Fuzzy级数(Ⅱ)

Based on the paper "Fuzzy Series (Ⅰ)" (Fuzzy Mathematics, 1984, No 4.), the concept of the fuzzy series of positive terms is presented, the fuzzy double series is defined and the properties concerned are discussed in this paper. We have worked out a matrix: Where is a fuzzy set in the real numbdr field R of which the membership function is not constantly a zero. Definition 1. A fuzzy double series is convergent     

Research on Fuzzy Synthetic Evaluation of Stamping Process Scheme

Stamping process,which is widely used in automobile,aerospace,machine-building industries,and etc.,is a creative process needing time and experiences.The lead time is mainly spent on stamping die design and manufacturing.As the ba- sis of die design,process design is a non-linearity and creative process,which can be solved by using the fuzzy synthetic evaluation. In this paper,the potential o f fuzzy synthetic evaluation for dealing with stamping process design was explored.The influencing factor set,factor weight set,evaluation set,single factor fuzzy evaluation matrix,and fuzzy synthetic evaluation scheme were studied.Finally,the washer part,considering forming equipment,part dimensions and other factors,was selected to testify the evaluation process.     

Generation and Display System of Measurement Matrix Based on DMD

A measurement matrix is the key to sampling and signal reconstruction during the process of compressed sensing. On the basis of digital light processing (DLP) technology, a generation and display system of measurement matrix based on digital micro-mirror device (DMD) is proposed and well designed. In this system, the generation and controlling of measurement matrix are implemented on a PC, which reduces the hardware requirement to generate a random matrix and overcomes the difficulty of the hardware implementation for the random matrix. It can set up the display number of the measurement matrix, the mode of display and display time according to the requirements from users. The display information can be designed to complete the display of measurement matrix with a better adaptability. The system can be easily embedded into a variety of compressed sensing applications, which can be used to generate and display the corresponding measurement matrice with strong portability. In addition, the DMD of this system will be used as a spatial optical modulator to manipulate near-infrared light in a fast, accurate and efficient way in several applications such as in 3D scanning devices and spectrometers.     

Fuzzy拓扑线性空间的局部P凸性与赋拟P范

In this paper, the fuzzy topological linear space is expressed as ftls., P∈(0,1]. Definition 1. Let X be alinear space. For every X_λ∈X(X is the classical set of all fuzzy points on X) there is a real number ||x_λ||p≥0, which, corres-     

Mercer Kernel Based Fuzzy Clustering Self-Adaptive Algorithm

A novel mercer kernel based fuzzy clustering self-adaptive algorithm is presented. The mercer kernel method is introduced to the fuzzy c-means clustering. It may map implicitly the input data into the high-dimensional feature space through the nonlinear transformation. Among other fuzzy c-means and its variants, the number of clusters is first determined. A self-adaptive algorithm is proposed. The number of clusters, which is not given in advance, can be gotten automatically by a validity measure function. Finally, experiments are given to show better performance with the method of kernel based fuzzy c-means self-adaptive algorithm.     

L—U Fuzzy目标规划

We give a fuzzy goal programming (L-UFGP).Definition 1 Let X(?)E_n,A is called a generalized fuzzy set on E_n with respect toX iff (?)(x)∈[0,1] for x∈X and (?)(x)∈E_1 for x∈E_n\X.Definition 2 Let i∈(1,...,p),R(?)E_n,(?)={x∈R|l_i≤f_i(x)≤u_i} and (?)(f_i(x)) be ageneralized fuzzy set on E_n with respect to (?),(?) is called a fuzzy goal set of f_i(x)iff (?)(y) is a strictly increasing function on E_(?) and (?)(l_i)=0,(?)(u_i)=1.Here l_i iscalled a lower goal of f_i(x) and u_i is called an upper goal of f_i(x).     

Ranking Method for Complementary Judgment Matrixes with Fuzzy Numbers Based on Hausdorff Metric Distance

A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.     

