, the score function, and accuracy function have been developed. Then several distance measures for hesitant interval-valued Pythagorean fuzzy values have been presented including the Hamming distance, Euclidean distance, and generalized distance, and so on. Based on the operational laws, a series of aggregation operators have been developed including the hesitant interval-valued Pythagorean fuzzy weighted averaging (HIVPFWA) operator, the hesitant interval-valued Pythagorean fuzzy geometric weighted averaging (HIVPFGWA) operator, the hesitant interval-valued Pythagorean fuzzy ordered weighed averaging (HIVPFOWA) operator, and hesitant interval-valued Pythagorean fuzzy ordered weighed geometric averaging (HIVPFOWGA) operator. By using the generalized mean operator, we also develop the generalized hesitant interval-valued Pythagorean fuzzy weighed averaging (GHIVPFWA) operator, the generalized hesitant interval-valued Pythagorean fuzzy weighed geometric averaging (GHIVPFWGA) operator, the generalized hesitant interval-valued Pythagorean fuzzy ordered weighted averaging (GHIVPFOWA) operator, and generalized hesitant interval-valued Pythagorean fuzzy ordered weighted geometric averaging (GHIVPFOWGA) operator operator. We further develop several hybrid aggregation operators including the hesitant interval-valued Pythagorean fuzzy hybrid averaging (HIVPFHA) operator and the generalized hesitant interval-valued Pythagorean fuzzy hybrid averaging (GHIVPFHA) operator. Based on the distance measures and the aggregation operators, we propose a hesitant interval-valued Pythagorean fuzzy VIKOR method to solve multiple attribute decision problems with multiple periods. Finally, an illustrative example for evaluating the metro project risk is given to demonstrate the feasibility and effectiveness of the proposed method.     

区间Pythagorean犹豫模糊连续熵及灰色关联度的应用

区间Pythagorean犹豫模糊集,可以更加全面完整地描述决策者给出的决策结果,因此它是一个表示不确定现象的强有力的工具。针对模糊信息下的决策问题,提出了一种基于区间Pythagorean犹豫模糊连续熵的多属性决策方法。提出连续区间Pythagorean犹豫模糊有序加权平均（CIPHFOWA）算子,并提出了区间Pythagorean犹豫模糊连续熵,同时给出了属性权重完全未知和部分已知时的权重确定方法;提出了一种基于区间Pythagorean犹豫模糊连续熵-灰色关联度的多属性决策方法,并通过新型农村医疗制度完善情况评价案例说明该方法的可行性和有效性。     

勾股模糊偏好关系及其在群体决策中的应用

以区间模糊偏好关系(IVFPR)和直觉模糊偏好关系(IFPR)的理论框架为依据,将勾股模糊数(PFN)引入偏好关系中,定义勾股模糊偏好关系(PFPR)和加性一致性PFPR.然后,提出标准化勾股模糊权重向量(PFWV)的概念,并给出构造加性一致性PFPR的转换公式.为获取任意给定的PFPR的权重向量,建立以给定的PFPR与构造的加性一致性PFPR偏差最小为目标的优化模型.针对多个勾股模糊偏好关系的集结,利用能够有效处理极端值并满足关于序关系单调的勾股模糊加权二次(PFWQ)算子作为集结工具.进一步,联合PFWQ算子和目标优化模型提出一种群体决策方法.最后,通过案例分析表明所提出方法的实用性和可行性.     

模糊 Kano 与情景 FBS 模型集成创新设计方法

为提高情景化玩具的满意系数和创新应用,提出了基于模糊 Kano 与情景 FBS 模 型构建创新设计方法。首先,运用模糊 Kano 模型的调查问卷、评估表、调查结果表对市场不 同情景玩具进行调研分析,并依次按照调研结果质量要素的重要程度进行排序,从而获取关键 设计要素。其次,将获得的关键要素作为重要目标,并引用情景功能-行为-结构模型(FBS)与模 糊 Kano 模型相结合的集成创新方法,解决情景化玩具创新性不足的问题,挖掘行之有效创新 方法与新流程。通过情景 FBS 的应用将用户需求分析结果更加直观、准确、多角度地反映实际 需要。最后,以一款情景玩具的创新设计为例,综合模糊 Kano 与情景 FBS 模型具备的互补优 势,有效提高了玩具的满意系数,并通过制作实物模型验证了创新设计的可行性,为同类型玩 具的不同用户群体需求研究提供一定的参考价值。     

