Monotone Set-Valued Function Defined by Set-Valued Choquet Integral

Structural characteristics and absolute continuities of monotone set-valued function defined by set-valued Choquet integral are discussed. Similar to the single-valued monotone set function,several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions,such as null-additivity,weakly null-additivity,order continuity,strong order continuity and property(S). A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function,and all been proven valid with respect to the original set functions.

基于Choquet模糊积分的煤矿安全投入经济效益评价

为提高煤矿企业的经济效益,合理安排各项安全投入,构建一种解决指标间相关性的模型。首先,剖析基于安全投入的经济效益的影响因素,在此基础上构建一套较为科学合理的结构指标体系;其次,利用熵权法确定各个指标的权重;然后,针对指标之间存在的相关性,基于安全投入结构,引入熵权-基于2-可加模糊测度的Choquet模糊积分模型,计算经济效益评价值;最后,选取某煤矿进行实证分析,验证所构建模型的可行性和有效性。结果表明:所构建的模型比逼近理想解排序(TOPSIS)法更具有可靠性;该模型考虑指标之间相互影响、相互关联情况,能够得到较为准确、科学的评价结果。

Emotional inference by means of Choquet integral and λ-fuzzy measurement in consideration of ambiguity of human mentality

Research on human emotions has started to address psychological aspects of human nature and has advanced to the point of designing various models that represent them quantitatively and systematically. Based on the findings, a method is suggested for emotional space formation and emotional inference that enhance the quality and maximize the reality of emotion-based personalized services. In consideration of the subjective tendencies of individuals, AHP was adopted for the quantitative evaluation of human emotions, based on which an emotional space remodeling method is suggested in reference to the emotional model of Thayer and Plutchik, which takes into account personal emotions. In addition, Sugeno fuzzy inference, fuzzy measures, and Choquet integral were adopted for emotional inference in the remodeled personalized emotional space model. Its performance was evaluated through an experiment. Fourteen cases were analyzed with 4.0 and higher evaluation value of emotions inferred, for the evaluation of emotional similarity, through the case studies of 17 kinds of emotional inference methods. Matching results per inference method in ten cases accounting for 71% are confirmed. It is also found that the remaining two cases are inferred as adjoining emotion in the same section. In this manner, the similarity of inference results is verified.

Supplier Evaluation Model Based on Fuzzy Measures and Choquet Integral

To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation criteria pair are obtained by using the diamond pairwise comparison method.Based on comparison results,the maximum eigenvector method of analytic hierarchy process (AHP),the hierarchical clustering method,and the phi(s) transformation are utilized to generate values of the fuzzy measure for each subset of the evaluation criterion set.Overall evaluation on each supplier is aggregated by Choquet integral with respect to the fuzzy measure.Finally,an illustrative example demonstrates the practical feasibility and validity of the proposed method.

Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application

We first propose the normal Pythagorean neutrosophic set(NPNS)in this paper,which synthesizes the distribution of the incompleteness,indeterminacy,and inconsistency of the Pythagorean neutrosophic set(PNS)and normal fuzzy number.We also define some properties of NPNS.For solving the decision-making problem of the nonstrictly independent and interacting attributes,two kinds of NPNS Choquet integral operators are proposed.First,the NPNS Choquet integral average(NPNSCIA)operator and the NPNS Choquet integral geometric(NPNSCIG)operator are proposed.Then,their calculating formulas are derived,their properties are discussed,and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied.Finally,the two kinds of operators are applied to validate the stability of the new method.

Some General Inequalities for Choquet Integral

With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.

Monotone Measures Defined by Pan-Integral

Given a pan-space ?and a nonnegative measurable function f on measurable space (X, A), the pan-integral of f with respect to monotone measure μ and pan-operation ?determines a new monotone measure ?on?(X, A). Such the new monotone measure ?is absolutely continuous with respect to the monotone measure μ. We show that the new monotone measure preserves some important structural characteristics of the original monotone measures, such as continuity from below, subadditivity, null-additivity, weak null-additivity and (S) property. Since the pan-integral based on a pair of pan-operations ?covers the Sugeno integral (based on ) and the Shilkret integral (based on ), therefore, the previous related results for the Sugeno integral are covered by the results presented here, in the meantime, some special results related the Shilkret integral are also obtained.

