A statistical mining from objective data to subjective knowledge based on granular perception

The relation between objectivity and subjectivity has been explored for many centuries in many aspects of fields. Most of the approaches used to study their relationship focus on the qualitative research, which is very difficult to resolve a decision problem regarding the closeness of their relation. In this article, we devise a non-parametric statistical mechanism to resolve such decision problem. The mechanism utilises the notion of granular knowledge which is regarded as the product of subjective perception toward objective notions. To measure the degree of conversion, we associate the perception with three metrics, which in turn derive three norms. These norms would measure the degree of the conversion from objectivity to subjectivity. Then by taking the set of Bell partitions as our sample space, and three norms as our statistics, we could then construct their non-parametric distributions. Based on these distributions, we could then conduct the statistical testing whether the subjectivity of a given notion (or target) is significantly related to the objectivity of that notion (or target).