Optimal Scale Combination Selection In Interval-valued Generalized Multi-scale Decision Systems

Based on the idea of multi-granularity,the multi-scale data analysis model analyzes and processes data from different angles and levels.It can better solve the problem of knowledge discovery and representation of specific complex data in reality.Intervalvalued information system,as an extended form of single-valued information system,can better describe the phenomenon and reflect the uncertainty of information.Therefore,it is of certain significance to introduce interval value into generalized multi-scale decision systems for knowledge discovery.(1)In the beginning,we construct interval-valued generalized multi-scale decision systems.Then,the Jaccard similarity is generalized to calculate the similarity between objects under multiple attributes.According to the ideas of rough set theory,-tolerance relation is constructed to form the concepts of upper approximation and lower approximation,and the basic properties of their production are discussed.Five objective functions of the interval-valued generalized multi-scale decision systems are defined,namely upper approximation distribution,lower approximation distribution,plausibility distribution,belief distribution and probability distribution.The optimal scale combinations obtained based on different objective functions.(2)In consistent interval-valued generalized multi-scale decision systems,it is proved that there is equivalence between the optimal scale combinations obtained according to the five distributions.When the number of attributes or scales increases,the problem of explosion of scale combination is faced.Therefore,according to the structure of the Hasse diagram,a method is proposed to select the optimal scale combination.Then,the proposed method and the existing methods are compared and analyzed experimentally.(3)Based on the inconsistent situation,the relationship between the optimal scale combinations obtained by the five distribution functions are discussed in a specific threshold range.Given a threshold ,we can find an interval in which the threshold is located such that the optimal scale combinations obtained in this interval is the same obtained by the threshold.Then the proposed method and the existing methods are further applied to the experiment,and the applicability of these methods is discussed.