基于Choquet积分法的施工项目劳动力与工期优化探索

建筑行业劳动力短缺,探究和理解工期、劳动力成本以及劳动力利用率三个变量的交互与权衡,对于项目做出准确决策,按时交付有重要的作用。本文以在建住宅楼项目为案例,根据不同施工场景构建了75种劳动力分配方案,并采用Takt-time计划法完善施工流程;同时基于Arena模拟平台建立施工流程仿真模型,分析每种劳动力组合方案所需3种变量的数据;最后,使用基于Choquet积分的效用评估与决策工具,研究基于不同项目管理人员的主观偏好下3个变量的交互与权衡。结果表明,本文所提出的方法有效解决了施工过程中的工序搭接混乱、工作面重叠等问题,表现出不同劳动力组合下3个变量的变化情况,并能评估不同劳动力组合在项目施工中的效用,帮助项目做出最满意的劳动力分配方案。

基于Choquet模糊积分SVM集成的企业信用评估模型

针对Bagging算法下基于模糊积分的SVM集成方法在企业信用评估应用中存在的不足,提出一种基于改进模糊密度-Choquet模糊积分SVM集成的企业信用评估模型。该模型借鉴Boosting算法“注重”错分样本的基本思想,考虑SVM基分类器的总体错分程度,重新定义SVM基分类器的模糊密度,实现对模糊密度的改进;在此基础上,采用Choquet模糊积分作为SVM基分类器的结合方法,从而将基于Choquet模糊积分的SVM集成方法引入到企业信用评估中。实证结果表明,与传统方法相比,该模型的预测准确率更高,第一类错误率和第二类错误率更低;精确率、召回率、F1值和Macro-F1值等分类性能指标也明显占优,说明了该模型的可行性和有效性。

产教融合视域下基于Choquet积分的应用型本科院校实践基地选择

对实践基地选择的多属性决策问题,提出一种基于Choquet积分的选择方法。首先,围绕应用型本科院校实践教学的人才培养目标和产教融合要求,构建实践基地选择的评价指标体系;进一步,建立基于Choquet积分的实践基地选择模型,有效解决评价指标间的关联问题;最后,通过实例说明该方法的有效性和合理性。

考虑耦合作用的电网业务组合投资优化

电网业务正处于传统业务向新兴业务变革的关键时期,由于电网业务发展的多样性,应考虑业务的相互影响,准确量化业务投资价值。分析业务间耦合作用,构建业务耦合作用评价体系,并通过Choquet模糊积分量化了电网业务耦合程度,构建适应未来发展新环境的电网业务投资价值评价体系,构建了考虑耦合作用的电网业务组合投资优化模型。在算例中,包含综合能源业务、储能业务、电动汽车业务的组合投资价值最高,为2.024,其中,业务基础投资价值为1.870,耦合投资价值为0.154。通过算例分析验证了考虑电网业务耦合作用的必要性与投资优化模型的适用性,支撑电网公司制定电网业务组合投资决策。

Application of Choquet Integral-Importance-Performance Analysis and TOPSIS Methods in Approaching the Preference Factors of Calligraphy and Seal Engraving Imagery

Classical Chinese characters,presented through calligraphy,seal engraving,or painting,can exhibit different aesthetics and essences of Chinese characters,making them the most important asset of the Chinese people.Calligraphy and seal engraving,as two closely related systems in traditional Chinese art,have developed through the ages.Due to changes in lifestyle and advancements in modern technology,their original functions of daily writing and verification have gradually diminished.Instead,they have increasingly played a significant role in commercial art.This study utilizes the Evaluation Grid Method(EGM)and the Analytic Hierarchy Process(AHP)to research the key preference factors in the application of calligraphy and seal engraving imagery.Different from the traditional 5-point equal interval semantic questionnaire,this study employs a non-equal interval semantic questionnaire with a golden ratio scale,distinguishing the importance ratio of adjacent semantic meanings and highlighting the weighted emphasis on visual aesthetics.Additionally,the study uses Importance-Performance Analysis(IPA)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)to obtain the key preference sequence of calligraphy and seal engraving culture.Plus,the Choquet integral comprehensive evaluation is used as a reference for IPA comparison.It is hoped that this study can provide cultural imagery references and research methods,injecting further creativity into industrial design.

