TY - JOUR
A2 - Yang, Xibei
AU - Zhang, Qinghua
AU - Wang, Jin
AU - Wang, Guoyin
AU - Hu, Feng
PY - 2014
DA - 2014/08/11
TI - Approximation Set of the Interval Set in Pawlak's Space
SP - 317387
VL - 2014
AB - The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory.
SN - 2356-6140
UR - https://doi.org/10.1155/2014/317387
DO - 10.1155/2014/317387
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -