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。     

基于动态P-模糊语言算子的VIKOR决策方法

针对直觉模糊信息解决动态多属性决策问题时存在的不足,将Pythagorean模糊语言信息引入到动态多属性决策问题,提出一种基于Pythagorean模糊语言信息集成算子的多准则妥协排序（VIKOR）决策方法。引入Pythagorean模糊语言得分函数、精确函数、距离计算公式等概念,提出动态 Pythagorean模糊语言加权平均（DPFLWA）算子,并研究DPFLWA算子的基本性质。最后,基于DPFLWA算子和VIKOR方法,构建一种动态 Pythagorean模糊语言多属性决策方法。通过第三方逆向物流服务商的选择实例,表明该方法的可行性和有效性。     

A design model of FBS based on interval-valued Pythagorean fuzzy sets

The FBS (Function-Behaviour-Structure) model is a research model that stimulates creative thinking of designers in the design process. In order to reduce the influence of user requirement ambiguity on design results in the product design process and improve the accuracy of user requirements in the function-behavior-structure (FBS) design model, this paper proposes an interval-valued Pythagorean fuzzy set-based FBS model integrating AHP and HOQ methods. Firstly, the design model will use IVPF-AHP method to study user requirements and use interval-valued Pythagorean linguistic terms to replace the traditional scoring method of AHP to get the weight of each user requirement. Secondly, the conversion between user requirements and functions will be realized by IVPF-HOQ method, which converts customer requirements into functional characteristics and calculates the weights of each functional characteristic. Finally, the design focus will be filtered according to the order of importance of the functional characteristics, which will be used as functions to guide the development of the FBS model. In this paper, the feasibility and effectiveness of the proposed method will be verified by an application example of a hand-held fluorescence spectrometer. The results show that the proposed FBS model can effectively reduce the subjectivity and ambiguity in the decision-making process, improve the accuracy and information richness of user requirements, and effectively highlight the focus of the design study. The innovation of the proposed method is to provide a more objective and accurate innovative design method for user requirements through the integration of AHP, HOQ and FBS to effectively explore and analyze user requirements. The use of IVPFS to deal with fuzzy information in the design process in a more flexible manner can reduce the ambiguity of requirements when user data is small, and effectively improve the limitations of the FBS design model which is more subjective.     

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.     

Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision-making process

Hesitant Pythagorean fuzzy (HPF) sets can easily express the uncertain information while Maclaurin symmetric mean (MSM) operator, can capture the interrelationship among the multiattributes, and are suitable for aggregating the information into a single number. By taking the advantages of both, in this paper, we extend the traditional MSM to HPF environment. For this, we develop the HPFMSM operator for aggregating the HPF information. The desirable characteristics, such as idempotency, monotonicity, and boundedness, are studied. Then, we discussed some special cases with respect to the parameter value of the HPFMSM operators and showed that it generalizes the various existing operators. Furthermore, we studied the weighted HPFMSM operator to aggregate the HPF information with different preferences to the input arguments. On the basis of these operators, we solved the multiattribute decision-making problems with HPF information. The practicality and effectiveness of the developed approach are demonstrated through a numerical example.     

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.     

Hesitant fuzzy sets

Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.     

区间直觉模糊信息下的双向投影决策模型

研究权重完全未知、评价信息为区间直觉模糊数的多准则决策问题. 考虑犹豫度影响, 给出备选方案与正理想方案、负理想方案形成的向量表达方式, 提出一种针对区间直觉模糊信息的向量投影测度方法; 构建基于方案投影总偏差最小的非线性规划准则权重确定模型; 给出基于方案投影的相对贴近度测算公式, 并以此对方案进行排序. 最后通过算例对比分析表明了所提出方法的有效性和可行性.

     

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.     

Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry

With the rapid development of Internet banking technology in Ghana, the website quality evaluation is the essential core of the customer, which is regarded as a multi-criteria decision making (MCDM) problem. Due to the uncertainty of Internet banking, the evaluation of criteria may be measured by Pythagorean fuzzy numbers (PFNs). In addition, the customer usually does not exhibit complete rationality in the decision procedure. Based on the traditional VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje) method of MCDM, this paper provides a new perspective of a compromised solution, which can handle the decision maker’s psychological behavior by inducing TODIM (a Portuguese acronym meaning Interactive Multi-Criteria Decision Making). By defining Pythagorean fuzzy entropy and cross-entropy measures, we study the determination of the weights of the criteria in advance. Then, considering the psychological behavior of the customer, we design two types of strategies for the combination between TODIM and VIKOR. Meanwhile, the corresponding methods have been developed, i.e., Approaches I and II. After that, a simulated example of ranking Internet banking websites in the Ghanaian banking industry is given to illustrate the validity and applicability of our proposed approaches. Finally, we utilize the Wilcoxon signed-rank test and then discuss the differences among VIKOR, TODIM and our proposed methods.     