基于Choquet模糊积分的决策层信息融合目标识别

引入模糊测度和 Choquet模糊积分的概念后,信息融合目标识别可转化为各信源识别结果关于信源重要程度的广义 Lebesgue积分。该文给出了 Choquet模糊积分应用于决策层信息融合目标识别的通用技术路线,并提供了信源重要程度的度量方法。算法实用于红外/毫米波融合目标识别系统,融合识别结果与 D-S 证据理论方法作了比较,证明了基于 Choquet模糊积分方法的有效性。

基于Choquet模糊积分的运动目标检测算法

本文提出了一种基于Choquet模糊积分的运动目标检测算法(CIMOD,Choquet Integrate-Based Moving Ob-ject Detection).将模糊测度和模糊积分理论应用于运动目标与背景分类中,提出了自适应阈值的Choquet积分算法,实现了图像的颜色特征和纹理特征相融合;选择YCbCr颜色空间代替传统RGB空间,将图像亮度与色度分离,降低了光照变化对运动检测的影响;利用局部二元模式(LBP,Local Binary Pattern)纹理特征对亮度级的单调变化具有不变性的特点,将其融合到检测算法中,有效抑制了阴影的干扰.仿真实验结果表明,即使在光照变化、阴影干扰等复杂背景情况下,该算法也能够准确的检测出运动区域.

基于Choquet积分的综合风险测评方法

针对多个风险之间存在关联情形的综合风险测评问题,提出了一种基于Choquet积分的风险测评方法.首先引入了Choquet积分的相关概念及其计算公式;然后,在描述风险之间存在关联情形的综合风险测评问题的基础上,给出了有关风险损失和风险发生概率以及每个风险值的计算公式,进一步地,给出了基于Choquet积分的综合风险测评计算公式.最后,通过一个实例说明了给出方法的实用性和有效性.

基于Choquet模糊积分的非线性组合预测及其应用

预测模型有多种,各种预测模型有其特点和优势,我们需要建立一种博采众长的组合预测模型。本文利用Choquet模糊积分作为组合算子,给出一种基于模糊积分的非线性组合预测模型,该模型既能反映各种预测模型的“重要性”,又能反映各个预测模型之间的交互作用,并用此模型给出中国卫生总费用的预测。

基于模糊Choquet积分的图像融合效果评价

针对多源图像的融合效果评价问题,提出了一种基于模糊Choquet积分的图像融合效果评价方法。该方法采用融合图像熵值、交叉熵平均值、交叉熵均方根值、平均梯度值构成单因素评价指标集,基于知识确定F测度和各单因素评价指标的隶属度函数,应用Choquet积分综合各单因素指标得到一个综合评价指标。该方法综合利用了多个单因素指标的信息,并将人的知识引入到对图像融合效果的评价中,其评价结果更为全面客观。将该方法应用于CCD/SAR图像的融合效果评价,评价结果与理论分析结果和目视效果是一致的,表明了该评价方法的有效性。

基于Choquet积分与证据理论的产品方案协同评价方法

利用α-截集的模糊评价法对产品方案的各个准则进行评价.考虑到不同评价准则之间具有关联性和非线性组合关系,提出基于Choquet模糊积分的产品方案总体评价合成模型.构建偏好度比较矩阵,采用模糊互补排序算法确定产品方案的优劣排序关系.针对不同领域的评价专家会给出不一致的排序结果,利用改进的证据理论来集结各专家的评价意见并得到相对稳定与协调的方案优劣排序结果.以大型空气分离设备的方案评价与选择作为实例,对该方法进行检验,证实了该方法的可行性与有效性.

基于Choquet积分的区间灰数多属性决策方法

针对多属性决策中属性间的关联性对决策结果的影响,提出了基于区间灰数灰度和Choquet积分的区间灰数多属性决策方法。根据区间灰数灰度的定义,证明了区间灰数的灰度是一种灰测度,由此定义了关于区间灰数灰度的离散Choquet积分并证明其性质;依据各方案的综合属性值的方差最小的原则建立多目标优化模型,确定了各属性或属性集的权重,最后利用Choquet积分对各方案的效果评价向量进行集成。通过实例说明了该方法的有效性。

基于诱导Choquet积分算子的群决策方法

研究了决策者对方案有模糊偏好且偏好间存在相互关联的群决策问题。给出了诱导Choquet积分算子的定义,研究了它的性质;探讨了它与诱导有序权重平均、Choquet积分算子之间的相互关系;利用重要指数诱导Choquet积分和偏好诱导Choquet积分算子,给出了决策者对方案的个人偏好是模糊偏好关系的一种群决策方法。最后,通过实例说明这种方法的具体应用及计算过程。