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双语推荐：广义模糊滤子

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给出了点态化(ε、εVq(λ、μ))-模糊滤子和广义模糊滤子的概念，讨论了两者之间的等价关系；得到了(ε、εVq(λ、μ))-模糊滤子的若干等价刻画，并研究了其相关性质；讨论了(ε、εVq(λ、μ))-模糊滤子的同态像与同态原像的基本性质；最后研究了(ε、εVq(λ、μ))-模糊滤子的直积。
Firstly, this paper introduces the concepts of the pointwise (ε、εVq(λ、μ))-fuzzy filter and generalized fuzzy filter, and discusses the relationship between them. Secondly, this paper obtains some equivalent descriptions of the (ε、εVq(λ、μ))-fuzzy filter, and studies the related properties. Thirdly, this paper discusses some basic properties of homomorphic image and homomorphic preimage of the (ε、εVq(λ、μ))-fuzzy filter. Finally, this paper studies the direct product of the (ε、εVq(λ、μ))-fuzzy filter.

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作者讨论了广义梯形模糊数和它的重心之间的关系。一方面，通过一个已知广义梯形模糊数，利用公式可以确定出它的重心；另一方面，如果已知一个广义梯形模糊数的重心、宽度和左右扩张，则可以确定出这个广义梯形模糊数，并赋予相应的例子。
In this paper we discuss the relation between a generalized trapezoidal fuzzy numbers and its centroid.On the one hand,the centroid of a known generalized trapezoidal fuzzy numbers can be deter-mined by the centroid formulae;On the other hand,if the centroid,the width and the left/right spread of an unknown generalized trapezoidal fuzzy numbers are given,we can find this fuzzy numbers and some examples are given.

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模糊粗糙集是目前数据挖掘领域关注的热点之一,作者在Pawlak粗糙集模型基础上,把一个论域推广为两个论域;把等价关系推广为模糊关系,被近似对象换成模糊集,得到广义模糊粗糙集模型,建立了广义模糊近似空间。在广义模糊近似空间中定义了广义模糊粗糙集上的包含度和相似度,并讨论了此包含度和相似度相关性质。
Fuzzy rough set is the hot point of data mining ifeld nowadays. The paper obtains generalized fuzzy rough set model by expanding one domain to two domains, equation relation to fuzzy relation, approximate object to fuzzy set, sets up generalized fuzzy approximate space, deifnes inclusion and similarity degree and discusses their related properties.

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研究了时序广义双极值模糊环境下的群决策问题。针对实际问题中广义双极值模糊软集信息随时间动态变化的情形，定义了时序广义双极值模糊软集的概念，并讨论了相关运算及性质。考虑不同时刻广义双极值模糊软集信息对最终决策的不同影响，利用指数衰减模型的权重确定公式和集成思想，定义广义双极值模糊软集间的运算并给出几何加权平均算子的计算公式，将时序广义双极值模糊软集集成综合双极值模糊软集。然后，利用广义双极值模糊软集的集成算子计算各方案的属性值，利用得分函数得出最优决策。最后，通过实例分析证明了此决策方法的合理性与可行性。
Group decision-making problems based on time -series generalized bipolar -valued fuzzy soft set environment were investigated .For the situation that generalized bipolar -value fuzzy soft sets information dy-namic changes as time the concept of time -series generalized bipolar -value fuzzy soft sets was defined , and relative operations and properties were discussed , too.Considering generalized bipolar -value fuzzy soft sets in-formation of different time has different effect on final decision , the weight determination formulas were deter-mined based on the exponential decay model .Then operations of generalized bipolar -value fuzzy soft sets and the computational formula of the arithmetic weighted average operator were given with aggregating thought , and time-series generalized bipolar -value fuzzy soft sets were aggregated into collective generalized bipolar -value fuzzy soft sets.Then, the attribute values of every alternative were aggregated with the operator of genera

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在犹豫模糊环境下，主要研究了基于阿基米德范数的广义信息集成算法，并提出了一种新的多属性群决策方法。基于阿基米德T-范数和S-范数，定义了广义犹豫模糊运算法则；运用新定义的广义犹豫模糊运算法则，提出了广义犹豫模糊有序加权平均（G-HFOWA）算子，研究了其优良性质；探讨了在某些特殊情况下，广义犹豫模糊有序加权平均算子将转化为一些常见的犹豫模糊信息集成算子，包括犹豫模糊有序加权平均算子、犹豫模糊Einstein有序加权平均算子、犹豫模糊Hamacher有序加权平均算子以及犹豫模糊Frank有序加权平均算子；基于广义信息集成算子，构建了一种新的犹豫模糊多属性群决策方法，并将其应用于区域经济协调发展研究过程中，以验证提出的决策方法是可行的与有效的。
Based on the Archimedean t-norm and s-norm, the generalized hesitant fuzzy information aggregation operator is proposed under hesitant fuzzy environment, and a new method for multi-attribute group decision making is developed. The generalized hesitant fuzzy operational laws are defined, which is based on the Archimedean t-norm and s-norm. The generalized hesitant fuzzy ordered weighted averaging operator is proposed, and then discusses some of its desirable properties in detail. Discuss in some special circumstances, the generalized hesitant fuzzy ordered weighted averaging operator will be convert into some common hesitant fuzzy information aggregation operators, such as hesitant fuzzy ordered weighted averaging operator, hesitant fuzzy Einstein ordered weighted averaging operator, hesitant fuzzy Hamacher ordered weighted averaging operator and hesitant fuzzy Frank ordered weighted averaging operator. A new approach to hesitant fuzzy multi-attribute group decision making is

