Z-numbers的否定及其在多属性决策中的应用

否定命题是数理逻辑中的重要表示方式,也是智能信息处理中刻画信息的关键工具.Znumber是一种新的不确定性语言信息表示方式.回顾了否定的相关研究,并介绍了可能性分布的否定在Z-number理论中的应用.通过最大香农熵和粒子群算法,提出了一种优化模型,用于发现Z-number中隐藏的可能性分布.研究表明,Z-number的否定为语言决策分析和解决复杂问题提供了有效工具.

基于DEMATEL-ANP+Z-numbers方法的核安全文化评价研究

核安全文化是影响核电安全运行的关键要素之一。为了更加精准识别核电厂安全文化存在的弱点和定量评估核安全文化水平,文章首先基于安全文化冰山模型和文献分析,从价值观、行为、系统和环境四个方面建立核安全文化评价指标体系;然后,基于DEMATEL-ANP+Z-numbers方法构建了核安全文化评估方法,考虑到指标体系可能存在相互影响,因此运用DEMATEL-ANP方法确定各级指标的权重,考虑到专家评估的主观性、模糊性和不确定性,运用Z-numbers模糊综合评估方法进行综合评价,使评估结果更为精准;最后,以某核电厂为实例进行应用分析。结果显示,该核电厂安全文化评估总得分为0.671,处于“较高”水平,并识别存在的主要弱点,为提升核安全文化水平提供理论支持。

新型犹豫不确定Z-Numbers熵及其多准则群决策分析

犹豫不确定语言型Z-Numbers的语言尺度函数是由两种不同语义的集合构成,分别度量两种语言尺度函数,确定其三个基本性质。结合语言尺度函数和犹豫不确定语言型Z-Numbers的模糊因子及犹豫因子,构造了犹豫不确定语言型Z-Numbers的交叉熵和熵,引入求解决策者权重和准则权重的两种最优化模型,通过求解最优化模型确定综合熵决策矩阵,由排序值公式给出多准则群决策问题的最优方案。通过一个实例分析比较得出相同的最优方案和不同排序,验证了该决策方法的有效性与可行性。

Failure Mode and Effects Analysis Based on Z-Numbers and the Graded Mean Integration Representation

Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.

Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers:Application in Complex Decision Aid Systems

The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

A Review on Ranking of Z-numbers

There are numerous studies about Z-numbers since its inception in 2011.Because Z-number concept reflects human ability to make rational decisions,Z-number based multi-criteria decision making problems are one of these studies.When the problem is translated from linguistic information into Z-number domain,the important question occurs that which Z-number should be selected.To answer this question,several ranking methods have been proposed.To compare the performances of these methods,benchmark set of fuzzy Z-numbers has been created in time.There are relatively new methods that their performances are not examined yet on this benchmark problem.In this paper,we worked on these studies which are relative entropy based Z-number ranking method and a method for ranking discrete Z-numbers.The authors tried to examine their performances on the benchmark problem and compared the results with the other ranking algorithms.The results are consistent with the literature,mostly.The advantages and the drawbacks of the methods are presented which can be useful for the researchers who are interested in this area.

基于Z-numbers模糊数的改进PROMETHEE法

针对评价值为模糊数的工程方案优选问题,通过Z-numbers模糊数方法建立模糊评价矩阵,考虑了各决策主体的可靠程度,将模糊推理引入PROMETHE方法,对方案进行优先排序。运用Matlab的模糊推理系统工具箱构建模糊规则模型,计算每两对方案的差别度,采用模糊语言评价代替优先函数的选择,得到各方案在不同属性下的优先指数,并根据综合优序级别值对各备选方案进行排序,获得最优方案。最后通过一个工程案例进行计算和分析,证明了该方法对工程方案优选问题具有良好的实践价值。

区间二型模糊语言Z-numbers及其应用

针对区间二型模糊多属性群决策问题,提出了以区间二型模糊语言Z-numbers(IT2FLZNs)为信息环境的群决策方法。首先,在区间二型模糊集和Z-numbers理论基础上提出了区间二型模糊语言Znumbers并定义了其相关运算性质,提出了两个区间二型模糊语言Z-numbers之间的相似度与距离;其次,在专家和属性权重都未知的情况下,根据决策中总体不确定性最小原则,利用相似度构建最优化模型,确定专家和属性的权重,并且通过综合比较各方案的群体效用值、个体遗憾值和亲密度来选择最优方案;最后,通过一个银行流动风险的实例验证所提方法的有效性与可行性。

基于Z-numbers的城市内涝灾害应急能力评价研究

为降低城市内涝灾害应急能力评估过程中评价信息模糊性对评估结果的影响,提出1种基于Z-numbers的城市内涝灾害应急能力评价方法。对城市内涝灾害形成机理进行分析,从定性与定量相结合的角度建立评价体系;针对群决策过程中的信息不确定性问题,采用语言术语集表达评价信息;提出基于Z-numbers最优最劣方法(ZBWM)确定指标权重,并利用Z-numbers改进的交互式多指标决策方法(ZTODIM)计算备选方案的优势度;通过与传统决策方法进行对比分析,验证其灵活性和可靠性。结果表明:运用该方法可对重庆、武汉、常德和萍乡4座城市的内涝灾害应急能力展开有效评价,为今后改善城市内涝灾害应急能力提供参考。

基于Z-numbers方法的仓单质押融资风险评估研究

为提高仓单质押融资业务中物流金融风险定量评价的精度,文中通过整体业务模式的分析,从融资企业、物流企业、质押物、银行操作和法律风险建立5个风险评价指标体系,将Z-numbers方法和模糊理论进行有效地结合,建立基于Z-numbers的仓单质押融资风险定量评价方法,用于整体风险度量,最后进行实例分析,说明该方法的具体应用。研究结果表明,采用该方法可以有效提高风险评估的客观性和分析的精度,为仓单质押融资风险评估提供理论与实践支持。

区间直觉语言型Z-Numbers及其在多属性决策中的应用

文章首先提出了2个新的尺度函数用来度量语言型信息,并基于犹豫不确定语言型Z numbers(HULZNs)给出了区间直觉语言型Z-numbers (IILZNs),其次,基于尺度函数给出IILZNs之间的标准Hamming距离公式,最后将距离公式应用于解决属性权重未知时以IILZNs为信息环境下的多属性决策(MADM)问题.

