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

Abstract

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 attribute-granularity levels. Firstly, we analyze changes of object-induced three-way concept lattices when attribute-granularity levels are decreased. To classify changes of object-induced three-way 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 object-induced 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.