Uncertainty Study Based On Multi-threshold Tolerance Relation

There are a lot of information in life,some of which are uncertain information.Correspondingly,the amount of data and information in various fields will increasingly rising,so does the ability of people to collect data.However.the data incompleteness is caused by dealing w ith a great deal of data.Hence.there is an urgent need for theories and methods that can handle data with imprecise and incomplete characteristics.Rough set theory can solve the problem of uncertain information.At the same time.data storage,data omission and other reasons will cause data incompleteness,which extends classical information system to incomplete interval-valued decision information system(IIvDIS).From the perspective of granular computing,a binary relationship in an information system is considered as a granularity.Two precise concepts(upper approximation and lower approximation)can be used to describe the uncertain concept.and the concept is uncertain because of the existence of boundary regcion.Firstly.this paper defines a new binary relation on the universe based on the set pair analysis theory in order to facilitate the classification of objects.namely multi-threshold tolerance relation.And a single granularity rough set(SGRS)is established and its relevant properties are studied in the incomplete interval-valued decision information system.Secondly,incremental learning technique can acquire approximate sets under dynamic data.Methods and algorithms are provided to calculate approximate sets.Finally.two multi-granulation rough set models are constructed to research problems from the point of multi-view.The main innovations of this paper are described as follows:1.The similarity degree of the interval is combined with the set pair analysis theory to define a multi-threshold tolerance relation in IIvDIS.The relation is used to approximate the uncertain concept.and then a single granularity rough set model is established and its elementary properties are studied.In addition.the uncertainty research theory is enriched by utilizing the roughness and the degree of dependence in single granularity rough set.2.The IIvDIS is viewed as the researching background in the SGRS model.Same concept(a subset of the universe)will also changes as objects increase or decrease over time.Several methods and algorithms are presented for statically/dynamically solving approximate sets when attribute set remains unchangced.The experimental results show the advantages of proposed dynamic algorithms.3.Based on the multi-view characteristics of granular computing.multi-granulation rough set(MGRS)models are established:optimistic multi-granulation rough set(OMGRS)model and pessimistic multi-granulation rough set(PMGRS)model.The properties of these two rough sets are researched and the relationships with SGRS are explored.And then relations are discussed between uncertainty measurement methods of MGRS and SGRS.Finally,some UCI data sets were selected for performing experiments to verify the correctness of proposed theorems.