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凸集及其性质是最优化领域的一个重要研究课题.同样,凸模糊集也是模糊数学中研究的一个热点.本文通过将E-广义凸模糊集、凹模糊集和凸直觉模糊集相结合,定义了E-广义凹模糊集和E-广义凸直觉模糊集,并根据定义对它们的基本性质做了研究,从而推广了凸模糊集和反凸模糊集,并且引出一个相对较新的研究方向和领域.
The convex set and its properties are important research topics in the area of optimization .Sim-ilarly, the convex fuzzy set is a hot spot in fuzzy mathematics .The definitions of E-generalized concave fuzzy set and E-generalized convex intuitionistc fuzzy set were given by combining with E -generalized convex fuzzy set.Concave fuzzy set and convex intuitionistc fuzzy set in the related references , and some fundamental proper-ties of E-generalized concave fuzzy set and E -generalized convex intuitionistc fuzzy set were discussed in this paper, which expands the E -generalized convex fuzzy set and leads to a relatively new research direction and field.

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针对广义模糊熵图像阈值分割中参数的选取问题,采用两种算法实现自适应选取参数的广义模糊图像熵阈值分割。其中,算法二依据均匀性测度,通过遗传优化算法对参数m在(0,1)区间进行全局寻优,并以广义模糊熵为目标函数,通过粒子群优化算法,对S型隶属度函数中的参数进行全局组合寻优,从而实现广义模糊熵图像阈值分割方法的自动阈值选取。实验结果表明了算法二的有效性。
For the problem of parameter selection in generalised fuzzy entropy-based image threshold segmentation,we use the idea of combining and nesting two optimisation algorithms to implement the threshold segmentation of generalised fuzzy image entropy with the parameters adaptively selected.In Algorithm 2,according to uniformity measurement,it carries out global optimisation on parameter m within the interval (0,1 )through genetic optimisation,and takes the generalised fuzzy entropy as the objective function to carry out combinational global optimisation on the parameters in S-type membership function through particle swarm optimisation,thereby realises the automatic threshold selection in generalised fuzzy entropy-based image threshold segmentation approach.Experimental result illustrates the validity of Algorithm 2.

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在模糊时间序列模型的构架中,介绍了广义模糊时间序列模型建立过程和常用的模糊区间划分方法,提出了基于均匀划分、模糊C均值聚类和自动聚类3种模糊区间划分方法的广义模糊时间序列模型,并用Alabama大学入学人数和沪市股指两组数据对模型进行了详细的分析.实验结果不仅揭示了这3种方法对模型预测结果的影响,还证明了广义模型优于传统模型.
In the framework of fuzzy time series model ,the generalized fuzzy time series model and some methods for partitioning fuzzy interval are presented and summarized . Secondly , three generalized fuzzy time series models on the basis of average partition ,fuzzy C-mean (FCM ) clustering and automatic clustering techniques are presented .Enrollment of the University of Alabama and the close prices of Shanghai Stock Exchange Composite Index (SSECI) are served as the training data sets for the proposed models .The empirical analyses not only reveal the impact of three partition methods on the forecast results , but also show that the generalized model outperforms the conventional counterparts .

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基于广义模糊软集在处理不确定性问题中的应用，本文对已有的广义模糊软集的贴近度进行了修正，并将其应用于医疗诊断问题中。通过比较得到，修正的贴近度更合理，因而有更好的适用性。
Based on the extensive application of similarity measure for generalized fuzzy soft sets the simi-larity measure defined for generalized fuzzy soft sets was improved and applied to the medical diagnosis .By anal-ysis, it is found that the improved similarity measure is more available and reasonable .

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基于广义区间梯形模糊数的重心计算、广义区间梯形模糊集的有权算术集成算子和混合集成算子，建立一种新模型来处理大学生素质评价问题。算例结果显示该模型处理大学生素质评价问题是有效的。
Based on the calculating about the center of gravity (COG) point of generalized interval-valued trapezoidal fuzzy numbers ,the generalized interval-valued trapezoidal fuzzy sets''arithmetic weighted aggregation operator (IT-WA) and the generalized interval-valued trapezoidal fuzzy sets''hybrid aggregation operator (ITHA) ,a new model to deal with the college students''quality education evaluation problem is establisted .The example results show that the model is effective to deal with the college students''quality education evaluation .

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