Feature Selection Based On Fuzzy Neighborhood Decision Entropies

Feature selection is a commonly used method for data analysis to reduce the dimensionality of data,and effective feature evaluation method is the basis and key of feature selection.The fuzzy neighborhood rough set is a relatively new mathematical model for dealing with uncertainty,and uncertainty measurement based on it can be used as a tool for feature evaluation.However,the construction of uncertainty measures on fuzzy neighborhood rough set is not perfect,especially measures discussed from the aspect of information representation are still very few.In order to mine better feature selection algorithms,the decision entropy uncertainty measurement system of fuzzy neighborhood rough sets is established and deepened through a composition of algebraic representation and information representation in this thesis;based on granular monotonicity of the measures,feature evaluation methods are proposed and feature selection algorithms are implemented.The main research contents involve the following two aspects:(1)Information function of algebraic fuzzy neighborhood roughness induces fuzzy neigh-borhood decision entropy of each fuzzy decision class;then natural integration of fuzzy neigh-borhood decision entropy of every decision class induces fuzzy neighborhood decision entropy of fuzzy decision classification,and fuzzy neighborhood relative decision entropy is proposed via further fusing fuzzy neighborhood dependency.Based on the granular monotonicity of fuzzy neighborhood relative decision entropy,the importance of feature is defined,then a fea-ture selection algorithm(FSMFNRDE)is designed.Correctness of properties and effective-ness of feature selection algorithm are verified by numerical examples and data experiments;compared with other existing feature selection algorithms,such as FNRS,FNGRS,FSMRDE,FSMFNRDE achieves generally better results.(2)The fuzzy neighborhood decision entropy is the composition of fuzzy neighborhood roughness and function1)()=7)2)₂(+1),and then it is hierarchically integrated,and no calculation overflow occurs in the process of hierarchical integration.Making full use of this structural advantage of fuzzy neighborhood decision entropy,our research extends it with the same structure and completes the fuzzy neighborhood decision entropy system.Firstly,three decision indexes are defined on the fuzzy neighborhood rough set;based on the fuzzy neigh-borhood decision index,then three basic fuzzy neighborhood roughness and a combined fuzzy neighborhood roughness are proposed,and then the fuzzy neighborhood decision entropy is expanded from one to four by composing the function1)()=7)2)₂(+1).After comparing the granulation monotonicity,the most obvious one of the four fuzzy neighborhood decision entropies is selected and applied to feature selection.In comparison with the algorithm F-SMFNRDE,the same or even better results can be achieved.In general,this thesis discusses the feature selection algorithm based on the uncertainty measurement of decision entropies of fuzzy neighborhood rough set.After the proof of related theories,the calculation of examples and the comparison of feature selection results,the algo-rithm proposed in this research is effective and has generally better feature selection effects,and it provides a new better method for data dimensionality reduction.This result also proves that the corresponding fuzzy neighborhood decision entropies are superior,and the applica-tion of decision entropy is promoted,and the decision entropy system has been enriched and deepened.