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 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.

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 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.

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.

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.

Evaluation Model for Capability of Enterprise Agent Coalition Based on Information Fusion and Attribute Reduction

For the issue of evaluation of capability of enterprise agent coalition,an evaluation model based on information fusion and entropy weighting method is presented. The attribute reduction method is utilized to reduce indicators of the capability according to the theory of rough set. The new indicator system can be determined. Attribute reduction can also reduce the workload and remove the redundant information,when there are too many indicators or the indicators have strong correlation. The research complexity can be reduced and the efficiency can be improved. Entropy weighting method is used to determine the weights of the remaining indicators,and the importance of indicators is analyzed. The information fusion model based on nearest neighbor method is developed and utilized to evaluate the capability of multiple agent coalitions,compared to cloud evaluation model and D-S evidence method. Simulation results are reasonable and with obvious distinction. Thus they verify the effectiveness and feasibility of the model. The information fusion model can provide more scientific,rational decision support for choosing the best agent coalition,and provide innovative steps for the evaluation process of capability of agent coalitions.

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.

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.

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.

New Attribute Reduction Algorithm on Fuzzy Decision Table

Classical rough set has a limited processing capacity in fuzzy decision table. Combining fuzzy set with classical rough set,attribute reduction algorithm on fuzzy decision table is studied. First,new similarity degree and new similarity category are defined. In the meantime,similarity category clusters which are divided by condition attribute are provided. And then,two theorems are presented. Subsequently,a new attribute reduction algorithm is proposed. Finally,the new attribute reduction algorithm is verified through a performance evaluation decision table of the self-repairing flight-control system. The result shows the proposed attribute reduction algorithm is able to deal with fuzzy decision table to a certain extent.

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.

Attribute Reduction in Decision Systems Based on Relation Matrix

This paper proposes,from the viewpoint of relation matrix,a new algorithm of attribute reduction for decision systems.Two new and relative reasonable indices are first defined to measure significance of the attributes in decision systems and then a heuristic algorithm of attribute reduction is formulated.Moreover,the time complexity of the algorithm is analyzed and it is proved to be complete.Some numerical experiments are also conducted to access the performance of the presented algorithm and the results demonstrate that it is not only effective but also efficient.

An Innovative Approach for Attribute Reduction in Rough Set Theory

The Rough Sets Theory is used in data mining with emphasis on the treatment of uncertain or vague information. In the case of classification, this theory implicitly calculates reducts of the full set of attributes, eliminating those that are redundant or meaningless. Such reducts may even serve as input to other classifiers other than Rough Sets. The typical high dimensionality of current databases precludes the use of greedy methods to find optimal or suboptimal reducts in the search space and requires the use of stochastic methods. In this context, the calculation of reducts is typically performed by a genetic algorithm, but other metaheuristics have been proposed with better performance. This work proposes the innovative use of two known metaheuristics for this calculation, the Variable Neighborhood Search, the Variable Neighborhood Descent, besides a third heuristic called Decrescent Cardinality Search. The last one is a new heuristic specifically proposed for reduct calculation. Considering some databases commonly found in the literature of the area, the reducts that have been obtained present lower cardinality, i.e., a lower number of attributes.