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.

Attribute Reduction on Decision Tables Based on Hausdorff Topology

Attribute reduction through the combined approach of Rough Sets(RS)and algebraic topology is an open research topic with significant potential for applications.Several research works have introduced a strong relationship between RS and topology spaces for the attribute reduction problem.However,the mentioned recent methods followed a strategy to construct a new measure for attribute selection.Meanwhile,the strategy for searching for the reduct is still to select each attribute and gradually add it to the reduct.Consequently,those methods tended to be inefficient for high-dimensional datasets.To overcome these challenges,we use the separability property of Hausdorff topology to quickly identify distinguishable attributes,this approach significantly reduces the time for the attribute filtering stage of the algorithm.In addition,we propose the concept of Hausdorff topological homomorphism to construct candidate reducts,this method significantly reduces the number of candidate reducts for the wrapper stage of the algorithm.These are the two main stages that have the most effect on reducing computing time for the attribute reduction of the proposed algorithm,which we call the Cluster Filter Wrapper algorithm based on Hausdorff Topology.Experimental validation on the UCI Machine Learning Repository Data shows that the proposed method achieves efficiency in both the execution time and the size of the reduct.

Attribute Reduction Method Based on Sequential Three-Branch Decision Model

Attribute reduction is a research hotspot in rough set theory. Traditional heuristic attribute reduction methods add the most important attribute to the decision attribute set each time, resulting in multiple redundant attribute calculations, high time consumption, and low reduction efficiency. In this paper, based on the idea of sequential three-branch decision classification domain, attributes are treated as objects of three-branch division, and attributes are divided into core attributes, relatively necessary attributes, and unnecessary attributes using attribute importance and thresholds. Core attributes are added to the decision attribute set, unnecessary attributes are rejected from being added, and relatively necessary attributes are repeatedly divided until the reduction result is obtained. Experiments were conducted on 8 groups of UCI datasets, and the results show that, compared to traditional reduction methods, the method proposed in this paper can effectively reduce time consumption while ensuring classification performance.

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.

A Novel Incremental Attribute Reduction Algorithm Based on Intuitionistic Fuzzy Partition Distance

Attribute reduction,also known as feature selection,for decision information systems is one of the most pivotal issues in machine learning and data mining.Approaches based on the rough set theory and some extensions were proved to be efficient for dealing with the problemof attribute reduction.Unfortunately,the intuitionistic fuzzy sets based methods have not received much interest,while these methods are well-known as a very powerful approach to noisy decision tables,i.e.,data tables with the low initial classification accuracy.Therefore,this paper provides a novel incremental attribute reductionmethod to dealmore effectivelywith noisy decision tables,especially for highdimensional ones.In particular,we define a new reduct and then design an original attribute reduction method based on the distance measure between two intuitionistic fuzzy partitions.It should be noted that the intuitionistic fuzzypartitiondistance iswell-knownas aneffectivemeasure todetermine important attributes.More interestingly,an incremental formula is also developed to quickly compute the intuitionistic fuzzy partition distance in case when the decision table increases in the number of objects.This formula is then applied to construct an incremental attribute reduction algorithm for handling such dynamic tables.Besides,some experiments are conducted on real datasets to show that our method is far superior to the fuzzy rough set based methods in terms of the size of reduct and the classification accuracy.

Fusing Supervised and Unsupervised Measures for Attribute Reduction

It is well-known that attribute reduction is a crucial action of rough set.The significant characteristic of attribute reduction is that it can reduce the dimensions of data with clear semantic explanations.Normally,the learning performance of attributes in derived reduct is much more crucial.Since related measures of rough set dominate the whole process of identifying qualified attributes and deriving reduct,those measures may have a direct impact on the performance of selected attributes in reduct.However,most previous researches about attribute reduction take measures related to either supervised perspective or unsupervised perspective,which are insufficient to identify attributes with superior learning performance,such as stability and accuracy.In order to improve the classification stability and classification accuracy of reduct,in this paper,a novel measure is proposed based on the fusion of supervised and unsupervised perspectives:(1)in terms of supervised perspective,approximation quality is helpful in quantitatively characterizing the relationship between attributes and labels;(2)in terms of unsupervised perspective,conditional entropy is helpful in quantitatively describing the internal structure of data itself.In order to prove the effectiveness of the proposed measure,18 University of CaliforniaIrvine(UCI)datasets and 2 Yale face datasets have been employed in the comparative experiments.Finally,the experimental results show that the proposed measure does well in selecting attributes which can provide distinguished classification stabilities and classification accuracies.

Two-Layer Information Granulation:Mapping-Equivalence Neighborhood Rough Set and Its Attribute Reduction

Attribute reduction,as one of the essential applications of the rough set,has attracted extensive attention from scholars.Information granulation is a key step of attribute reduction,and its efficiency has a significant impact on the overall efficiency of attribute reduction.The information granulation of the existing neighborhood rough set models is usually a single layer,and the construction of each information granule needs to search all the samples in the universe,which is inefficient.To fill such gap,a new neighborhood rough set model is proposed,which aims to improve the efficiency of attribute reduction by means of two-layer information granulation.The first layer of information granulation constructs a mapping-equivalence relation that divides the universe into multiple mutually independent mapping-equivalence classes.The second layer of information granulation views each mapping-equivalence class as a sub-universe and then performs neighborhood informa-tion granulation.A model named mapping-equivalence neighborhood rough set model is derived from the strategy of two-layer information granulation.Experimental results show that compared with other neighborhood rough set models,this model can effectively improve the efficiency of attribute reduction and reduce the uncertainty of the system.The strategy provides a new thinking for the exploration of neighborhood rough set models and the study of attribute reduction acceleration problems.

