一种基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法

模糊语言决策方法是决策领域的热点研究内容之一.比较现有模糊语言决策方法研究中广泛使用的决策矩阵,提出对象-语言值决策矩阵表示决策专家根据决策属性给出的评价语言信息,分析对象-语言值决策矩阵在区分明晰、部分未知及犹豫的模糊语言决策问题中的优势;借鉴经典TOPSIS决策方法及向量运算,给出基于对象-语言值决策矩阵的正负理想解确定方法以及备选对象与正负理想解的伪距离和贴近度计算方法,分析伪距离和贴近度的相关性质;基于2-元组语言表示模型,提出基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法.通过实例分析,并与已有3种重要的模糊语言决策方法进行比较,比较结果说明所提出的决策方法可以克服已有决策方法的不足, 是一种可选的模糊语言决策方法.     

Fermatean fuzzy linguistic set and its application in multicriteria decision making

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.     

语言犹豫模糊集的相关系数及其在决策中的应用

语言犹豫模糊集是指决策者可以用一些有隶属度的语言术语项表示他/她对一件事情的偏好.这种类型的集合很好地反映了决策者定性和定量的认知以及它的不确定性,因此受到越来越多学者的关注.首先,提出语言犹豫模糊集的相关系数概念,并给出语言犹豫模糊集的相关系数和加权相关系数的计算法则和性质;然后,指出引入的相关系数的显着特征是它位于区间[-1,1]内,这与统计中的经典相关系数一致,而其他文献中提出的语言犹豫模糊集的相关系数都位于区间[0,1]内;最后,将所提出的方法应用于医疗诊断中,并将该方法得到的计算结果与已有的语言犹豫模糊集的相关系数进行比较,比较结果表明,新的语言犹豫模糊集的相关系数的分布更好,能更准确地反映出病人的身体状况与各疾病的关系,从而迅速高效地作出诊断.     

区间模糊语言多属性群决策方法及应用研究

基于我国银行业所面临的数据匮乏、信息披露制度不完善等问题,国际上先进的统计量化方法并不能完全适用于对我国操作风险的评价,从定性和定量相结合的角度出发,针对操作风险评价中的多属性群决策问题,提出一种在区间模糊语言信息下基于不确定的拓展有序加权平均算子（UEOWA）和不确定语言混合集结算子（ULHA）的多专家多属性商业银行操作风险评价方法,构建基于区间模糊语言的评价集来描述专家不精确、难量化的意见,梳理评价思路,设计评价步骤,通过实例验证了该方法的可操作性和有效性。     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

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。     

二元语义密度算子及其在不确定多属性决策中的应用

针对二元语义信息形式的不确定多属性决策问题,将密度中间算子由精确值形式拓展到二元语义形式.首先,基于二元语义信息对应的数值提出一种简单有效的二元语义聚类方法;然后,给出了密度加权向量的确定方法,并且在此基础上,将二元语义密度中间算子与已知的信息集结算子合成,得到二元语义密度合成算子（T-DM）;最后,通过一个算例对二元语义密度算子的应用进行了说明.     

Pythagorean模糊环境下基于交叉熵和TOPSIS的多准则决策方法

考虑到Pythagorean模糊集（Pythagorean Fuzzy Set,PFS）具有的优势,提出了一个Pythagorean模糊环境下解决多准则决策（Multicriteria Decision Making,MCDM）问题的新方法。根据TOPSIS理论计算Pythagorean模糊环境下的正、负理想解,同时提出两个Pythagorean模糊集之间的交叉熵定义,并对其性质给予证明。计算每个方案各自和正、负理想解之间的交叉熵,再根据相对贴近度对所有方案进行排序。通过一个在绿色环境下的供应商选择的算例验证了有效性和实用性。     

Group decision making with fuzzy linguistic preference relations via cooperative games method

When we consider the weighting approach for group decision making with fuzzy linguistic preference relations, the groupment of experts has merely been studied. In this paper, a novel weighting approach on the basis of cooperative games method is developed. The group decision error matrix is built to reflect the deviations of all experts with given initial weighting vector. An iterative algorithm is designed to lower the sum of the decision error so that a final convergence result can be obtained. The advantage of the weighting algorithm is that it can consider the contribution of each expert and reduce the sum of decision error with increasing iteration numbers. Then an optimization model using triangular fuzzy numbers as alternatives’ weights is constructed, whose results are used to rank the alternatives. Finally, a numerical example of subjective evaluation of vehicle sound quality is considered to illustrate the feasibility and validity of the proposed weighting approach in the group decision making problem.     

Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information

With the rapid information explosion and sharing, recommender systems (RS) play an auxiliary role in assisting the Internet users to make decision especially in the e-service platform. Normally, the information in this process is related to opinions and preferences, which are usually expressed through a qualitative way such as linguistic evaluation terms (LETs). However, the LETs may come from different sources such as experts, users, etc., which makes the linguistic evaluation scales (LESs) used in this process probably be different due to their different backgrounds and levels of knowledge. The diversity and flexibility of these LESs determine the quality of information, and further affect the effectiveness of a RS. In this paper, we focus on improving the accuracy of the multi-granular linguistic recommender system by supporting customers to find out the most eligible items according their own preferences. We first propose the probabilistic linguistic vector-term sets (PLVTSs) to promote the application of multi-granular linguistic information. Based on the PLVTSs, we then develop a novel algorithm to tackle multi-attribute group decision making (MAGDM) problems with multiple LESs. Furthermore, the effectiveness of the PLVTSs is validated by an illustration of personalized hospital selection-recommender problem. Finally, we point out some possible research directions regrading to the PLVTSs.     

