Generation of mass assignment with nested focal elements-computation of perceptual information processing (PIP)

A robust information processing method with respect to user's perceptions, named perceptual information processing (PIP), is studied. This method uses fuzzy sets representing concepts biased by perception and a soft computing method called mass assignment theory to manage consistencies between a histogram as actual data and a fuzzy set as a concept. In order to generate a fuzzy set from a mass assignment its focal elements must be nested, i.e. any focal element with fewer number of elements is subsumed to others with the larger one. This is problematic for PIP particularly for the aggregation of histograms at mass assignment level in conceptualization and refinement tasks. It is thus necessary to generate a fuzzy set from any mass assignment without nested focal elements. The reconstruction of a mass assignment with nested focal elements through the probability distribution of the one without them is studied.