A Neighborhood Rough Set Attribute Reduction Method Based on Attribute Importance

Attribute reduction is a hot topic in rough set research. As an extension of rough sets, neighborhood rough sets can effectively solve the problem of information loss after data discretization. However, traditional greedy-based neighborhood rough set attribute reduction algorithms have a high computational complexity and long processing time. In this paper, a novel attribute reduction algorithm based on attribute importance is proposed. By using conditional information, the attribute reduction problem in neighborhood rough sets is discussed, and the importance of attributes is measured by conditional information gain. The algorithm iteratively removes the attribute with the lowest importance, thus achieving the goal of attribute reduction. Six groups of UCI datasets are selected, and the proposed algorithm SAR is compared with L2-ELM, LapTELM, CTSVM, and TBSVM classifiers. The results demonstrate that SAR can effectively improve the time consumption and accuracy issues in attribute reduction.

Co-evolutionary cloud-based attribute ensemble multi-agent reduction algorithm

In order to improve the performance of the attribute reduction algorithm to deal with the noisy and uncertain large data, a novel co-evolutionary cloud-based attribute ensemble multi-agent reduction（CCAEMR） algorithm is proposed.First, a co-evolutionary cloud framework is designed under the M apReduce mechanism to divide the entire population into different co-evolutionary subpopulations with a self-adaptive scale. Meanwhile, these subpopulations will share their rewards to accelerate attribute reduction implementation.Secondly, a multi-agent ensemble strategy of co-evolutionary elitist optimization is constructed to ensure that subpopulations can exploit any correlation and interdependency between interacting attribute subsets with reinforcing noise tolerance.Hence, these agents are kept within the stable elitist region to achieve the optimal profit. The experimental results show that the proposed CCAEMR algorithm has better efficiency and feasibility to solve large-scale and uncertain dataset problems with complex noise.

Adaptive multicascade attribute reduction based on quantum-inspired mixed co-evolution

Due to the fact that conventional heuristic attribute reduction algorithms are poor in running efficiency and difficult in accomplishing the co-evolutionary reduction mechanism in the decision table, an adaptive multicascade attribute reduction algorithm based on quantum-inspired mixed co-evolution is proposed. First, a novel and efficient self- adaptive quantum rotation angle strategy is designed to direct the participating populations to mutual adaptive evolution and to accelerate convergence speed. Then, a multicascade model of cooperative and competitive mixed co-evolution is adopted to decompose the evolutionary attribute species into subpopulations according to their historical performance records, which can increase the diversity of subpopulations and select some elitist individuals so as to strengthen the sharing ability of their searching experience. So the global optimization reduction set can be obtained quickly. The experimental results show that, compared with the existing algorithms, the proposed algorithm can achieve a higher performance for attribute reduction, and it can be considered as a more competitive heuristic algorithm on the efficiency and accuracy of minimum attribute reduction.

Cooperative extended rough attribute reduction algorithm based on improved PSO

Particle swarm optimization （PSO） is a new heuristic algorithm which has been applied to many optimization problems successfully. Attribute reduction is a key studying point of the rough set theory, and it has been proven that computing minimal reduc- tion of decision tables is a non-derterministic polynomial （NP）-hard problem. A new cooperative extended attribute reduction algorithm named Co-PSAR based on improved PSO is proposed, in which the cooperative evolutionary strategy with suitable fitness func- tions is involved to learn a good hypothesis for accelerating the optimization of searching minimal attribute reduction. Experiments on Benchmark functions and University of California, Irvine （UCI） data sets, compared with other algorithms, verify the superiority of the Co-PSAR algorithm in terms of the convergence speed, efficiency and accuracy for the attribute reduction.

Enhanced minimum attribute reduction based on quantum-inspired shuffled frog leaping algorithm

Attribute reduction in the rough set theory is an important feature selection method, but finding a minimum attribute reduction has been proven to be a non-deterministic polynomial （NP）-hard problem. Therefore, it is necessary to investigate some fast and effective approximate algorithms. A novel and enhanced quantum-inspired shuffled frog leaping based minimum attribute reduction algorithm （QSFLAR） is proposed. Evolutionary frogs are represented by multi-state quantum bits, and both quantum rotation gate and quantum mutation operators are used to exploit the mechanisms of frog population diversity and convergence to the global optimum. The decomposed attribute subsets are co-evolved by the elitist frogs with a quantum-inspired shuffled frog leaping algorithm. The experimental results validate the better feasibility and effectiveness of QSFLAR, comparing with some representa- tive algorithms. Therefore, QSFLAR can be considered as a more competitive algorithm on the efficiency and accuracy for minimum attribute reduction.