二元语义粗算子及其语言多属性决策中的应用

针对语言多属性决策,提出一种基于二元语言信息处理和粗糙集理论的求解方法。利用规范的语言评价信息建立决策信息表,提出了一种由属性依赖度和信息度来形成属性客观权重的方法,通过二元语义集成算子计算属性的主观权;根据决策者的偏好,将各属性的主客观权重信息集成,得到属性综合权重;将规范化的语言评价信息转化为二元语言形式,并与已有的信息集结算子合成,得到二语义粗算子;举例说明二元语义粗算子的应用。     

Soft fuzzy rough sets and its application in decision making

Recently, the theory and applications of soft set has brought the attention by many scholars in various areas. Especially, the researches of the theory for combining the soft set with the other mathematical theory have been developed by many authors. In this paper, we propose a new concept of soft fuzzy rough set by combining the fuzzy soft set with the traditional fuzzy rough set. The soft fuzzy rough lower and upper approximation operators of any fuzzy subset in the parameter set were defined by the concept of the pseudo fuzzy binary relation (or pseudo fuzzy soft set) established in this paper. Meanwhile, several deformations of the soft fuzzy rough lower and upper approximations are also presented. Furthermore, we also discuss some basic properties of the approximation operators in detail. Subsequently, we give an approach to decision making problem based on soft fuzzy rough set model by analyzing the limitations and advantages in the existing literatures. The decision steps and the algorithm of the decision method were also given. The proposed approach can obtain a object decision result with the data information owned by the decision problem only. Finally, the validity of the decision methods is tested by an applied example.     

属性权重未知picture模糊多属性决策方法及其应用

针对属性权重未知的picture模糊多属性决策问题,提出一种基于picture模糊熵和picture模糊加权对称交叉熵的多属性决策方法.首先,基于余弦函数提出一类新的picture模糊熵,并验证该熵值满足picture模糊熵的公理化定义;其次,针对标准化处理后的picture模糊决策矩阵,以picture模糊熵确定各属性权重,同时确定正、负理想方案;再次,分别计算各方案与正、负理想方案的picture模糊加权对称交叉熵,考虑决策者的主观评价倾向以模糊折中值得到各备选方案的排序结果;最后,将所提多属性决策方法应用于河南自贸试验区郑州片区创新型项目遴选,并通过对比分析验证该决策方法的有效性与合理性.     

The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making

The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.     

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision maker’s knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.     

Uncertain linguistic hesitant fuzzy sets and their application in multi‐attribute decision making

To denote the quantitative and qualitative fuzzy information simultaneously, this paper introduces a new type of fuzzy sets called uncertain linguistic hesitant fuzzy sets, which are denoted by an uncertain linguistic variable with several possible interval membership degrees. Considering the application of this type of fuzzy sets, several basic operational laws are defined, and several properties are studied. Meanwhile, an ordered relationship is introduced. Then, two types of uncertain linguistic hesitant fuzzy aggregation operators are defined. One uses additive measures, and the other is based on λ‐fuzzy measures. Then, a similarity measure is presented, by which models for the optimal weight vector are constructed. After that, an approach to uncertain linguistic hesitant fuzzy multi‐attribute decision making is developed. Finally, an illustrative example for evaluating corporate environmental performance is offered to show the concrete practicality of the procedure.     

Group decision making with incomplete fuzzy linguistic preference relations

The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two‐tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert. It is guided by the additive consistency property to maintain experts' consistency levels. Additionally, we present a selection process of alternatives in group decision making with incomplete fuzzy linguistic preference relations and analyze the use of our estimation procedure in the decision process. © 2008 Wiley Periodicals, Inc.     

犹豫模糊语言群决策的共识性模型

针对犹豫模糊语言群决策问题,研究其共识性调整方法.首先,定义犹豫模糊语言术语集的距离测度;然后,基于该距离测度定义犹豫模糊决策矩阵间的共识性水平及其相关概念,建立共识性调整模型,该模型采用反馈机制,并且尽可能提供给专家较多的信息,以方便专家进行信息修正,达到群体共识;最后,通过具体实例说明了所提出的共识性方法的可行性和实用性.     

Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection

The double hierarchy linguistic term set is a linguistic technique to elaborately and accurately represent complex linguistic information for qualitative decision-making problems. Considering that unbalanced semantics may appear in the first and second hierarchy linguistic term sets, the unbalanced double hierarchy linguistic term set (UDHLTS) is proposed in this paper. To characterize the unbalanced distribution of semantics of the second hierarchy linguistic terms, we propose three linguistic scale functions with cognitive bias parameters. Then, a non-linear fitting method is presented to determine these parameters. Combining the first and second hierarchy linguistic term set, we construct eight semantic models with distinct risk appetite parameters and linguistic cognitive bias parameters to capture the semantics of linguistic terms in the UDHLTS. In this way, we can use specific semantic model to represent experts’ opinions associated with the UDHLTS. In addition, by using the semantic model of the UDHLTS, linguistic information from different experts can be compared and aggregated quantitatively. To illustrate the applicability of the UDHLTS, we develop a UDHL-TOPSIS method for multi-expert qualitative decision making problems. An engineering example concerning green mine selection is given to illustrate the proposed method.     

模糊语言多属性群决策的客观综合赋权方法

针对一类属性及专家权重完全未知且评价值为直觉不确定语言数的多属性群决策问题,提出一种基于客观综合赋权模型的模糊群决策方法。通过定义直觉不确定语言数的不确定度和距离测度,对单个专家内部以及专家群体之间的评价值进行分析,分别建立基于离差最大化和熵值的属性综合赋权模型以及基于不确定度和偏离度的专家综合赋权模型,提出一种基于客观综合权重的直觉不确定语言多属性群决策方法。通过实例分析表明了该方法的可行性和实用性。