Theoretic Research On The Methods Of Uncertainty Measures For Intervel-set Information Systems

Knowledge is a summary of experience collected from data by human beings.With the increasing of methods and amounts of data acquisition,how to acquire the valuable knowledge from the massive data correctly and accurately is one of the most important issues in the current fields of artificial intelligence.As an effective mathematical tool for dealing with uncertain and fuzzy information,rough set theory has been successfully applied to many research fields such as data analysis,data mining,knowledge acquisition and cluster analysis.In classical rough set model,data is in the form of an information system.In an information system,each object has several attribute values to explain the specific information of the object itself.Generally,the value of each attribute of each object is unique and complete.However,during the process of data acquisition,since the data missing,the data errors or the data incompleteness are induced by the methods of data acquisition,it is difficult to obtain a complete information system directly.Hence,the common single-valued information system is no longer suitable to represent this type of data.In order to represent this type of data more effectively,this paper considers interval sets as the attribute values of objects and constructs the interval-set information systems.The interval set is represented by a pair of lower bound and upper bound,which the elements in the lower bound represent the values definitely belong to the attribute and the elements in the upper bound represent the values possibly belong to the attribute.This fuzzy representation keeps the original information more completely and effectively than the single-valued representation.Uncertainty measurement is one of the most important research contents in rough set theory.Analyzing and discussing the uncertainty of information systems are helpful to mine the potential information and knowledge of data.Besides,uncertainty measurement has some important applications in attribute reduction and rule extraction.Based on rough set theory,this paper systematically studies the theoretical methods of uncertainty measurement in interval-set information systems.The mainly work and contributions are summarized as follows.(1)The uncertainty measurement of interval-set information tables is proposed.intervalset information tables,since the attribute values of objects are no longer single-valued or nominal,the equivalent relation or other similar relations in the classical rough set model are no longer considered as the indistinguishable relation between the objects.Aiming at the problem,from the perspective of the importance degree of attribute values in the lower bound and upper bound,this paper proposes a new binary relation based on the average importance degree of attribute values.Based on the similarity relation,the uncertainty measures are defined by using the methods of the standard rough set and the information theory.By combining the information theory and the rough set theory,four kinds of new joint measures are proposed finally and provide a novel sight for evaluating the uncertainty.Besides,the paper also proposes a twostage algorithm for transforming ordinary information tables to interval-set information tables.The algorithm provides a guarantee of data support for verifying the proposed measures and studying the attribute reduction and dynamic updating of interval-set information systems.(2)The uncertainty measurement of interval-set decision tables is proposed.In intervalset decision tables,each object has a unique decision attribute and a decision behaviour,which plays an important role in the decision applications.However,no one has studied the intervalset decision table and the associated uncertainty measures.Aiming at the problem,this paper firstly provides the definition of interval-set decision tables.Based on the proposed similarity relation considered the degree of interaction among attribute values of object,a rough set model of interval-set decision tables is established.On this basis,a new uncertainty measure combined with conditional information entropy is proposed.The new uncertainty measure not only solves the problem that the approximate accuracy and approximate roughness are not sensitive to the change of granularity,but also can measure the uncertainty caused by the rough classification,which makes it more reasonable and effective as the uncertainty of the interval-set decision tables.Experiments on UCI datasets show that the new measure achieves better performance than the approximate accuracy and approximate roughness on KNN classifier and PNN classifier,which provides favourable conditions for attribute reduction in interval-set decision tables.(3)The attribute reduction algorithms based on uncertainty measures are provided in intervalset decision tables.Considering the proposed uncertainty measures are monotonic,the reduct needs not to check all subsets,which can simplify the process of attribute reduction.Based on it,a new reduct is defined based on uncertainty measure,and the core attributes and attribute significance are defined as well.Then,two heuristic algorithms are developed based on the deletion strategy and the addition-deletion strategy respectively.At last,the algorithms are test on UCI datasets and show that the classification accuracy on KNN classifier by reduct is higher than that by no-reduct.Not only that,the reduct defined by the similarity relation based on the degree of interaction among attribute values of object has better performance than the reducts defined by other binary relations.(4)Four algorithms of dynamic updating approximate sets in interval-set information systems are developed.This paper analyzes the rules of the lower and upper approximate set when the data is updated frequently.Considering that when adding or deleting some objects and attributes,the original approximate sets will only partially change,and the size of the changing approximate sets is much smaller than that of the original approximate sets.Therefore,these algorithms only calculate the changed approximate sets,and obtain the updated approximate sets quickly by merging or differentiating with the original approximate sets.The theoretical time complexity analysis and experiments on UCI datasets show that the proposed algorithms have the lower time complexity and the higher efficiency than the static algorithms.