Attribute reduction based on background knowledge and its application in classification of astronomical spectra data

To improve the efficiency of the attribute reduction, we present an attribute reduction algorithm based on background knowledge and information entropy by making use of background knowledge from research fields. Under the condition of known background knowledge, the algorithm can not only greatly improve the efficiency of attribute reduction, but also avoid the defection of information entropy partial to attribute with much value. The experimental result verifies that the algorithm is effective. In the end, the algorithm produces better results when applied in the classification of the star spectra data.

Attributes reduct and decision rules optimization based on maximal tolerance classification in incomplete information systems with fuzzy decisions

A new approach to knowledge acquisition in incomplete information system with fuzzy decisions is proposed. In such incomplete information system, the universe of discourse is classified by the maximal tolerance classes, and fuzzy approximations are defined based on them. Three types of relative reducts of maximal tolerance classes are then proposed, and three types of fuzzy decision rules based on the proposed attribute description are defined. The judgment theorems and approximation discernibility functions with respect to them are presented to compute the relative reduct by using Boolean reasoning techniques, from which we can derive optimal fuzzy decision rules from the systems. At last, three types of relative reducts of the system and their computing methods are given.

An improved reduction algorithm based on the degree of attribute discernibility

This paper deals with the problem of attribute discernibility reduction and proposes some new concepts to rough set theory （RST） based on the discernibility matrix of Skowron, such as secondary core, regeneration matrix and the degree of attribute discernibility （DAD）. This paper puts forward an attribute reduction algorithm based on maximum discernibility degree, which opens up an effective way of gaining minimum attribute reduction of decision table. The efficacy of this algorithm has been verified by practical application in a diagnostic system of loader, which substantially decreases information gathering requirement and lowers the overall cost with no loss of accuracy.

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.

MINIMUM ATTRIBUTE CO-REDUCTION ALGORITHM BASED ON MULTILEVEL EVOLUTIONARY TREE WITH SELF-ADAPTIVE SUBPOPULATIONS

Attribute reduction is an important process in rough set theory.Finding minimum attribute reduction has been proven to help the user-oriented make better knowledge discovery in some cases.In this paper,an efficient minimum attribute reduction algorithm is proposed based on the multilevel evolutionary tree with self-adaptive subpopulations.A model of multilevel evolutionary tree with self-adaptive subpopulations is constructed,and interacting attribute sets are better decomposed into subsets by the self-adaptive mechanism of elitist populations.Moreover it can self-adapt the subpopulation sizes according to the historical performance record so that interacting attribute decision variables are captured into the same grouped subpopulation,which will be extended to better performance in both quality of solution and competitive computation complexity for minimum attribute reduction.The conducted experiments show the proposed algorithm is better on both efficiency and accuracy of minimum attribute reduction than some representative algorithms.Finally the proposed algorithm is applied to magnetic resonance image(MRI)segmentation,and its stronger applicability is further demonstrated by the effective and robust segmentation results.

Application of Attribute Reduction to Well Logging

The quantity of well logging data is increasing exponentially, hence methods of extracting the useful information or attribution from the logging database are becoming very important in logging interpretation. So, the method of logging attribute reduction is presented based on a rough set, i.e., first determining the core of the information table, then calculating the significance of each attribute, and finally obtaining the relative reduction table. The application result shows that the method of attribute reduction is feasible and can be used for optimizing logging attributes, and decreasing redundant logging information to a great extent.

Attribute reduction algorithm based on discernibility for decision table

The attribute reduction algorithms of decision table based on discernible matrix are required to construct discernible matrix, which reduces efficiency of algorithms. In this paper, the relationship between attribute discernible matrix and its discernibility is first established for general information systems. Based on the idea that the equivalent discernible matrix has a same attribute reduction, existing matrices are modified and a formula of attribute discernibility associated with algebraic reduction for decision table is proposed. A heuristic attribute reduction algorithm based on attribute discernibility is presented. Experimental results indicate that the algorithm can more easily explore an optimal or sub-optimal reduction, and is efficient.

Comparison of Attribute Reduction Methods for Coronary Heart Disease Data by Decision Tree Classification

Attribute reduction is necessary in decision making system. Selecting right attribute reduction method is more important. This paper studies the reduction effects of principal components analysis (PCA) and system reconstruction analysis (SRA) on coronary heart disease data. The data set contains 1723 records, and 71 attributes in each record. PCA and SRA are used to reduce attributes number (less than 71 ) in the data set. And then decision tree algorithms, C4.5, classification and regression tree ( CART), and chi-square automatic interaction detector ( CHAID), are adopted to analyze the raw data and attribute reduced data. The parameters of decision tree algorithms, including internal node number, maximum tree depth, leaves number, and correction rate are analyzed. The result indicates that, PCA and SRA data can complete attribute reduction work,and the decision-making rate on the reduced data is quicker than that on the raw data; the reduction effect of PCA is better than that of SRA, while the attribute assertion of SRA is better than that of PCA. PCA and SRA methods exhibit goodperformance in selecting and reducing attributes.