On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

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.

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。

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.

Fuzzy-Val模糊值Choquet积分(Ⅱ)——函数关于模糊值模糊测度的Choquet积分(英文)

研究一种取值于模糊数集的 Choquet积分 ,该积分的被积函数是单值函数 ,所用的测度是模糊值模糊测度。给出其定义。

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies,selecting the optimal green supplier is one of the crucial issues for enterprises,and multi-criteria decision-making(MCDM)methodologies can more easily solve this green supplier selection(GSS)problem.In addition,prioritized aggregation(PA)operator can focus on the prioritization relationship over the criteria,Choquet integral(CI)operator can fully take account of the importance of criteria and the interactions among them,and Bonferroni mean(BM)operator can capture the interrelationships of criteria.However,most existing researches cannot simultaneously consider the interactions,interrelationships and prioritizations over the criteria,which are involved in the GSS process.Moreover,the interval type-2 fuzzy set(IT2FS)is a more effective tool to represent the fuzziness.Therefore,based on the advantages of PA,CI,BM and IT2FS,in this paper,the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with fuzzy measure and generalized prioritized measure are proposed,and some properties are discussed.Then,a novel MCDM approach for GSS based upon the presented operators is developed,and detailed decision steps are given.Finally,the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods.The advantages of the proposed method are that it can consider interactions,interrelationships and prioritizations over the criteria simultaneously.

A Choquet integral-based TODIM method for q-rung trapezoidal fuzzy numbers and its application in group decision-making

Purpose–The purpose of this paper is to develop a multi-attribute group decision-making(MAGDM)method under the q-rung orthopair trapezoidal fuzzy environment,which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral(q-ROTrFACI)and employ TODIM(an acronym in Portuguese of Interactive and Multi-criteria Decision Making)to consider the risk psychology of decision-makers,to determine the optimal ranking of alternatives.Design/methodology/approach–In MAGDM,q-rung orthopair trapezoidal fuzzy numbers(q-ROTrFNs)are efficient to indicate the quantitative vagueness of decision-makers.The q-ROTrFACI operator is defined and some properties are proved.Then,a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function.Based on the above,a Choquet integral-based TODIM(CI-TODIM)method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.Findings–The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria.Then,an approach is proposed to determine the center point of q–ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed.Furthermore,CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context.The illustration example of business models’solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.Originality/value–Thepaperdevelops a novelCI-TODIMmethodthat effectivelysolves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers,which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

Multi-attribute group decision-making method with linguistic q-rung orthopair fuzzy information based on bi-direction Choquet integral

Purpose-The purpose of this paper is to develop the linguistic q-rung orthopair fuzzy set(LqROFS)information VIKOR method based on the bi-direction Choquet integral(BDCI),taking into account the correlation between information.The method can enrich the existing studies related to LqROFS information and better solve the problem of MAGDM problem.Design/methodology/approach-Since applying Choquet integral(CI)depict information interaction is a common operation in MAGDM.However,the traditional CI has some limitations.The unidirectional alignment may affect the MAGDM results.Therefore,a LqROFS-VIKOR method based on BDCI is proposed,where BDCI is used to aggregate the decision matrix.Furthermore,it is not reasonable to apply exact numbers to express the similarity between two qualitative data.Then a new method of defining similarity using linguistics is proposed.The similarity is used to calculate attribute weights.Findings-The validity and potential application of MAGMD method with linguistic q-rung orthopair fuzzy information based on BDCI are demonstrated in a numerical examples study.Originality/value-According to the study of available literature,the current research on LqROFS is incomplete.The existing studies of both similarity and aggregate operators have certain shortcomings.The definition of similarity proposed in this paper is more in line with reality.And compared with the existing methods,the BDCI-based aggregate operator can describe the interaction between information more reasonably.Based on this VIKOR method based on BDCI under the LqROFS environment can better select the alternative.

