查询词典 fuzzy set

Fuzzy sets and rough sets are means handling on fuzzy and indetermination. Today, fuzzy set theory, and rough set theory are combined in mathematics, and the combination is been adverted more and more by international academy.

二者是处理Fuzzy性和不确定性的数学工具，将二者结合起来研究，近年来越来越受到国际学术界的关注。

Secondly, the author has set up the Factor Set, Factor Weight Set, Evaluation Set and Evaluation Matrix based on the Fuzzy Mathematics, therefore the quantification of expert's experiences is solved. Following the example of product design procedure consisting of designing, collating and checking, the Two-stage Fuzzy Synthetic Evaluation has been established in order to supply the evaluating method of design quality for drawing die-face. After two times of eligible analysis above, the synthetic optimizing design of geometry, material and process can be done with simulation.

以模糊数学为基础，通过确定影响覆盖件拉延模型面设计的因素集、因素权重集、备择集和评判矩阵，解决了专家设计经验知识的量化问题，并建立二级模糊综合评判方法，据此设计、校对、审核等技术人员可以共同对拉延模型面设计质量进行优劣评判和修改；在前面二次分析合格的基础上，利用有限元仿真技术进行几何、材料、工艺多因素综合的优化设计。

To analyze and compare the characters of Fuzzy c-Means clustering and artificial immune network aiNet clustering, conclude that Fuzzy c-Means clustering does not work well if the underlying classes or clusters deviate strongly from hyperspherical structures, aiNet is capable of reducing redundancy, describing data structure, including the shape of clusters by experiments on relatively gathering data set, scattering data set, annular data set and corkscrew data set.

分析比较了模糊C 均值聚类算法FCM 和人工免疫网络aiNet 聚类算法的特性，通过它们对相对集中数据、稀疏分散数据、环状和螺旋分布数据聚类来进行比较，得到当遇到潜在的类或簇背离超球面结构时，FCM 算法表现不佳，而aiNet 可以很好的发现数据的内在特征，减少数据中的冗余、描述数据结构和聚类形状，表现良好的适应性。

It is proved that the upper approximation of such fuzzy rough set in a fuzzy approximation space is just its image derived according to generalized extension principle and binary fuzzy similar relation.

通过对偶方式定义了模糊集的上、下近似算子，给出了模糊粗糙集在相应的模糊关系及模糊集的截集下的表示定理，证明了这种模糊粗糙集关于模糊近似空间的上近似恰为其在二元模糊相似关系下导出的广义扩张原理之下的像。

The membership function can exactly express the fuzzy satisfaction set by considering the vagueness of satisfaction degree of objectives and introducing the membership function for the fuzzy satisfaction sets of system reliability and system cost. The normal distribution and Cauchy distribution of this membership function is modified according to the fuzzy satisfaction sets. By doing this, the multi-objective optimization problem can be converted to a single-objective optimization problem to be solved.

模型充分考虑到目标满意度的模糊性，通过引入系统可靠度与费用的模糊满意集的隶属函数，并根据它们的模糊满意集对其正态分布、柯西分布进行适当修改，使之能够准确表达通常情况下的这两个目标的模糊满意集，最终，把两目标优化问题转化为常规单目标优化问题求解。

Considering about fuzzy relation between fault causeand symptom, commix fuzzy diagnosis module was set up by means of fuzzy synthesize judge.

本系统模仿了专家在诊断过程中正反向混合推理的思维特点，提高了诊断复杂故障的效率。

The main results of this paper are given as follows: In the first chapter , the concept of fuzzy filter is introduced. Some of its properties are investigated. The structure of fuzzy filters is discussed and it is proved that the set of all fuzzy filters of a residuated lattice is a distributive and complete lattice .

本文的主要内容如下：本文的第一章在剩余格中引入了Fuzzy滤子的概念，得到了它的一些特征性质；给出了Fuzzy滤子的结构，证明了剩余格中的Fuzzy滤子之集构成完备的分配格；利用Fuzzy滤子的特有结构，在剩余格中定义了Fuzzy滤子间的两个运算""，""

We introduce the notion of fuzzy-valued continuous function on a compact set K in a metric space, and discuss its properties; On this base, we study the uniformly d∞-convergence of a sequence of fuzzy-valued continuous function on K. We prove that the space of fuzzy-valued continuous functions on K, i.e. C(K, E1), is a complete metric space with respect to the metric D.

引入了定义在某度量空间的紧子集K上的模糊数值连续函数和水平连续函数的概念，讨论了它们的某些性质；在此基础上，研究了K上模糊数值连续函数列的一致d∞-收敛性，证明了K上模糊数值连续函数空间C(K， E1)关于度量 D 构成一个完备的度量空间。

In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved.

在研究模糊向量空间、模糊凸集和模糊凸映射的基础上，我们研究了模糊规划的Lagrange对偶和凸模糊规划的KKT条件，并将有关结果应用到模糊线性规划和模糊二次规划的研究中。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。