The Approximation And Combination Of Interval Structures

This paper proposes a method of the approximation and combination of interval structures, based on a basic set assignment. In order to obtain inner and outer clustering approximations of interval structures, the weak and strong inclusion relations of a basic set assignment firstly are introduced, and it is proved that strong inclusion is weak inclusion. Secondly, a clustering approach is provided for yielding strong inner and outer approximations of a basic set assignment, thus the approximation of interval structures is constructed. Lastly, give an example to illustrate the clustering approximation of rough sets.In the other hand, a conjunctive combination of a basic set assignment is discussed by the cylindrical extensions of a basic set assignment. So a conjunctive combination of interval structures can be defined, making use of one-to-one correspondence between a basic set assignment and an interval structure. Then, the Dempster-Shafer's combination rule is compared with the conjunctive combination of interval structures, and it is proved that the Dempster-Shafer's combination rule can be a numerical expression of the conjunctive combination of interval structures under a reasonable case.