Zadeh模糊集合理论的缺陷及其改进:C*-模糊集合理论

分析和证明了Zadeh模糊集合理论的三个缺点和两个错误,提出了一个考虑模糊集合之间关系,并且用相关系数来刻画这种关系的程度的新模糊集合理论(系统)——C*-模糊集合理论(系统).新理论(系统)能克服Zadeh模糊集合理论的三个缺点和两个错误;能正确地描绘客观世界的全部模糊现象;有补集;隶属度有统一的计算公式;并且是经典集合系统的特例,能满足全部经典集合的公式,与正常思维、逻辑和概念一致.

[0,1]-拓扑空间中模糊网的m-收敛性的非标准刻画

在非标准扩大模型下,以非标准分析的方法研究了[0,1]-拓扑空间中模糊网的m-收敛理论,给出了模糊网m-收敛性的非标准刻画.首先,利用转换原理,定义了*-模糊集合,提出了N-单子和Q-单子的概念.其次,借助这两类单子给出了模糊网的N-收敛性和Q-收敛性的非标准特征.最后,由这些特征得到了模糊网的m-收敛性的非标准刻画,并讨论了模糊Haudorff分离性与模糊网的m-收敛性之间的关系.

Collaborative planning approach for anti-bioterrorism emergency facility location based on aerodynamics

To smooth the correlation process from bio-virus diffusion to emergency relief response,the Gaussian plume model is used to describe the diffusion of dangerous sources,where the bio-virus concentration at any given point in affected areas can be calculated.And the toxic load rule is introduced to define the borderline of the dangerous area at different levels.Combined with this,different emergency levels of different demand points in dangerous areas are confirmed using fuzzy clustering,which allows demand points at the same emergency level to cluster in a group.Some effective emergency relief centers are chosen from the candidate hospitals which are located in different emergency level affected areas by set covering.Bioterrorism experiments which were conducted in Nanjing,Jiangsu province are simulated,and the results indicate that the novel method can be used efficiently by decision makers during an actual anti-bioterrorism relief.

Uncertainty Representation of Ocean Fronts Based on Fuzzy-Rough Set Theory

Analysis of ocean fronts＇ uncertainties indicates that they result from indiscemibility of their spatial position and fuzziness of their intensity. In view of this, a flow hierarchy for uncertainty representation of ocean fronts is proposed on the basis of fuzzy-rough set theory. Firstly, raster scanning and blurring are carried out on an ocean front, and the upper and lower approximate sets, the indiscernible relation in fuzzy-rough theories and related operators in fuzzy set theories are adopted to represent its uncertainties, then they are classified into three sets： with members one hundred percent belonging to the ocean front, belonging to the ocean front＇s edge and definitely not belonging to the ocean front. Finally, the approximate precision and roughness degree are utilized to evaluate the ocean front＇s degree of uncertainties and the precision of the representation. It has been proven that the method is not only capable of representing ocean fronts＇ uncertainties, but also provides a new theory and method for uncertainty representation of other oceanic phenomena.

Criteria Selecting Knowledge Base in the FuzzyController of the Electrohydraulic Position Control System

Aim To analyse the influence of knowledge base on the performance of the fuzzy controller of the electrohydraulic position control system,and to determine their selection cri- teria. Methods Experiments based on different membership functions,scaling factors and con-trol rules were done separately.The experiment results and the influence of different know- ledge base on the control performance were analysed in theory so that criteria of selcting knowledge base can be summarized correctly.Results Knowledge base,including membershipfunctions, scaling factors and control rules,has a crucial effect on the fuzzy control system.Suitably selected knowledge base can lead to good control performance of fuzzy control sys-tem. Conclusion Being symmetric,having an intersection ratio of 1 and satisfying width con- dition are three necessities for selecting membership functions.Selecting scaling factors dependson both the system requirement and a comprehensive analysis in the overshoot,oscillation, rising time and stability. Integrity and continuity must be guaranteed when determining control rules.

Comprehensive Evaluation Model of Reservoir Operation Based on Improved Set Pair Analysis

A comprehensive evaluation model based on improved set pair analysis is established. Considering the complexity in decision-making process, the model combines the certainties and uncertainties in the schemes, i.e., identical degree, different degree and opposite degree. The relations among different schemes are studied, and the traditional way of solving uncertainty problem is improved. By using the gray correlation to determine the difference degree, the problem of less evaluation indexes and inapparent linear relationship is solved. The difference between the evaluation parameters is smaller in both the fuzzy comprehensive evaluation model and fuzzy matter-element method, and the dipartite degree of the evaluation result is unobvious. However, the difference between each integrated connection degree is distinct in the improved set pair analysis. Results show that the proposed method is feasible and it obtains better effects than the fuzzy comprehensive evaluation method and fuzzy matter-element method.

THE CLASSIFICATION OF THE SURROUNDINGS OF COAL MINING ROADWAYS

This paper introduces the calculation of the deformation of the surroundings of roadways and the division of surroundings into 5 levels by means of fuzzy integral assess matrix, which serves as the scientific basis for selecting supporting pattern of roadways and determining the parameters of support.