Hesitant fuzzy best-worst multi-criteria decision-making method and its applications

Best-worst method (BWM) is extended to uncertain situations, hesitant fuzzy best-worst method (HFBWM) is proposed by using hesitant fuzzy multiplicative preference relation for multiple-criteria group decision-making problems. The reference comparison of the best criterion and the worst criterion are described by the linguistic terms, which are expressed in hesitant fuzzy elements, of the decision makers. Weights of criteria are calculated by using score function. Using the concept of BWM, nonlinearly constrained optimization problems are formed to obtain hesitant fuzzy weights (HFWs) of different criteria and alternatives. To check the reliability of the HFBWM, consistency ratio is proposed. The advantage and suitability of the proposed HFBWM are determined by three case studies. The results indicate that the HFBWM, due to higher comparison consistency as compared to BWM, obtain plausible preference ranking for alternatives.     

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.     

A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments

Neural Computing and Applications - This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal...     

Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

     

犹豫模糊软集

犹豫模糊集是对模糊集的一种推广,它是一类关于域中每个元素所含隶属度的集合,常应用于群决策中,但由于其本身在参数工具上的缺乏使得难于处理不确定数据。为了提高决策的精确性,将软集与犹豫模糊集结合起来,提出犹豫模糊软集的概念,并给出犹豫模糊软集的基本运算法则和性质。     

Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets

Out of several generalizations of fuzzy set theory for various objectives, the notions introduced by Atanassov, 1983, Atanassov and Gargov, 1989 in defining intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. Ranking of interval-valued intuitionistic fuzzy sets plays a vital role in decision-making, data analysis, artificial intelligence and socioeconomic system and it was studied in Xu, 2007c, Xu and Chen, 2007a, Ye, 2009. In this paper a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and studied. The method is illustrated by numerical examples and compared with other methods. And then a new method for handling multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets is presented in which criterion values for alternatives are interval-valued intuitionistic fuzzy sets. The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision. An illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Pythagorean fuzzy preference ranking organization method of enrichment evaluations

Recently, a new extension of fuzzy sets, Pythagorean fuzzy sets (PFS), has attracted a lot of attention from scholars in various fields of research. Due to PFS’s powerfulness in modeling the imprecision of human perception in multicriteria decision-making (MCDM) problems, this paper aims to extend the classical preference ranking organization method of enrichment evaluations (PROMETHEE) into the Pythagorean fuzzy environment. The proposed method takes not only the weights related to different criteria but also the preference relations as Pythagorean fuzzy numbers, therefore providing a broader range of choices for the decision-maker to express their preferences. Five properties are put forward to regulate the designing of both intuitionistic and Pythagorean fuzzy PROMETHEE (PF-PROMETHEE) preference functions. Furthermore two illustrative examples are given to demonstrate the detailed procedure of PF-PROMETHEE, and comparisons are made to distinguish the differences among our proposed method, the classical PROMETHEE and intuitionistic PROMETHEE. The results show that PF-PROMETHEE is effective, comprehensive, and applicable to a wide range of MCDM problems.     

毕达哥拉斯模糊Heronian算子的多属性决策方法

针对毕达哥拉斯模糊环境下的多属性决策问题中的信息集成问题,其中方案的属性间相互关联相互影响,提出了一种毕达哥拉斯模糊Heronian算子的多属性决策方法。首先将毕达哥拉斯模糊数与Heronian算子相结合,提出了毕达哥拉斯模糊Heronian算子和毕达哥拉斯模糊加权Heronian算子,并讨论了这些算子的性质,给出了相应的证明。在此基础上,提出了基于毕达哥拉斯模糊Heronian算子的多属性决策方法;最后将其应用到国内四家航空公司服务质量评价中,说明了该算子的有效性和可行性。     

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Pyt...