Determining the importance weights for the design requirements in the house of quality using the fuzzy analytic network approach

Quality function deployment (QFD) has been used to translate customer needs (CNs) and wants into technical design requirements (DRs) in order to increase customer satisfaction. QFD uses the house of quality (HOQ), which is a matrix providing a conceptual map for the design process, as a construct for understanding CNs and establishing priorities of DRs to satisfy them. This article uses the analytic network process (ANP), the general form of the analytic hierarchy process (AHP), to prioritize DRs by taking into account the degree of the interdependence between the CNs and DRs and the inner dependence among them. In addition, because human judgment on the importance of requirements is always imprecise and vague, this work concentrates on a fuzzy ANP approach in which triangular fuzzy numbers are used to improve the quality of the responsiveness to CNs and DRs. A numerical example is presented to show the proposed methodology. © 2004 Wiley Periodicals, Inc.     

基于信息测度的勾股模糊决策模型及其应用

相对于直觉模糊集，勾股模糊集能够更为全面和有效地表达描述复杂问题中的不确定和非一致信息，使其受到了广泛研究。对于属性评价值为勾股模糊数并且属性指标权重信息数据完全未知的多属性决策问题，以提出的勾股模糊信息测度为基础，设计了新的多属性决策模型。该模型运用对数函数设计了一种新的勾股模糊数信息熵计算方法；引入了勾股模糊相似度概念，并结合对数行数提出勾股模糊数相似度的衡量方法，随后挖掘出勾股模糊数的信息熵和相似度之间的内在联系；运用提出的勾股模糊熵和相似度计算方法，构建新的多属性决策模型，并进行应用研究。实验结果表明，提出的模型合理有效，同时拓展了模型的使用范围。     

Supporting user participation design using a fuzzy analytic hierarchy process approach

There are three fundamental problems that may occur in the process of user participation design: first, the participants/users may not be able to express their requirements clearly; second, they have little knowledge about design; and third, they are generally unfamiliar with the software that designers use. Based on this understanding, a method that considers design rationale is proposed in this work to support the process of user participation design. In addressing the user participation process, a fuzzy analytic hierarchy process (AHP) approach is applied to grasp people's ideas, in the initial design phase. A case study on creating house layout design is employed to illustrate the proposed approach. In this regard, to help participants/users create layout designs, it is proposed that a 3D generative system is used, which integrates navigational concepts, direct manipulation, and the design rationale theory. In a nutshell, this research proposes a system to implement a design rational model and improve design communication in the user participation process. To demonstrate the effectiveness of the proposed prototype system, a user test is performed and we put forward some findings and research questions for further research and industry practices.     

基于E/HOQ/TRIZ 的人机产品创新方法研究

为了快速准确地进行设计阶段的人机产品创新,开发了E/HOQ/TRIZ 集成模型并 描述了具体步骤,提出了基于人体工程学(E)的人机用户需求三维分类的需求获取方式;通过质 量屋(HOQ)确立人机设计关键问题与关键人机设计区域;利用发明问题解决理论(TRIZ)分析人 机设计关键问题中的冲突类型,借助TRIZ 发明原理消除冲突。E/HOQ/TRIZ 集成模型有效弥补 了单一设计理论与方法的局限性,并发挥三种理论与方法的优势,实现人机产品创新设计。通 过人机洗浴设施创新设计,论证了所提出E/HOQ/TRIZ 集成模型与方法的可行性。     

Strategic logistics outsourcing: An integrated QFD and fuzzy AHP approach

This paper develops an integrated approach, combining quality function deployment (QFD), fuzzy set theory, and analytic hierarchy process (AHP) approach, to evaluate and select the optimal third-party logistics service providers (3PLs). In the approach, multiple evaluating criteria are derived from the requirements of company stakeholders using a series of house of quality (HOQ). The importance of evaluating criteria is prioritized with respect to the degree of achieving the stakeholder requirements using fuzzy AHP. Based on the ranked criteria, alternative 3PLs are evaluated and compared with each other using fuzzy AHP again to make an optimal selection. The effectiveness of proposed approach is demonstrated by applying it to a Hong Kong based enterprise that supplies hard disk components. The proposed integrated approach outperforms the existing approaches because the outsourcing strategy and 3PLs selection are derived from the corporate/business strategy.     