Fuzzy Metrics Characterized by Molecules and Sets

Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and

Determination of the Sets of Sequences with the Standard Fuzzy Metric

Following George and Veeramani et. al. [On some results in Fuzzy Metric Spaces, Fuzzy Sets Syst. 64 （1994） 395-399], we essentially deal with the classical sequence spaces using of the standard fuzzy metric with t-norm. We consider well-known classical sequence spaces such as l∞ , C, C0 and l p, and we have construct it with standard fuzzy metric. Finally, the completeness of these spaces was given by using the same metric.

Research on the Model of Performance Evaluation of the Industry Cluster Brand

Firstly, this article carry on the theory research combined with the related theories of cluster brand and the relevant theories of performance evaluation, and distill four main indicators factors of performance evaluation of the cluster brand. Then proceed analysts survey and questionnaire investigation, and then use SPSS software to process date for statistical analysis; use AMOS software to formulate the second-order model, at last, establish structure relationship model of performance evaluation of the cluster brand. Build the model of the cluster brand performance evaluation with fuzzy-synthetic evaluation model.

Developing an Assessment Model for Factors Affecting the Quality in the Construction Industry

Quality is considered as one of the most important elements in the construction industry. The factors affecting quality in the construction industry should be assessed. This paper aims to introduce a new model to assess these factors. The model is namely Fuzzy Assessment Model for Quality （FAMQ）. Fuzzy set theory provides a useful way to deal with ill-defined and complex problems in a decision-making environment that incorporates vagueness. The proposed model employs the combined effect of both; the factors probability of occurrence and their impacts on the quality of construction. Twenty five logical rules for each factor were implemented in the model. The model was evaluated using data that collected from the infrastructure projects in Egypt. It was applied to many factors that affect the quality of this kind of projects as a case study. The results of the study proved that the proposed model can be used successfully in the assessment of factors affecting quality in the construction industry. In addition, the results provided a platform of useful assessment reference to those infrastructure＇s finns, who plan to establish their businesses in Egypt.

Fuzzy Views on Black-Litterman Portfolio Selection Model

In this paper, views of investor are described in fuzzy sets, and two fuzzy Black-Litterman models are constructed with fuzzy views and fuzzy random views respectively. In the models, expected returns and uncertainty matrix of views are redefined and the views are formulated by fuzzy approaches suitably. Then the models are tested with data from Chinese financial markets. Empirical results show that the fuzzy random views model performs the best, and both the fuzzy models are better than the traditional ones, demonstrating that the fuzzy approaches can contain more information in the views and measure the uncertainty more correctly.

A Nonlinear Interval Portfolio Selection Model and Its Application in Banks

In classical Markowitz＇s Mean-Variance model, parameters such as the mean and covari- ance of the underlying assets＇ future return are assumed to be known exactly. However, this is not always the case. The parameters often correspond to quantities that fall within a range, or can be known ambiguously at the time when investment decision must be made. In such situations, investors determine returns on investment and risks etc. and make portfolio decisions based on experience and economic wisdom. This paper tries to use the concept of interval numbers in the fuzzy set theory to extend the classical mean-variance portfolio selection model to a mean-downside semi-variance model with consideration of liquidity requirements of a bank. The semi-variance constraint is employed to control the downside risk, filling in the existing interval portfolio optimization model based on the linear semi-absolute deviation to depict the downside risk. Simulation results show that the model behaves robustly for risky assets with highest or lowest mean historical rate of return and the optimal investment proportions have good stability. This suggests that for these kinds of assets the model can reduce the risk of high deviation caused by the deviation in the decision maker＇s experience and economic wisdom.

THE 'HYBRID' TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

Based on the data obtained from a survey recently made in Shanghai, this paper presents the hybrid technique for risk analysis and evaluation of some diseases. After determination of main risk factors of these diseases by analysis of variance, the authors introduce a new concept ’Illness Fuzzy Set’ and use fuzzy comprehensive evaluation to evaluate the risk of suffering from a disease for residents. Optimal technique is used to determine the weights wi in fuzzy comprehensive evaluation, and a new method ’Improved Information Distribution’ is also introduced for the treatment of small sample problem. It is shown that the results obtained by using the hybrid technique are better than by using single fuzzy technique or single statistical method.

On well posedness of best simultaneous approximation problems in Banach spaces

The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.

Development of a mathematical model to evaluate the rate of aggregate risk of invasive alien plant species： Fuzzy risk assessment approach

This study presents a novel approach to evaluate the rate of aggregate risk of Invasive Alien Plant Species. Using risk values and grade of importance of weights of risk factors which may reflect invasiveness of plant species are considered. We use Linguistic Ordered Weighted Averaging operator to evaluate the grade of important of weights. Since the risk values and important weights are identified from two different linguistic term sets, fuzzy set theory techniques were used to combine the two sets. The rates obtained from the model were compared with NRA risk levels and the model was validated with data from known and non-invasive species. The model is improved by weighting the risk values of risk factors. The improved model produced significant results and resulted a better tracking system for identifying potential invaders than the conventional risk assessment.