Attribute Reduction of Neighborhood Rough Set Based on Discernment

For neighborhood rough set attribute reduction algorithms based on dependency degree,a neighborhood computation method incorporating attribute weight values and a neighborhood rough set attribute reduction algorithm using discernment as the heuristic information was proposed.The reduction algorithm comprehensively considers the dependency degree and neighborhood granulation degree of attributes,allowing for a more accurate measurement of the importance degrees of attributes.Example analyses and experimental results demonstrate the feasibility and effectiveness of the algorithm.

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set(SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging(SNNPWA) operator, simplified neutrosophic number power weighted geometric(SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging(SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric(SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multiattribute group decision making(MAGDM) within the framework of SNSs is developed by the above aggregation operators.Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Numerical Characterizations of Covering Rough Sets Based on Evidence Theory

Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough sets.First,we present belief and plausibility functions in covering information systems and study their properties.With these measures we characterize lower and upper approximation operators and attribute reductions in covering information systems and decision systems respectively.With these discussions we propose a basic framework of numerical characterizations of covering rough sets.

Approximation Maintenance When Adding a Conditional Value in Set-Valued Ordered Decision Systems

The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.

A Study to Improve the Method of Ascertaining Attribute Weight Based on Rough Sets Theory

There are some shortages to ascertain attribute weight based on rough set in current studies. In this paper,attribute importance represented by rough set is studied deeply. Aiming at the existing problems,algebra presentation of rough sets is proved to be more comprehensive than its information presentation,then a new method of ascertaining attribute weigh is put forward based on rough set conditional entropy. Finally,it is shown that the new method is more reasonable than the old one by an example.

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.

Major Characteristics of the Lajishan Orogenic Belt of the South Qilian Mountains and Its Geotectonic Attribute

The Lajishan orogenic belt is one of the E-W-trending Caledonian orogenicbelts within the Qinling-Qilian orogenic system. It was formed upon the Jiningian basement byintensive taphrogenesis. Its major characteristics comprise the prominent faulting along the northand south boundaries, the highly complicated petrological and petro-geochemical features of thevolcanic rock series, and the development of a new type of ophiolite suite. In terms of tectonicanalysis and the sequential analysis of tectonic settings of magmatic rocks, it is suggested thatthe Lajishan orogenic belt has undergone a complete 'opening-closing' cycle, which can be furtherdivided into 3 second-order 'opening-closing' cycles. The composite characteristics of the'opening-closing' movement show that Laji Mountain is a typical fault orogenic belt. The faultorogenic belt is one of the most important types of intracontinental orogens. It is of criticaltheoretical and practical significance to summarize the characteristics and the diagnostic criteriaof this kind of orogenic belts, and study the mechanism of their formation and build models of theirevolution.

Extracting Decision Rules for Cooperative Team Air Combat Based on Rough Set Theory

In order to reduce redundant features in air combat information and to meet the requirements of real-time decision in combat, rough set theory is introduced to the tactical decision analysis in cooperative team air combat. An algorithm of attribute reduction for extracting key combat information and generating tactical rules from given air combat databases is presented. Then, considering the practical requirements of team combat, a method for reduction of attribute-values under single decision attribute is extended to the reduction under multi-decision attributes. Finally, the algorithm is verified with an example for tactical choices in team air combat. The results show that, the redundant attributes in air combat information can be reduced, and that the main combat attributes, i.e., the information about radar command and medium-range guided missile, can be obtained with the algorithm mentioned above, moreover, the minimal reduced strategy for tactical decision can be generated without losing the result of key information classification. The decision rules extracted agree with the real situation of team air combat.

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.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

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.

