On the Proof of the Contradiction of Set Theory

The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.

About the Strange Tree Paradox and Possible Inconsistency of Set Theory

The existence of “strange trees” is proven and their paradoxical nature is discussed, due to which set theory is suspected of being contradictory. All proofs rely on informal set-theoretic reasoning, but without using elements that were prohibited in axiomatic set theories in order to overcome the difficulties encountered by Cantor’s naive set theory. Therefore, in fact, the article deals with the possible inconsistency of existing axiomatic set theories, in particular, the ZFC theory. Strange trees appear when uncountable cardinals appear.

The Application of Goal-Setting Theory in the Second Classroom Teaching Activities of College English

Interest is the precondition and motivation for people's accomplishment.However,due to the exam-oriented system,millions of parents and teachers neglect the interests of children,and our children nearly forget their interests or hobbies.Based on different interests of children,the thesis analyzes how to apply the goal-setting theory in the second classroom teaching activities of College English,using the example of Lushan College of Guangxi University of Technology.

Automatic web services classification based on rough set theory

With development of web services technology, the number of existing services in the internet is growing day by day. In order to achieve automatic and accurate services classification which can be beneficial for service related tasks, a rough set theory based method for services classification was proposed. First, the services descriptions were preprocessed and represented as vectors. Elicited by the discernibility matrices based attribute reduction in rough set theory and taking into account the characteristic of decision table of services classification, a method based on continuous discernibility matrices was proposed for dimensionality reduction. And finally, services classification was processed automatically. Through the experiment, the proposed method for services classification achieves approving classification result in all five testing categories. The experiment result shows that the proposed method is accurate and could be used in practical web services classification.

Half-global discretization algorithm based on rough set theory

It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.

Autonomous Clustering Using Rough Set Theory

This paper proposes a clustering technique that minimizes the need for subjective human intervention and is based on elements of rough set theory （RST）. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease. The results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency.

Research on knowledge acquisition method about the IF/THEN rules based on rough set theory

The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.

New Image Recognition Method Based on Rough-Sets and Fuzzy Theory

A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that the new method gives better results than fuzzy or rough sets method when used alone.

Condition Monitoring and Fault Diagnosis Based on Rough Set Theory

In order to raise the efficiency,automatization and intelligentization of condition monitoring and fault diagnosis for complex equipment systems,rough set theory is used to the field. A feature reduction algorithm based on rough set theory is adopted to extract condition information in monitoring and diagnosis for an engine,so that the technology condition monitoring parameters are optimized. The decision tables for each fault source are built and the diagnosis rules rooting in rough set reduction is applied to carry through intelligent fault diagnosis. The cases studied show that rough set method in condition monitoring and fault diagnosis can lighten the work burden in feature selection and afford advantages for autonomic learning and decision during diagnosis.

Seismic vulnerability assessment of urban buildings using the rough set theory and weighted linear combination

Seismic vulnerability assessment of urban buildings is among the most crucial procedures to post-disaster response and recovery of infrastructure systems.The present study proceeds to estimate the seismic vulnerability of urban buildings and proposes a new framework training on the two objectives.First,a comprehensive interpretation of the effective parameters of this phenomenon including physical and human factors is done.Second,the Rough Set theory is used to reduce the integration uncertainties,as there are numerous quantitative and qualitative data.Both objectives were conducted on seven distinct earthquake scenarios with different intensities based on distance from the fault line and the epicenter.The proposed method was implemented by measuring seismic vulnerability for the seven specified seismic scenarios.The final results indicated that among the entire studied buildings,71.5%were highly vulnerable as concerning the highest earthquake scenario(intensity=7 MM and acceleration calculated based on the epicenter),while in the lowest earthquake scenario(intensity=5 MM),the percentage of vulnerable buildings decreased to approximately 57%.Also,the findings proved that the distance from the fault line rather than the earthquake center(epicenter)has a significant effect on the seismic vulnerability of urban buildings.The model was evaluated by comparing the results with the weighted linear combination(WLC)method.The accuracy of the proposed model was substantiated according to evaluation reports.Vulnerability assessment based on the distance from the epicenter and its comparison with the distance from the fault shows significant reliable results.

Evaluation and Analysis of Battery Technologies Applied to Grid-Level Energy Storage Systems Based on Rough Set Theory

Interest in the development of grid-level energy storage systems has increased over the years.As one of the most popular energy storage technologies currently available,batteries offer a number of high-value opportunities due to their rapid responses,flexible installation,and excellent performances.However,because of the complexity,multifunctionality,and wide deployment of power grids,trade-offs in battery performance exist,especially when considering economics,environmental effects,and safety.Therefore,establishing a comprehensive assessment of battery technologies is an urgent undertaking.In this work,we present an analysis of rough sets to evaluate the integration of battery systems(e.g.,lead-acid batteries,lithium-ion batteries,nickel/metal-hydrogen batteries,zinc-air batteries,and Na-S batteries)into a power grid.Specifically,technological properties,economic significance,environmental effects,and safety of these battery systems are evaluated on the basis of rough set theory.In addition,some perspectives are provided to promote the development of battery technologies for grid-level energy storage.

