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.

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.

Improved Rough Set Algorithms for Optimal Attribute Reduct

Feature selection（FS） aims to determine a minimal feature（attribute） subset from a problem domain while retaining a suitably high accuracy in representing the original features. Rough set theory（RST） has been used as such a tool with much success. RST enables the discovery of data dependencies and the reduction of the number of attributes contained in a dataset using the data alone,requiring no additional information. This paper describes the fundamental ideas behind RST-based approaches,reviews related FS methods built on these ideas,and analyses more frequently used RST-based traditional FS algorithms such as Quickreduct algorithm,entropy based reduct algorithm,and relative reduct algorithm. It is found that some of the drawbacks in the existing algorithms and our proposed improved algorithms can overcome these drawbacks. The experimental analyses have been carried out in order to achieve the efficiency of the proposed algorithms.

Fault Diagnosis of a Rotary Machine Based on Information Entropy and Rough Set

There exists some discord or contradiction of information during the process of fault diagnosis for rotary machine. But the traditional methods used in fault diagnosis can not dispose of the information. A model of fault diagnosis for a rotary machine based on information entropy theory and rough set theory is presented in this paper. The model has clear mathematical definition and can dispose both complete unification information and complete inconsistent information of vibration faults. By using the model, decision rules of six typical vibration faults of a steam turbine and electric generating set are deduced from experiment samples. Finally, the decision rules are validated by selected samples and good identification results are acquired.

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.

Lower Approximation Reduction in Ordered Information System with Fuzzy Decision

Attribute reduction is one of the most important problems in rough set theory. This paper introduces the concept of lower approximation reduction in ordered information systems with fuzzy decision. Moreover, the judgment theorem and discernable matrix are obtained, in which case an approach to attribute reduction in ordered information system with fuzzy decision is constructed. As an application of lower approximation reduction, some examples are applied to examine the validity of works obtained in our works..

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.

IMPROVED ACCURACY AND ROUGHNESS MEASURES FOR ROUGH SETS

Accuracy and roughness, proposed by Pawlak(1982), might draw a conclusion inconsistent with our intuition in some cases. This letter analyzes the limitations in these measures and proposes improved accuracy and roughness measures based on information theory.

Extension of information entropy-based measures in incomplete information systems

It is helpful for people to understand the essence of rough set theory to study the concepts and operations of rough set theory from its information view. In this paper we address knowledge expression and knowledge reduction in incomplete information systems from the information view of rough set theory. First, by extending information entropy-based measures in complete information systems, two new measures of incomplete entropy and incomplete conditional entropy are presented for incomplete information systems. And then, based on these measures the problem of knowledge reduction in incomplete information systems is analyzed and the reduct definitions in incomplete information system and incomplete decision table are proposed respectively. Finally, the reduct definitions based on incomplete entropy and the reduct definitions based on similarity relation are compared. Two equivalent relationships between them are proved by theorems and an in equivalent relationship between them is illustrated by an example. The work of this paper extends the research of rough set theory from information view to incomplete information systems and establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in incomplete information systems.

Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems

In this paper we address information measures of roughness of knowledge and rough sets for incomplete information systems. The definition of rough entropy of knowledge and its important properties are given. In particular, the relationship between rough entropy of knowledge and the Hartley measure of uncertainty is established. We show that rough entropy of know1edge decreases monotonously as granularity of information become smaller. This gives an information interpretation for roughness of knowledge. Based on rough entropy of knowledge and roughness of rough set. a definition of rough entropy of rough set is proposed, and we show that rough entropy of rough set decreases monotonousIy as granularity of information become smaller. This gives more accurate measure for roughness of rough set.

Generalized binary discernibility matrix for attribute reduction in incomplete information systems

To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.

A general approach to attribute reduction in rough set theory

The concept of a consistent approximation representation space is introduced. Many types of information systems can be treated and unified as consistent approximation representation spaces. At the same time, under the framework of this space, the judgment theorem for determining consistent attribute set is established, from which we can obtain the approach to attribute reductions in information systems. Also, the characterizations of three important types of attribute sets （the core attribute set, the relative necessary attribute set and the unnecessary attribute set） are examined.

General medical practice in China:evaluation of urban community health care service functions based on a rough set reduction theory

Objective:This study aims to achieve an empirical evaluation on the functional performances of urban community health care services in fi ve administrative districts of Nanchang city in China.Methods:In order to increase effectiveness,data collected from fi ve administrative districts of Nanchang city were processed to exclude redundant information.Rough set reduction theory was brought in to evaluate the performances of community health care services in these districts through calculating key indices’weighed importance.Results:Comprehensive evaluation showed the score rankings from high to low as Qing-yunpu district,Xihu district,Qingshanhu district,Donghu district,and Wanli district.Conclusion:The objective performance evaluation had actually reflected the general situation(including social-economic status)of community health care services in these administrative districts of Nanchang.Attention and practical works of community health service management were needed to build a more harmonious and uniform community health care service system for residents in these districts of Nanchang.

Attribute reduction in interval-valued information systems based on information entropies

Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.

An information-based rough set approach to critical engineering factor identification

In order to analyze the main critical engineering factors, an information-based rough set approach that considers conditional information entropy as a measurement of information has been developed. An algorithm for continuous attribute discretization based on conditional information entropy and an algorithm for rule extraction considering the supports of rules are proposed. The initial decision system is established by collecting enough monitoring data. Then, the continuous attributes are discretized, and the condition attributes are reduced. Finally, the rules that indicate the action law of the main factors are extracted and the results are explained. By applying this approach to a crack in an arch gravity dam, it can be concluded that the water level and the temperature are the main factors affecting the crack opening, and there is a negative correlation between the crack opening and the temperature. This conclusion corresponds with the observation that cracks in most concrete dams are influenced mainly by water level and temperature, and the influence of temperature is more evident.

Emergency Decision-Making Based on q-Rung Orthopair Fuzzy Rough Aggregation Information

With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.

一种基于粗糙熵的改进K-modes聚类算法

K-modes聚类算法被广泛应用于人工智能、数据挖掘等领域。传统的K-modes聚类算法有不错的聚类效果,但是存在迭代次数多、计算量大、容易受到冗余属性的干扰等问题,且仅采用简单的0-1匹配的方法来定义2个样本属性值之间的距离,没有充分考虑每个属性对聚类结果的影响。针对上述问题,该文将粗糙熵引入K-modes算法。首先利用粗糙集属性约简算法消除冗余属性,确定各属性的重要程度;然后利用粗糙熵确定每个属性的权重,从而定义新的类内距离。将该文所提算法与传统的K-modes聚类算法分别在4组公开数据集上进行对比试验。试验结果表明,该文所提算法聚类准确率比传统的K-modes聚类算法更高。