Variable Sets principle and method for flood classification

Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.

Variable sets method for urban flood vulnerability assessment

On the basis of dialectics basic laws and mathematical theorems of variable sets,this paper proposes a variable sets method for urban flood vulnerability assessment.In this method,the comprehensive relative membership degree of multi-indices is represented by an index relative difference degree,which follows the characteristics of dialectical philosophy and mathematics.According to the quality-quantity exchange theorem,the relative difference degree of two adjacent levels(h and h+1),whose index standard interval values cross the boundaries,equals 0 in the urban flood vulnerability assessment.On the basis of the opposite unity theorem,the sum of relative membership degrees should be equal to 1 when indices lie in the adjacent degrees h and h+1.The variable sets method is proved to be theoretically rigorous and computationally simple.This paper takes 29 cities of Hunan province as an example to assess the urban flood vulnerability,and then compares the results from this newly developed method with the assessment results obtained from the fuzzy comprehensive evaluation and fuzzy set pair analysis methods.

Variable Precision Rough Set and a Fuzzy Measure of Knowledge Based on Variable Precision Rough Set

Variable precision rough set (VPRS) is an extension of rough set theory (RST). By setting threshold value β , VPRS looses the strict definition of approximate boundary in RST. Confident threshold value for β is discussed and the method for deriving decision making rules from an information system is given by an example. An approach to fuzzy measures of knowledge is proposed by applying VPRS to fuzzy sets. Some properties of this measure are studied and a pair of lower and upper approximation operato...

Basin flood control system risk evaluation based on variable sets

Flood control system risk evaluation is an effective measure for flood risk management and decisions.In order to make better flood risk decisions and thereby improve social and economic benefits,the flood control risk evaluation index system should be built to quantify and normalize flood risk effectively and efficiently.Because the current evaluation index has the binary miscibility characteristic of fuzziness and clarity,this paper establishes a new flood control system risk evaluation method based on the theory of variable sets(VS).Through a comparison of flood control risk evaluation with variable fuzzy sets(VFS) in the same basin flood control system risk evaluation,it is revealed that the new method,i.e.,flood control risk evaluation with variable fuzzy/clear mixture sets(variable sets),will be reasonable in all cases.Finally,in one case study,i.e.,the flood control system risk evaluation of Fengman Reservoir Basin,which is located in the southeast central of Jilin Province in China,the risk evaluation levels for each county in the basin as well as the whole flood risk distribution map of the basin could be provided with the new method.This provides useful information for basin flood control planning and design.

Assessment on Agricultural Drought Risk Based on Variable Fuzzy Sets Model

Drought is one of the major natural disasters causing huge agricultural losses annually. Regional agricultural drought risk assessment has great significance for reducing regional disaster and agricultural drought losses. Based on the fuzzy characteristics of agricultural drought risk, variable fuzzy sets model was used for comprehensively assessing agricultural drought risk of Liaoning Province in China. A multi-layers and multi-indices assessment model was estab-lished according to variable fuzzy sets theory, and agricultural drought risk of all 14 prefecture-level cities was respec-tively estimated in terms of dangerousness, vulnerability, exposure and drought-resistibility. By calculating the combi-nation weights of four drought risk factors, agricultural drought risk grade of each city was obtained. Based on the as-sessment results, the spatial distribution maps of agricultural drought risk were drawn. The results shows that eastern cities have lower drought dangerousness than western cities in Liaoning Province totally. Most cities are located in low drought vulnerability region and high drought exposure region. Because of frequent and severe drought since 2000, most cities are located in lower drought-resistibility region. Comprehensive agricultural drought risk presents apparent spatial characteristics, escalating from the east to the west. Drought dangerousness is the most important factor influencing comprehensive agricultural drought risk. Through the spatial distribution maps of drought risk, decision makers could find out drought situation and make decisions on drought resistance conveniently.

A Method of Gene-Function Annotation Based on Variable Precision Rough Sets

It is very important in the field of bioinformatics to apply computer to perform the function annotation for new sequenced bio-sequences. Based on GO database and BLAST program, a novel method for the function annotation of new biological sequences is presented by using the variable-precision rough set theory. The proposed method is applied to the real data in GO database to examine its effectiveness. Numerical results show that the proposed method has better precision, recall-rate and harmonic mean value compared with existing methods.

Synthetic security assessment based on variable consistency dominance-based rough set approach

Security assessment can help understand the security conditions of an information system and yield results highly conducive to the solution of security problems in it. Taking the computer networks in a certain university as samples, this paper, with the information system security assessment model as its foundation, proposes a multi-attribute group decision-making （MAGDM） security assessment method based on a variable consistency dominance-based rough set approach （VC-DRSA）. This assessment method combines VC-DRSA with the analytic hierarchy process （AHP）, uncovers the inherent information hidden in data via the quality of sorting （QoS）, and makes a synthetic security assessment of the information system after determining the security attribute weight. The sample findings show that this method can effectively remove the bottleneck of MAGDM, thus assuming practical significance in information system security assessment.

Variable precision rough set for multiple decision attribute analysis

A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA problem with multiple decision attributes and multiple condition attributes. Empirical results show that the decision rule with the highest confidence measures will be used as the final decision rules in the MADA problem with multiple conflicting decision attributes and multiple condition attributes if there are some conflicts among decision rules resulting from multiple decision attributes. The confidence-measure-based VPRS model can effectively solve the conflicts of decision rules from multiple decision attributes and thus a class of MADA problem with multiple conflicting decision attributes and multiple condition attributes are solved.

