Attribute Reduction Of Variable Precision Fuzzy Rough Sets Based On Misclassification Cost And Self Information Measure

Rough set theory is a mathematical tool proposed by Pawlak in the 1980 s,which can quantitatively analyze and deal with imprecise,inconsistent and incomplete information and knowledge.Variable precision fuzzy rough set is an extension of Pawlak's classical rough set.It can deal with uncertain information and improve the anti-interference of data to noise,so as to reduce the possibility of wrong decision-making.Attribute reduction is one of the core problems in rough set theory.It is a process to delete redundant attributes in order to simplify the original information system without affecting the classification ability of the information system.The core step of attribute reduction is to construct the attribute evaluation function used to measure the classification ability of attribute subsets.However,due to the different requirements in practical application and the limitations of various conditions,the existing attribute reduction methods will have some limitations,resulting in the reduction results are not optimal.Therefore,the research and discussion of more effective and targeted attribute evaluation function and attribute reduction methods have much practical significance,and more and more scholars pay attention to it.Based on variable precision fuzzy rough set,this paper defines two attribute evaluation functions and explores two attribute reduction methods.The research findings and innovations are as follows:(1)The minimum misclassification degree under fuzzy background is defined,and the decision-making process is introduced into the variable precision fuzzy rough set model.On this basis,the calculation method of misclassification cost is given,and its related properties are studied.(2)Taking the misclassification cost as the attribute evaluation function,a heuristic attribute reduction algorithm is proposed,and the result of attribute reduction and misclassification cost are analyzed.(3)Three decision indexes are given in the variable precision fuzzy rough set model,and three decision precision and roughness are defined.The relationship between the three decision precision,roughness and attribute subset and threshold is studied respectively,and then,three kinds of self-informations are defined and their related properties are studied.(4)This paper presents a method to find the accuracy threshold value with the strongest ability to describe the classification of attribute subsets,proposes a heuristic attribute reduction algorithm based on self-information measure,and then studies the classification accuracy of attribute subsets obtained by attribute reduction through this algorithm.