Big Data Audit of Banks Based on Fuzzy Set Theory to Evaluate Risk Level

The arrival of big data era has brought new opportunities and challenges to the development of various industries in China.The explosive growth of commercial bank data has brought great pressure on internal audit.The key audit of key products limited to key business areas can no longer meet the needs.It is difficult to find abnormal and exceptional risks only by sampling analysis and static analysis.Exploring the organic integration and business processing methods between big data and bank internal audit,Internal audit work can protect the stable and sustainable development of banks under the new situation.Therefore,based on fuzzy set theory,this paper determines the membership degree of audit data through membership function,and judges the risk level of audit data,and builds a risk level evaluation system.The main features of this paper are as follows.First,it analyzes the necessity of transformation of the bank auditing in the big data environment.The second is to combine the determination of the membership function in the fuzzy set theory with the bank audit analysis,and use the model to calculate the corresponding parameters,thus establishing a risk level assessment system.The third is to propose audit risk assessment recommendations,hoping to help bank audit risk management in the big data environment.There are some shortcomings in this paper.First,the amount of data acquired is not large enough.Second,due to the lack of author’knowledge,there are still some deficiencies in the analysis of audit risk of commercial banks.

Research on the Information Fusion Method of Oil Diagnosis and Vibration Diagnosis Based on the Rough Sets Theory

The improved method has been presented for knowledge reduction in rough sets （R-S） theory, when R-S is used to model the information expression of oil and vibration diagnosis. Therefore, the typical fault simulation tests of rolling bearings have been made, and the application method of R-S has been also analysed in this paper. The diagnosis model of holding rack fault in rolling bearing was presented based on the improved reduction method. It is suited to information fusion to combine information when oil analysis and vibration analysis are combined for fault diagnosis.

AN INTRUSION DETECTION SYSTEM BASED ON EVIDENCE THEORY AND ROUGH SET THEORY

In this paper,we propose a novel Intrusion Detection System (IDS) architecture utilizing both the evidence theory and Rough Set Theory (RST). Evidence theory is an effective tool in dealing with uncertainty question. It relies on the expert knowledge to provide evidences,needing the evidences to be independent,and this make it difficult in application. To solve this problem,a hybrid system of rough sets and evidence theory is proposed. Firstly,simplification are made based on Variable Precision Rough Set (VPRS) conditional entropy. Thus,the Basic Belief Assignment (BBA) for all evidences can be calculated. Secondly,Dempster’s rule of combination is used,and a decision-making is given. In the proposed approach,the difficulties in acquiring the BBAs are solved,the correlativity among the evidences is reduced and the subjectivity of evidences is weakened. An illustrative example in an intrusion detection shows that the two theories combination is feasible and effective.

Rough Set Theory Based Approach for Fault Diagnosis Rule Extraction of Distribution System

As the first step of service restoration of distribution system,rapid fault diagnosis is a significant task for reducing power outage time,decreasing outage loss,and subsequently improving service reliability and safety.This paper analyzes a fault diagnosis approach by using rough set theory in which how to reduce decision table of data set is a main calculation intensive task.Aiming at this reduction problem,a heuristic reduction algorithm based on attribution length and frequency is proposed.At the same time,the corresponding value reduction method is proposed in order to fulfill the reduction and diagnosis rules extraction.Meanwhile,a Euclid matching method is introduced to solve confliction problems among the extracted rules when some information is lacking.Principal of the whole algorithm is clear and diagnostic rules distilled from the reduction are concise.Moreover,it needs less calculation towards specific discernibility matrix,and thus avoids the corresponding NP hard problem.The whole process is realized by MATLAB programming.A simulation example shows that the method has a fast calculation speed,and the extracted rules can reflect the characteristic of fault with a concise form.The rule database,formed by different reduction of decision table,can diagnose single fault and multi-faults efficiently,and give satisfied results even when the existed information is incomplete.The proposed method has good error-tolerate capability and the potential for on-line fault diagnosis.

Multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory-based environmental risk evaluation for tailings reservoirs

Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.

Generalization Rough Set Theory

In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.

A BENCHMARK EXERCISE ON FUZZY SET THEORY BASED EXPERT JUDGEMENT TECHNIQUE

It is sometimes impossible to make a correct decision in a certain engineering task without the help from professional expert judgments. Even though there are different expert opinions available, however, they should be appropriately aggregated to a useful form for making an acceptable engineering decision. This paper proposed a technique which utilizes the fuzzy set theory in the aggregation of expert judgments. In the technique, two main key concepts are employed: linguistic variables and fuzzy numbers. Linguistic variables first represent the relative importance of evaluation criteria under consideration and the degree of confidence on each expert perceived by the decision maker, and then are replaced by suitable triangular fuzzy numbers for arithmetic manipulation. As a benchmark problem, the pressure increment in the containment of Sequoyah nuclear power plant due to reactor vessel breach was estimated to verify and validate the proposed technique.

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.

La Shalle＇s invariant-set-theory based asymptotic synchronization of duffing system with unknown parameters

A novel La Shalle＇s invariant set theory （LSIST） based adaptive asymptotic synchronization （LSISAAS） method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.