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。

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。

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。

Diagnosis of lumbar degenerative disc disease by using L^(p)-spaces related to generalized interval-valued m-polar neutrosophic choquet integral Operator

Innovative and astonishing developments in the field of spine analysis can commence with this manuscript.The lumbar disks(L1−L2 to L5−S1)are most commonly impaired by degeneration due to their long-standing degeneration and associated strain.We investigate the indications,purposes,risk factors,and therapies of lumbar degenerated disc disease(L-DDD).We assume that the degeneration of five discs creates many effects,making it difficult to differentiate between the different types of degenerated discs and their seriousness.Since the indeterminacy and falsity portions of science or clinical diagnosis are often ignored.Due to this complexity,the reliability of the patient’s progress report cannot be calculated,nor can the period of therapy be measured.The revolutionary concept of interval-valued m-polar neutrosophic Choquet integral aggregation operator(IVmPNCIAO)is proposed to eliminate these problems.We associate generalized interval-valued m-polar neutrosophic Choquet integral aggregation operator(GIVmPNCIAO)with the statistical formulation of L^(p)-spaces and use it to identify the actual kind of degenerative disc in the lumbar spine.For the classification of interval-valued m-polar neutrosophic numbers(IVMPNNs),we set the ranking index and score function.These concepts are appropriate and necessary in order to better diagnose degeneration by associating it with mathematical modeling.We construct a pre-diagnosis map based on the fuzzy interval[0,1]to classify the types of degenerative discs.We develop an algorithm by using GIVmPNCIAO based on interval-valued m-polar neutrosophic sets(IVMPNNs)to identify the degenerative disc appropriately and to choose the most exquisite treatment for the corresponding degeneration of every patient.Furthermore,we discuss the sensitivity analysis with parameter p in GIVmPNCIAO to investigate the patient’s improvement record.

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。

具有Choquet积分形式的模糊合作对策

结合模糊数的限制运算,探讨了一类具有模糊支付的模糊合作对策——Choquet积分形式的模糊合作对策,研究了其单调性和连续性。具有模糊支付的模糊合作对策是凸模糊合作对策时,研究了Choquet积分形式的模糊合作对策的模糊核心和模糊Shapley值,并探讨了两者之间的关系,有趣的是这种关系与经典情形相一致。需要指出的是,所给有关模糊合作对策的定义都是对经典情形的推广。最后通过一个算例来说明其应用。

基于语言Choquet积分算子的多属性群决策方法

在现实的多属性群决策问题中,决策属性及专家偏好间均在不同程度上存在相互关联。为此,提出了一种基于语言Choquet积分算子的语言多属性群决策方法。首先,介绍了语言评估标度集上的一些运算法则。基于这些运算法则和模糊测度,定义了一种语言Choquet积分算子。然后,探讨该算子的一些性质,给出了一种基于语言Choquet积分算子的语言多属性群决策途径。研究表明,该算子是语言有序权重平均算子的一般化形式。最后,通过一个具体实例来说明这种方法的具体应用及计算过程。

直觉正态模糊数Choquet积分算子及其决策应用

针对属性间存在关联且属性值为直觉正态模糊数的多属性决策问题,利用模糊测度λ,在直觉正态模糊数运算的基础上,构建了直觉正态模糊数Choquet积分平均(INFCA)算子和直觉正态模糊数Choquet积分几何(INFCG)算子,并探讨了这些算子的性质和特殊形式。通过构建线性规划模型,提出了一种确定各属性子集模糊测度λ的方法,进而给出了基于直觉正态模糊数Choquet积分(INFC)算子的多属性决策方法(MADM)。最后,通过实例验证了方法的可行性和有效性。

基于Choquet延拓n人模糊对策的Shapley值

由于n人对策任意联盟可由它的特征向量来等价地表示,利用Choquet积分,将n人对策从集合{0,1}n延拓到[0,1]n上,通过建立公理化体系,对具有Choquet延拓形式n人模糊对策的Shapley值进行深入研究,证明了这类n人模糊对策Shapley值存在性与惟一性,并给出了此模糊对策Shapley值的解释表达式.最后将此模糊对策的Shapley值作为收益分配方案应用到供应链协作企业收益分配的实例中.