Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.     

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。     

Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets

Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper the interval-valued fuzzy TOPSIS method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy sets concepts.     

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson-like correlation-based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval-valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real-life decision-making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well-known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson-like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation-based closeness coefficients to simultaneously measure the relative closeness to the positive-ideal PF/IVPF solutions and the relative remoteness from the negative-ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson-like correlation-based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.     

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.     

Extension of the ELECTRE method based on interval-valued fuzzy sets

Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection problem.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set (PFS) can provide more flexibility than intuitionistic fuzzy set (IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multi-attribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean (PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable (PULV) and explore some properties of the operator. Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.      

Site selection in waste management by the VIKOR method using linguistic assessment

Site selection is an important issue in municipal solid waste (MSW) management. Selection of the appropriate solid waste site is an extensive evaluation process that requires consideration of multiple alternative solutions and evaluation criteria. In reality, it is easier for decision makers to express their judgments on the alternatives by using linguistic terms, and there usually exists uncertain and incomplete assessment information. Moreover, decision makers may have different risk attitudes in the siting process because of their different backgrounds and personalities. Therefore, an attitudinal-based interval 2-tuple linguistic VIKOR (ITL-VIKOR) method is proposed in this paper to select the best disposal site for MSW. The feasibility and practicability of the proposed method are further demonstrated through an example of refuse-derived fuel (RDF) combustion plant location. Results show that the new approach is more suitable and effective to handle the MSW site selection problems by considering the decision maker's attitudinal character and incorporating the uncertain and incomplete assessment information.     

基于广义Choquet积分的Pythagorean不确定语言TODIM方法及其应用

针对评价信息为Pythagorean不确定语言变量且指标具有关联性的多指标决策问题,考虑到决策者的参照依赖和损失规避等有限理性行为,提出一种基于广义Choquet积分的Pythagorean不确定语言TODIM方法.首先,给出Pythagorean 不确定语言变量的定义及其相关理论;其次,考虑决策者的参照依赖行为,计算各方案相对于其他方案关于各指标的收益或损失值;再次,考虑决策者的损失规避行为,集成指标关联情形下方案的收益或损失值,得到每个方案相对于其他各个方案的个体感知优势度;最后,计算各方案的总体感知优势度,并依据总体感知优势度进行方案排序.一个雾霾污染治理的算例验证了所提出方法的实用性和有效性.     

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.     

Some interval-valued q-rung orthopair weighted averaging operators and their applications to multiple-attribute decision making

Q-rung orthopair fuzzy sets (q-ROFSs), initially proposed by Yager, are a new way to reflect uncertain information. The existing intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets are special cases of the q-ROFSs. However, due to insufficiency in available information, it is difficult for decision makers to exactly express the membership and nonmembership degrees by crisp numbers, and interval membership degree and interval nonmembership degree are good choices. In this paper, we propose the concept of interval-valued q-rung orthopair fuzzy set (IVq-ROFS) based on the ideas of q-ROFSs and some operational laws of q-rung orthopair fuzzy numbers (q-ROFNs). Then, some interval-valued q-rung orthopair weighted averaging operators are presented based on the given operational laws of q-ROFNs. Further, based on these operators, we develop a novel approach to solve multiple-attribute decision making (MADM) problems under interval-valued q-rung orthopair fuzzy environment. Finally, a numerical example is provided to illustrate the application of the proposed method, and the sensitivity analysis is further carried out for the parameters.     

基于Pythagorean不确定语言的扩展VIKOR多属性群决策方法

针对属性值为Pythagorean不确定语言变量,属性权重和专家权重完全未知的群决策问题,提出一种扩展VIKOR多属性群决策方法.首先,给出Pythagorean不确定语言变量的概念,提出考虑语义变化的Pythagorean不确定语言变量运算规则、大小比较方法和Hamming距离测度;其次,提出基于Pythagorean 不确定语言模糊熵的属性权重确定方法和基于相似度的专家权重确定方法,进而提出一种新的扩展VIKOR方法;最后,通过国内航空公司服务质量评估实例验证所提出方法的有效性和可行性.     

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。     

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.     

区间值比例二元组语言集成算子及其决策方法

结合区间不确定性语言集与比例二元组,提出区间值比例二元组的概念;基于得分函数与精确函数,给出了两个区间值比例二元组的比较方法,并介绍了区间值比例二元组与区间数之间的转换函数;在此基础上,提出区间值比例二元组加权几何算子及区间值比例二元组有序加权几何算子;针对不同语言标度的群决策问题,通过统一标度给出了相应的多属性群决策方法,并将其用于投资商投资过程中。     

Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process

In this article, a new linguistic Pythagorean fuzzy set (LPFS) is presented by combining the concepts of a Pythagorean fuzzy set and linguistic fuzzy set. LPFS is a better way to deal with the uncertain and imprecise information in decision making, which is characterized by linguistic membership and nonmembership degrees. Some of the basic operational laws, score, and accuracy functions are defined to compare the two or more linguistic Pythagorean fuzzy numbers and their properties are investigated in detail. Based on the norm operations, some series of the linguistic Pythagorean weighted averaging and geometric aggregation operators, named as linguistic Pythagorean fuzzy weighted average and geometric, ordered weighted average and geometric with linguistic Pythagorean fuzzy information are proposed. Furthermore, a multiattribute decision‐making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.     

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.     

区间直觉二元语言集成算子及其群决策方法

基于下标以零为中心对称的语言评估标度,将区间不确定二元语言集与区间直觉模糊集结合,提出区间直觉二元语言集及变量的概念;讨论区间直觉二元语言变量的运算及可能度;提出区间直觉二元语言加权算术平均算子、区间直觉二元语言有序加权平均算子,并在此基础上,通过可能度矩阵对区间直觉二元语言变量进行排序提出区间直觉二元语言混合加权平均算子;最后基于这些算子构建了一种新的直觉模糊多属性群决策方法,并将其运用于供应商选择过程中。