Families of the Granules for Association Rules and Their Properties

We employed the granule (or the equivalence class) defined by a descriptor in tables, and investigated rough set-based rule generation. In this paper, we consider the new granules defined by an implication, and propose a family of the granules defined by an implication in a table with exact data. Each family consists of the four granules, and we show that three criterion values, support, accuracy, and coverage, can easily be obtained by using the four granules. Then, we extend this framework to tables with non-deterministic data. In this case, each family consists of the nine granules, and the minimum and the maximum values of three criteria are also obtained by using the nine granules. We prove that there is a table causing support and accuracy the minimum, and generally there is no table causing support, accuracy, and coverage the minimum. Finally, we consider the application of these properties to Apriori-based rule generation from uncertain data. These properties will make Apriori-based rule generation more effective.10th International Conference, RSKT 2015, Held as Part of the International Joint Conference on Rough Sets, IJCRS 2015, November 20-23, 2015, Tianjin, Chin