Correction of seismic attribute-based smallstructure prediction errors using GPR data-a case study of the Shuguang Coal Mine,Shanxi

Small structures in coal mine working face is one of the main hidden dangers of safe and effi cient production in coal mine.Currently,seismic exploration is often used as the main method for detecting such structures.However,limited by the accuracy of seismic data processing and interpretation,the interpreted location of small structures is often deviated.Ground-penetrating radar(GPR)can detect small structures accurately,but the exploration depth is shallow.The combination of the two methods can improve the exploration accuracy of small structures in coal mine.Aiming at the 1226#working face of Shuguang coal mine,we propose a method of seismic-attributes based small-structure prediction error correction using GPR data.First,we extract the coherence,curvature,and dip attributes from seismic data,that are sensitive to small structures,then by considering factors such as the eff ective detection range of GPR and detection environment,we select two structures from the prediction results of seismic attributes for GPR detection.Finally,based on the relationship between the positions of small structures predicted by the two methods,we use statistical methods to determine the overall off set distance and azimuth of the small structures in the entire study area and use the results as a standard for correcting each structure position.The results show that the GPR data can be used to correct the horizontal position errors of small structures predicted by seismic attribute analysis.The accuracy of the prediction results is greatly improved,with the error controlled within 5 m and reduced by more than 80%.Therefore,the feasibility of the method proposed in this study is verified.

Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

Support vector machine ensemble using rough sets theory

A support vector machine （SVM） ensemble classifier is proposed. Performance of SVM trained in an input space eonsisting of all the information from many sources is not always good. The strategy that the original input space is partitioned into several input subspaces usually works for improving the performance. Different from conventional partition methods, the partition method used in this paper, rough sets theory based attribute reduction, allows the input subspaces partially overlapped. These input subspaces can offer complementary information about hidden data patterns. In every subspace, an SVM sub-classifier is learned. With the information fusion techniques, those SVM sub-classifiers with better performance are selected and combined to construct an SVM ensemble. The proposed method is applied to decision-making of medical diagnosis. Comparison of performance between our method and several other popular ensemble methods is done. Experimental results demonstrate that our proposed approach can make full use of the information contained in data and improve the decision-making performance.

A New Method for Constructing Decision Tree Based on Rough Sets Theory

Decision trees induction algorithms have been used for classification in a wide range of application domains. In the process of constructing a tree, the criteria of selecting test attributes will influence the classification accuracy of the tree.In this paper,the degree of dependency of decision attribute to condition attribute,based on rough set theory,is used as a heuristic for selecting the attribute that will best separate the samples into individual classes.The result of an example shows that compared with the entropy-based approach,our approach is a better way to select nodes for constructing decision trees.

Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

A Method of Attribute Reduction Based on Rough Set

The logging attribute optimization is an important task in the well-logging interpretation. A method of attribute reduction is presented based on rough set. Firstly, the core information of the sample by a general reductive method is determined. Then, the significance of dispensable attribute in the reduction-table is calculated. Finally, the minimum relative reduction set is achieved. The typical calculation and quantitative computation of reservoir parameter in oil logging show that the method of attribute reduction is greatly effective and feasible in logging interpretation.

Clustering of Web Learners Based on Rough Set

The demand for individualized teaching from E-learning websites is rapidly increasing due to the huge differences existed among Web learners. A method for clustering Web learners based on rough set is proposed. The basic idea of the method is to reduce the learning attributes prior to clustering, and therefore the clustering of Web learners is carried out in a relative low-dimensional space. Using this method, the E-learning websites can arrange corresponding teaching content for different clusters of learners so that the learners’ individual requirements can be more satisfied. Key words rough set - attributes reduction - k-means clustering - individualized teaching CLC number TP 391.6 Foundation item: Supported by the National “863” Program of China (2002AA111010, 2003AA001032)Biography: LIU Shuai-dong (1979-), male, Master candidate, research direction: knowledge discovery and individualized learning techniques.

Forecast of Power Generation for Grid-Connected Photo-voltaic System Based on Grey Theory and Verification Model

Being photovoltaic power generation affected by radiation strength, wind speed, clouds cover and environment temperature, the generating in each moment is fluctuating. The operational characteristics of grid-connected PV systems are coincided with gray theory application conditions. A gray theory model has been applied in short-term forecast of grid-connected photovoltaic system. The verification model of the probability of small error will help to check the accuracy of the gray forecast results. The calculated result shows that the ?model accuracy has been greatly enhanced.