Uncertainty Measurement And Attribute Reduction Of Interval-set Decision Information Systems

Rough set theory is an effective mathematical tool for uncertainty analysis and intelligent computing.In rough set theory,uncertainty measurement and attribute reduction are the core content and research hotspots.The uncertainty measurement can quantitatively describe the classification abilities of decision information systems.The attribute reduction can optimize decision information systems while maintaining the same classification abilities.Interval-set decision information systems extend classical decision information systems and have stronger information expression abilities,but its uncertainty measurement and attribute reduction are less studied.Therefore,this thesis makes a systematic study on the uncertainty measurement and attribute reduction of interval-set decision information systems,and the relevant work involves the following four aspects.(1)In the interval-set rough set model,the interval positive region and interval dependency degree for decision classification are defined,and the granulation monotonicity is proved.Based on the interval dependency degree,the attribute reduction is proposed,the inner/outer attribute significance is mined to become heuristic information,so a heuristic reduction algorithm is designed and analyze its time complexity.Finally,the correctness of the measures properties and the effectiveness of the reduction algorithm are verified by an example of interval-set decision information system.(2)The interval neighborhood granulation system is established by using the distance and radius between two objects,the conditional equivalence between the distance granulation and similarity characterization is proved,and the interval approximate roughness is obtained.The interval relative knowledge granularity is constructed from the classical relative knowledge granularity,and it is further fused with the interval approximate roughness,the interval approximate knowledge granularity is proposed and has good properties such as the granulation monotonicity.Based on the interval approximate knowledge granularity,the attribute reduction is proposed,the inner/outer attribute significance is mined to become heuristic information,so a heuristic reduction algorithm is designed and analyze its time complexity.Finally,the correctness of the measures properties and the effectiveness of the reduction algorithm are verified by an example of interval-set decision information system.(3)The relationship between “interval dependency degree attribute reduction” and “interval approximate knowledge granularity attribute reduction” is explored.For the consistent interval-set decision information system,the two attribute reductions are equivalent.However,for the inconsistent interval-set decision information system,“interval approximate knowledge granularity attribute reduction” is stronger than and different from “interval dependence attribute reduction”.The relevant conclusions are verified by an example of interval-set decision information system.(4)The UCI data experiments are carried out to verify the correctness of the relevant measurement properties,and then the effectiveness of the corresponding heuristic reduction algorithm is verified.As shown by experimental results,“interval approximation knowledge granularity attribute reduction” is superior to “interval dependence attribute reduction”.In summary,this thesis studies the dependency degree,approximate knowledge granularity and corresponding attribute reduction of interval-set decision information systems.The related results deepen dependency learning,knowledge learning and feature optimization,and they have significance to the knowledge discovery and rule derivation of interval-set decision information systems.