Abstract
A relation is viewed as a granularity from a granular computing perspective. A classic rough set contains only one granularity. A multi-granulation rough set contains multiple granularities, which promotes the applications of classical rough set. Firstly, this paper uses the incomplete interval-valued decision information system (IIVDIS) as research object and constructs two rough set models in the light of single granularity rough set model for applying the rough set theory to real life more widely, which are optimistic multi-granulation rough set (OMGRS) model and pessimistic multi-granulation rough set (PMGRS) model in the IIVDIS. Secondly, we design two algorithms to compute the roughness and the degree of dependence that are two tools for measuring uncertainty of rough set. Finally, several experiments are performed on six UCI data sets to verify the validity of the proposed theorems.
Highlights
Pawlak raised rough set theory (RST) [1] in 1982, which has become a relatively complete system after more than thirty years of rapid development
We can utilize (a) and (b) to depict lower approximation and upper approximation of the multi-granulation rough set under optimistic situation. (c) and (d) are treated as main idea for defining approximations of the multi-granulation rough set under pessimistic circumstance
When all objects are classified by attribute set, we mainly study the degree of dependence in incomplete interval-valued decision information system (IIVDIS), which represents the percentage of objects that can be exactly classified into D j optimistically/pessimistically
Summary
Pawlak raised rough set theory (RST) [1] in 1982, which has become a relatively complete system after more than thirty years of rapid development. Many professors pretreated the data, and used the ideology of the classical RST to solve the problem These articles [27,28] adopted complete methods to study and deal with the incomplete information system. In practical problems, a discourse is divided by one relation, sometimes it will be divided by multiple relations Faced with this problem, the previously studied single-granularity rough set theory was powerless. Experts and professors have less researches on MGRS in incomplete interval-valued information systems. A single granularity rough set model is established based on the multi-threshold tolerance relation that is defined as the connection degree of Zhao’s [54] set pair analysis.
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