Application of Operational Approaches to Solving Decision Making Problem Using Z-Numbers

The combination of fuzzy logic tools and multi-criteria decision making has a great relevance in literature. Compared with the classical fuzzy number, Z-number has more ability to describe the human knowledge. It can describe both restraint and reliability. Prof. L. Zadeh introduced the concept of Z-numbers to describe the uncertain information which is a more generalized notion closely related to reliability. Use of Z-information is more adequate and intuitively meaningful for formalizing information of a decision making problem. In this paper, Z-number is applied to solve multi-criteria decision making problem. In this paper, we consider two approaches to decision making with Z-information. The first approach is based on converting the Z-numbers to crisp number to determine the priority weight of each alternative. The second approach is based on Expected utility theory by using Z-numbers. To illustrate a validity of suggested approaches to decision making with Z-information the numerical examples have been used.

基于决策者偏好构造的概率语言型Z-number多属性决策方法

由于决策环境的日益复杂,专家评价信息往往会包含专家偏好,因此有必要对专家偏好进行识别与处理。针对这一情况,提出了基于决策者偏好构造的概率语言型Z-number并应用于多属性决策问题中。首先,针对专家偏好未知的情况,提出了一种基于修正的平均得分距离,由专家评价信息确定专家偏好。然后,依据得到的专家偏好,利用GOWPA算子与最大熵生成概率语言型Z-number。同时,获得专家评价信息的可信度,由专家可信度聚合专家信息并采用TODIM方法对方案进行排序。最后,在国家大力提倡节能减排的背景下,将所提方法应用于国家绿色矿山试点企业的选取上,验证了所提方法的有效性和可行性。

基于Z-number-IBWM-TODIM的应急供应商评估与选择研究

文章针对应急供应商选择过程中评价信息的不完全可靠性及专家背景的多样性问题,提出了一种基于Z-number和IBWM-TODIM方法相结合的评估框架,以此来选择应急供应商。该方法利用Z-number同时描述认知信息的不确定性和可靠性,增强了决策结果的可靠性和合理性;使用解释结构模型ISM确定最优指标和最劣指标,降低BWM方法的主观性,得到了指标权重;通过群体一致性和Z-number中的可靠性信息确定专家权重,使用TODIM方法进行排序,为应急供应商选择提供了更为准确和可靠的决策依据。

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、λ截集和Cλ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.

基于Z-number和改进DS证据理论的风险评估方法

针对任务风险难度量、评估信息不确定性强等问题,提出一种Z-number和改进DS证据理论的风险评估方法。利用Z-number方法描述评估指标,得到各风险等级的初始基本概率分配(basic probability assignment,BPA);基于信度熵和皮尔逊相关系数改进DS证据理论克服悖论问题进行信息融合,确定风险的最终等级;接着,基于信息融合结果引入Joussleme距离求解专家可信度。最后,以重装空投任务为例,验证本文所提风险评估方法的合理性,并对比分析不同改进DS证据理论方法得到的结果,验证所提方法的有效性和准确性。

TODIM and TOPSIS with Z-numbers

In this paper, we present an approach that can handle Z-numbers in the context of multi-criteria decision-making problems. The concept of Z-number as an ordered pair Z=(A, B) of fuzzy numbers A and B is used, where A is a linguistic value of a variable of interest and B is a linguistic value of the probability measure of A. As human beings, we communicate with each other by means of natural language using sentences like "the journey from home to university most likely takes about half an hour." The Z-numbers are converted to fuzzy numbers. Then the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. The results obtained show the feasibility of the approach.

基于Z-number和DEMATEL的报废汽车回收产业发展影响因素研究

【目的/意义】科学识别和分析报废汽车回收产业发展的影响因素,对于优化机制推动产业高质量发展具有重要的意义。【设计/方法】首先,通过文献分析从政府、消费者、企业和行业组织的不同视角确定影响报废汽车回收产业发展的15个因素。其次,邀请多位专家评估影响因素之间的直接关系,引入Z-number语言描述专家评价信息的复杂不确定性,采用最大共识法计算专家权重;基于DEMATEL(决策试验与评估实验室)方法计算得到影响因素的中心度和因果度,据此进行影响因素分类和重要性分析。【结论/发现】通过算例验证了所提方法的可行性与合理性,并根据研究结果提出促进报废汽车回收产业发展的对策与措施。

基于GBM算子的不平衡概率语言Z-number多属性群决策

Z-number作为一种有效的信息表达方式,能够很好的描述带有不确定信息的自然语言.但大多数关于Z-number的研究依赖于均匀分布的语言术语集,并且用于聚合Z-number信息的聚合算子很少能够考虑属性之间的关系.提出一种非均匀分布的语言尺度函数,讨论了概率语言Z-number在不平衡语义下的情形,运用定义的新型算子对于概率语言Z-number进行聚合.定义相关运算以及得分函数,构建多目标线性优化模型确定最佳投资比例.通过实例说明了所提出方法的可行性与有效性,并进行了灵敏度分析.