Optimal Scale Selections In Multi-scale Information Systems With Multi-scale Decisions

Granular computing is currently a popular research direction in the field of data mining and artificial intelligence,and it emphasizes analyzing and processing information from multiple granularities.Multi-scale data analysis is a research frontier in the field of granular computing.Data sets studied by multi-scale data analysis are multi-scale information systems,which are characterized by the fact that objects can have multiple values under the same attribute.Multi-scale information systems with multi-scale decision are a special class of multi-scale information systems,which have multiple scales for both conditional attributes and the decision attribute.Select some appropriate subsystems from a multi-scale information system with a multi-scale decision for final decision making and classification is a key issue in acquiring knowledge in thus a data set,and the process is called optimal scale selection.This dissertation investigates optimal scale selection for multi-scale information systems with a multi-scale decision,and quantitatively portrays the numerical characteristics of optimal scale selection by using information entropy.The main innovations are as follows:1.The concept of incomplete information systems with a multi-scale decision is proposed,and it is clarified that all scale selections constitute a complete lattice.The representation of information granules under different scale selections and their interrelationships are given using similarity relations.Optimal scale selection for consistent incomplete multi-scale information systems with a multi-scale decision is discussed,and an algorithm for searching all optimal scale selections is designed and the progress of seeking for optimal scale selections is shown with examples.2.Optimal scale selection and attribute reduction for Wu-Leung information systems with a multi-scale decision are investigated.Firstly,the concept of entropy-based optimal scale selection is defined in a consistent Wu-Leung information system with a multi-scale decision.The concept of local optimal scale selection based on entropy is further introduced and attribute reduction method based on the optimal scale selection is also explored.Furthermore,a method is given for transforming an inconsistent Wu-Leung information system with a multi-scale decision into a consistent Wu-Leung information system with a multi-scale decision by introducing generalized decision functions,and the corresponding optimal scale selection and attribute reduction methods are developed.Finally,the search algorithms for all optimal scale selections and one optimal scale selection are designed respectively.