区间Pythagorean模糊前景多阶段多属性应急决策方法

针对属性权重未知且决策信息为区间Pythagorean模糊语言的应急决策问题,提出一种基于组合赋权和前景理论的多阶段多属性决策方法。根据方案信息熵确定属性权重范围,并以区间Pythagorean模糊熵最小为目标构建模型并求解,以确定属性权重。定义正负理想点作为参考点,运用前景理论求出每一阶段各状态下的前景值,并考虑前一阶段方案对后一阶段状态概率的影响,求出方案链的前景值。在此基础上,以方案链的前景值最大和成本最小为目标构建优化模型,并将多目标转化为单目标,求解模型以确定各阶段的最优方案。以某传染病疫情防控应急决策问题为算例验证了该方法的可行性,并将多阶段决策效果与单一阶段的决策结果进行比较分析,验证了该方法的有效性。     

基于ISM与AHP组合的需求优先级排序方法

当前需求优先级排序方法将用户需求放在同一层次上进行比较,然后设定优先级,而对需求层次性考虑不 多。对此,从需求的层次性出发,提出以解释结构模型和层次分析法相结合的需求优先级排序方法,其中用解释结构 模型对需求进行分层处理,然后对最上层的需求使用层次分析法进行需求优先级排序,最后给出案例分析。结果表 明,该方法能够提高需求优先级设定的合理性,明显降低需求的比较次数,降低因需求导致项目失败的风险。     

The interval-valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral-based method

The hesitant Pythagorean fuzzy set is frequently considered as a solution for decision making under uncertainty. Whereas the representation of uncertain information might be not sufficient in the hesitant Pythagorean fuzzy environment, thus the concept of interval-valued hesitant Pythagorean fuzzy sets (IVHPFSs) is proposed. Specifically, we first propose the concept of IVHPFSs and then study the operational rules and distance measures of IVHPFSs in detail. To ease the possible application, we explore two decision-making processes in the setting of IVHPFSs by drawing support from the technique for order preference by similarity to ideal solution and Choquet integral-based method. Finally, the selecting processes of project private partner are also presented to demonstrate the decision-making processes based on IVHPFSs and compared with some similar techniques.     

Polynomial regression interval-valued fuzzy systems

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have implemented the proposed non-linear (polynomial regression) statistical interval-valued type-2 FLS to perform smart washing machine control. The results show that our quadratic statistical method is more robust to design a reliable type-2 FLS and also can be extend to polynomial model.     

软件需求定量分析及其映射的模糊层次分析法

在用数量化理论3类(quantification theory of type 3,简称QT3)定量地分析软件需求的基础上,以质量功能展开(quality function deployment,简称QFD)中的质量屋(house of quality,简称HOQ)系列矩阵为纲领,基于由模糊技术改进后的模糊层次分析法(fuzzy analytic hierarchy process,简称FAHP),提出了一种软件需求定量分析及其向设计实现过程模糊映射的方法.将该方法具体应用于CD-R/RW光盘刻录机软件的开发过程,其有效性得到了验证.     

基于云模型的区间直觉模糊数多属性群决策

针对属性值为区间直觉模糊数的多属性群决策问题,考虑到模糊性和随机性对群决策过程及结果的影响,本研究将利用云模型理论结合区间直觉模糊数的特征,运用灰色关联系数法和信息熵理论确定专家和属性权重,通过信息集结构建综合评价云模型.不同于传统的区间直觉模糊数的排序方法,本研究利用云模型的3En规则将区间直觉模糊数进行云转换并通过云相似度确定方案的综合评价值和犹豫度,然后对决策方案进行比较分析.研究结果表明:该方法能够科学有效地进行决策,进而为决策方提供科学依据.     

