An efficient method of renewing object-induced three-way concept lattices involving decreasing attribute-granularity levels

In three-way concept analysis, changing (decreasing or increasing) attribute -granularity levels is needed to seek desirable information. Reconstructing three-way concept lattices often requires huge computation and long elapsed time when attribute -granularity levels are changed. To avoid this problem, a good strategy is indirectly renewing three-way concept lattices. Our paper studies how to renew object -induced three-way concept lattices involving decreasing attributegranularity levels. Firstly, we analyze changes of object -induced three-way concept lattices when attribute -granularity levels are decreased. To classify changes of object -induced threeway concepts, we classify these concepts into six categories, derive sufficient and necessary conditions of identifying these categories, and investigate their properties. To explore changes of covering relations among object -induced three-way concepts, we classify covering relations into three categories, and identify them by finding which are the destructors of deleted objectinduced three-way concepts before the decrease, and analyzing which are children concepts of object -induced three-way concepts as destructors after the decrease. Secondly, by using the above analysis results, we put forward a novel algorithm called OEL-Collapse to renew object -induced three-way concept lattices when attribute -granularity levels are decreased. Finally, experiments are conducted to illustrate the efficiency of the OEL-Collapse algorithm.