A fuzzy method to learn text classifier from labeled and unlabeled examples

In text classification, labeling documents is a tedious and costly task, as it would consume a lot of expert time. On the other hand, it usually is easier to obtain a lot of unlabeled documents, with the help of some tools like Digital Library, Crawler Programs, and Searching Engine. To learn text classifier from labeled and unlabeled examples, a novel fuzzy method is proposed. Firstly, a Seeded Fuzzy c-means Clustering algorithm is proposed to learn fuzzy clusters from a set of labeled and unlabeled examples. Secondly, based on the resulting fuzzy clusters, some examples with high confidence are selected to construct training data set. Finally,the constructed training data set is used to train Fuzzy Support Vector Machine, and get text classifier. Empirical results on two benchmark datasets indicate that, by incorporating unlabeled examples into learning process,the method performs significantly better than FSVM trained with a small number of labeled examples only. Also, the method proposed performs at least as well as the related method-EM with Naieve Bayes. One advantage of the method proposed is that it does not rely on any parametric assumptions about the data as it is usually the case with generative methods widely used in semi-supervised learning.     

Analytical Model and Algorithm of Fuzzy Fault Tree

In the past, the probabilitise of basic events were deseribed as triangular or trapezoidal fuzzy numberthat cannot characterize tile common distribution of the primary events in cogineering and thc fault tree mlalyzcd by fuzzy set theory did not include repeated basic events. This paper presents a new method to analyze the fault tree by using normal fuzy number to describc the fuzy probability or cach basic which is more suitably used to analyzc the reliability in safety systcns,and then the formulae of computing the fuzzy probability of the top cvent of the fault trce which includes repeaed cvents are derivcd,Finally,an example is givcn.     

A neurofuzzy system based on rough set theory and genetic algorithm

This paper presents a hybrid soft computing modeling approach for a neurofuzzy system based on rough set theory and the genetic algorithms ( NFRSGA ). The fundamental problem of a neurofuzzy system is that when the input dimension increases, the fuzzy rule base increases exponentially. This leads to a huge infrastructure network which results in slow convergence. To solve this problem, rough set theory is used to obtain the reductive rules, which are used as fuzzy rules of the fuzzy system. The number of rules decrease, and each rule does not need all the conditional attribute values. This results in a reduced, or not fully connected, neural network. The structure of the neural network is relatively small and thus the weights to be trained decrease. The genetic algorithm is used to search the optimal discretization of the continuous attributes. The NFRSGA approach has been applied in the practical application of building a soft sensor model for estimating the freezing point of the light diesel fuel in a Fluid Catalytic Cracking Unit (FCCU) , and satisfying results are obtained.     

Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints： A Credibility Approach

A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure.     

(QL)型Fuzzy拓扑线性空间的乘积和商空间(英文)

In this paper, we have got some properties of product and quotient spaces of fuzzy topologioal vector spaces of type (QL) (cf. Wu Congxin, Fang Jinxuan, Annals of Math., 6A (1985), 3: 355-364), whereby we work out a representation theorem of locally ccnvex spaces. Fuzzy topological vector space is short for FTVS in the following text. Lemma 1. Let (X,T) be a FTVS of type (QL) and {‖·‖_d: d∈D} be the family of Lasalle pseudonorms generating T, then the fuzzy net {X_(λα)~((α)): α∈A} converges to x_λiff for each ε>o, o<δ<λand ‖·‖_d, there exists α∈A such that ‖x-x_(λn)~((n))‖_d<ε, λ_n>λ-δwhenever n≥α. Let (X,T) be the product space of a family of FTVSs(X_α,T_α) (a∈A); P_α     

A special hierarchical fuzzy neural-networks based reinforcement learning for multi-variables system

Proposes a reinforcement learning scheme based on a special Hierarchical Fuzzy Neural-Networks （HFNN） for solving complicated learning tasks in a continuous multi-variables environment. The output of the previous layer in the HFNN is no longer used as if-part of the next layer, but used only in then-part. Thus it can deal with the difficulty when the output of the previous layer is meaningless or its meaning is uncertain. The proposed HFNN has a minimal number of fuzzy rules and can successfully solve the problem of rules combination explosion and decrease the quantity of computation and memory requirement. In the learning process, two HFNN with the same structure perform fuzzy action composition and evaluation function approximation simultaneously where the parameters of neural-networks are tuned and updated on line by using gradient descent algorithm. The reinforcement learning method is proved to be correct and feasible by simulation of a double inverted pendulum system.     

