Knowledge Granularity for Continuous Parameters

In the community of Granular Computing, knowledge is interpreted as one classification ability of realistic or abstract objects. Generally, the concept of granularity is used for characterizing such an ability, which has been widely explored in literatures. To calculate the parameterized granularity, a naive approach is to find the granularity in terms of the parameter one by one. Nevertheless, such approach can only generate the single parameter based knowledge granularity, and the difference of knowledge granularities among different parameters may be slight. It follows that the knowledge granularity derived from single parameter may be lack of representativeness. In this paper, the continuous parameters based knowledge granularity is proposed, and the corresponding calculation approach is presented. Inspired by the thinking of definite integral in mathematical problems, the calculation approach is mainly implemented by following steps: firstly, the graph formed by granularity and parameter interval is divided into several small rectangles whose length of interval tends to be 0; secondly, the sum of area values of all the small rectangles is calculated; finally, the obtained area value divided by the whole length of parameter interval can be considered as the continuous parameters based knowledge granularity. This study suggests a new trend of handling problems related to knowledge from the viewpoint of continuity.