Establishment and Optimization of Status Assessment Variables for Heavy Haul Railway Line Service Performance

In order to address the issues of complex system structure and variable selection difficulty for the current heavy haul railway line status evaluation system, a three-category and three-layer heavy-haul line status evaluation variable set construction and reduction optimization method is proposed. Firstly, the status of heavy haul railway line is analyzed, and an initial set of evaluation variables affecting the line status is constructed. Then, based on the association rule and the principal component analysis method, key variables are extracted from the initial variable set to establish the evaluation system. Finally, this method is verified with actual data of a line. The results show that the service performance of heavy haul railway line can still be evaluated accurately when the evaluation variables are reduced by 60% in the proposed method.

Application of Rough Set Theory in Fault Diagnostic Rules Acquisition

Rough set theory is a new mathematical tool to deal with vagneness and uncertainty. But original rough sets theory only generates deterministic rules and deals with data sets in which there is no noise. The variable precision rough set model （VPRSM） is presented to handle uncertain and noisy information. A method based on VPRSM is proposed to apply to fault diagnosis feature extraction and rules acquisition for industrial applications. An example for fault diagnosis of rotary machinery is given to show that the method is very effective.

Multi-Span and Multiple Relevant Time Series Prediction Based on Neighborhood Rough Set

Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource planning and management,reservoir and river regulation.Most research is focused on constructing the better model for improving prediction accuracy.In this paper,a rainfall runoff forecast model based on the variable-precision fuzzy neighborhood rough set(VPFNRS)is constructed to predict Watershed runoff value.Fuzzy neighborhood rough set dene the fuzzy decision of a sample by using the concept of fuzzy neighborhood.The fuzzy neighborhood rough set model with variable-precision can reduce the redundant attributes,and the essential equivalent data can improve the predictive capabilities of model.Meanwhile VFPFNRS can handle the numerical data,while it also deals well with the noise data.In the discussed approach,VPFNRS is used to reduce superuous attributes of the original data,the compact data are employed for predicting the rainfall runoff.The proposed method is examined utilizing data in the Luo River Basin located in Guangdong,China.The prediction accuracy is compared with that of support vector machines and long shortterm memory(LSTM).The experiments show that the method put forward achieves a higher predictive performance.

A Generalized Rough Set Modeling Method for Welding Process

Modeling is essential, significant and difficult for the quality and shaping control of arc welding process. A generalized rough set based modeling method was brought forward and a dynamic predictive model for pulsed gas tungsten arc welding (GTAW) was obtained by this modeling method. The results show that this modeling method can well acquire knowledge in welding and satisfy the real life application. In addition, the results of comparison between classic rough set model and back-propagation neural network model respectively are also satisfying.

MAINTENANCE LEVEL DECISION OF AERO-ENGINE BASED ON VPRS THEORY

An aero-engine is a typically repairable and complex system and its maintenance level has a close relationship with the maintenance cost. The inaccurate measurement for the maintenance level of an aero-engine can induce higher overhaul maintenance costs. Variable precision rough set （VPRS） theory is used to determine the maintenance level of an aero-engine. According to the relationship between condition information and performance parameters of aero-engine modules, decision rules are established for reflecting the real condition of an aeroengine when its maintenance level needs to be determined. Finally, the CF6 engine is used as an example to illustrate the method to be effective.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

Architecture Design of a Variable Length Instruction Set VLIW DSP

The cost of the central register file and the size of the program code limit the scalability of very long instruction word（VLIW） processors with increasing numbers of functional units.This paper presents the architectural design of a six-way VLIW digital signal processor（DSP） with clustered register files.The architecture uses a variable length instruction set and supports dynamic instruction dispatching.The one-level memory system architecture of the processor includes 16-KB instruction and data caches and 16-KB instruction and data on-chip RAM.A compiler based on the Open64 was developed for the system.Evaluations show that the processor is suitable for high performance applications with a high code density and small program code size.

Product Approximation of Grade and Precision

The normal graded approximation and variable precision approximation are defined in approximate space. The relationship between graded approximation and variable precision approximation is studied, and an important formula of conversion between them is achieved The product approximation of grade and precision is defined and its basic properties are studied.

A Low Complexity VCS Method for PAPR Reduction in Multicarrier Code Division Multiple Access

This paper investigates a peak to average power ratio （PAPR） reduction method in multicarrier code division multiple access （MC-CDMA） system. Variable code sets （VCS）, a spreading codes selection scheme, can improve the PAPR property of the MC-CDMA signals, but this technique requires an exhaustive search over the combinations of spreading code sets. It is observed that when the number of active users increases, the search complexity will increase exponentially. Based on this fact, we propose a low complexity VCS （LC-VCS） method to reduce the computational complexity. The basic idea of LC-VCS is to derive new signals using the relationship between candidature signals. Simulation results show that the proposed approach can reduce PAPR with lower comtational pucomplexity. In addition, it can be blindly received without any side information.

Text Classification Using Sentential Frequent Itemsets

Text classification techniques mostly rely on single term analysis of the document data set, while more concepts, especially the specific ones, are usually conveyed by set of terms. To achieve more accurate text classifier, more informative feature including frequent co-occurring words in the same sentence and their weights are particularly important in such scenarios. In this paper, we propose a novel approach using sentential frequent itemset, a concept comes from association rule mining, for text classification, which views a sentence rather than a document as a transaction, and uses a variable precision rough set based method to evaluate each sentential frequent itemset＇s contribution to the classification. Experiments over the Reuters and newsgroup corpus are carried out, which validate the practicability of the proposed system.

THE IMPLICIT CONVEX FEASIBILITY PROBLEM AND ITS APPLICATION TO ADAPTIVE IMAGE DENOISING

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. By allowing the variable sets to undergo scaling, shifting and rotation, this work generalizes pre^ious results -vherein the implicit convex feasibility problem was used for cooperative wireless sensor network positioning where sets are balls and their centers were implicit.