On Locating Numbers of Graphs

Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W is said to be a locating set of G if distinct vertices have the distinct locating code,and the locating number of G is defined as: Loc( G) = min{ | W| : W is a locating set of G}.We study the locating set and locating number of a graph G,obtain some bounds for the locating numbers of graphs,and determine the exact value of Loc( G) for some special classes of graphs,such as cycles,wheels,complete t-partite graph and some Cartesian products of paths and cycles. In addition,we also prove that Loc( T) ≥Δ-1 holds for all trees T with maximum degree Δ,and shows a tree T with Loc( T) = Δ-1.     

Number of Negative Entries in A2≤0

Let A be a real matrix or a sign pattern of order n. N-(A) denotes the number of negative entries in A. In 1972 R DeMarr and A Steger conjectured: If A is a real matrix of order n such that A2≤0, then N_(A2)≤(n-1)2 1. Now the conjecture is proved to be true when A is reducible or a matrix of order n≤3 and some sufficient conditions for N_(A2)≤(n-1)2 1 are given. It is also proved that N_(A2)≤n2-4n 5 when A is a reducible combinatorially symmetric sign pattern such that A2≤0, and the extreme sign patterns are characterized.     

Profit Allocation Scheme among Partners in Virtual Enterprises Based on Fuzzy Shapley Values

Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.     

The multi--intersection number of a graph

The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.     

Number of Negative Entries in A2≤0

Let A be a real matrix or a sign pattern of order n. N_ (A) denotes the number of negative entries in A. In 1972 R DeMarr and A Steger conjectured: If A is a real matrix of order n such that A^2≤0, then N- (A^2)≤( n - 1)^2 1. Now the conjecture is proved to be true when A is reducible or a matrix of order n≤3 and some sufficient conditions for N- (A^2)≤(n - 1)^2 1 are given. It is also proved that N_ (A^2)≤n^2 -4n 5 when A is a reducible combinatorially symmetric sign pattern such that A^2≤0, and the extreme sign patterns are characterized.     

Multi-channel fast super-resolution image reconstruction based on matrix observation model

A multi-channel fast super-resolution image reconstruction algorithm based on matrix observation model is proposed in the paper,which consists of three steps to avoid the computational complexity: a single image SR reconstruction step,a registration step and a wavelet-based image fusion. This algorithm decomposes two large matrixes to the tensor product of two little matrixes and uses the natural isomorphism between matrix space and vector space to transform cost function based on matrix-vector products model to matrix form. Furthermore,we prove that the regularization part can be transformed to the matrix formed. The conjugate-gradient method is used to solve this new model. Finally,the wavelet fusion is used to integrate all the registered highresolution images obtained from the single image SR reconstruction step. The proposed algorithm reduces the storage requirement and the calculating complexity,and can be applied to large-dimension low-resolution images.     

Two Hybrid Methods Based on Rough Set Theory for Network Intrusion Detection

In this paper,we propose two intrusion detection methods which combine rough set theory and Fuzzy C-Means for network intrusion detection.The first step consists of feature selection which is based on rough set theory.The next phase is clustering by using Fuzzy C-Means.Rough set theory is an efficient tool for further reducing redundancy.Fuzzy C-Means allows the objects to belong to several clusters simultaneously,with different degrees of membership.To evaluate the performance of the introduced approaches,we apply them to the international Knowledge Discovery and Data mining intrusion detection dataset.In the experimentations,we compare the performance of two rough set theory based hybrid methods for network intrusion detection.Experimental results illustrate that our algorithms are accurate models for handling complex attack patterns in large network.And these two methods can increase the efficiency and reduce the dataset by looking for overlapping categories.