Projection Model for Fusing the Information of Pythagorean Fuzzy Multicriteria Group Decision Making Based on Geometric Bonferroni Mean

As a new generalization of fuzzy sets, Pythagorean fuzzy sets (PFSs) can availably handle uncertain information more flexibly in the process of decision making. Through synthesizing the Bonferroni mean and the geometric mean, the geometric Bonferroni mean (GBM) captures the interrelationship of the input arguments. Considering the interrelationship among the input arguments, we introduce GBM into Pythagorean fuzzy situations and expand its applied fields. Under the Pythagorean fuzzy environment, we develop the Pythagorean fuzzy geometric Bonferroni mean and weighted Pythagorean fuzzy geometric Bonferroni mean (WPFGBM) operators describing the interrelationship between arguments and some special properties of them are also investigated. Then, we employ the WPFGBM operator to fuse the information in the Pythagorean fuzzy multicriteria group decision making (PFMCGDM) problem, which can obtain much more information in the process of group decision making. With the aid of the projection model, we present its extension and further design a new method for the application of PFMCGDM. Finally, an example is given to elaborate on the performance of our proposed method.     

Stakeholder requirement evaluation of smart industrial service ecosystem under Pythagorean fuzzy environment for complex industrial contexts: A case study of renewable energy park

This study focuses on ways to systematically evaluate stakeholder requirements when developing a smart industrial service ecosystem (SISE) in a complex industrial context. The SISE development requires considering the service requirement from both the complex industrial context and service ecosystem manners. This study proposes a systematic framework for stakeholder requirement evaluation in SISE. The first part of the framework is the industrial context-viable system model with ecological thinking (IC-VESM) to elicit the service requirements for the SISE, which facilitates a systematic analysis of the service value proposition and service requirement elicitation in the operational lifecycle of an entire industrial context. This second part of the framework proposes a method for evaluating service requirements that is both feasible and systematic. This is achieved by combining the Fuzzy Kano and AHP methods in a Pythagorean fuzzy (PF) environment. The PF Kano computes the categories and determines the weights of service requirements from a consumer perspective, while the PF AHP hierarchically analyzes the service requirements and provides pairwise comparison paths for design experts. Finally, an illustrative case study in a renewable energy context was used to demonstrate the feasibility and effectiveness of the methodology. The proposed theoretical model provides more reliable and systematic outcomes than traditional methods when eliciting service requirements and evaluating complex smart industrial service solutions. The study has practical implications by providing useful insights for companies to recognize key smart service requirements in complex industrial contexts and to improve sustainable development.     

A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is an important tool in product planning that could contribute to increase in customer satisfaction and shorten product design and development time. During the QFD process, determination of the importance weights of customer requirements is a crucial and essential step. The analytic hierarchy process (AHP) has been used in weighting the importance. However, due to the vagueness and uncertainty existing in the importance attributed to judgement of customer requirements, the crisp pairwise comparison in the conventional AHP seems to be insufficient and imprecise to capture the degree of importance of customer requirements. In this paper, fuzzy number is introduced in the pairwise comparison of AHP. An AHP based on fuzzy scales is proposed to determine the importance weights of customer requirements. The new approach can improve the imprecise ranking of customer requirements which is based on the conventional AHP. Finally, an example of bicycle splashguard design is used to illustrate the proposed approach.     

基于模糊回归的质量屋决策模型

基于带有对称三角形模糊系数的模糊回归及模糊规划理论，提出关联函数及自 相关函数的数学模型，并在系统考虑资源约束影响的基础上，分别建立了基于质量屋的产品 规划精确模型及模糊模型．仿真研究表明，这些模型适合于各种工程设计问题，尤其是在不 确定的、模糊的条件下，能够有效地确定关联函数及自相关函数，帮助开发人员优化顾客需 求的满意水平，在资源约束下使产品的顾客满意度最大．