A New Granular Computing Model Based on Qualitative Criterion Topological Space

Abstract

It was discussed that the way to reflect the internal relations between judgment and identification, the two most fundamental ways of thinking or cognition operations, during the course of granular information processing. Although it is conducive for the establishment of classical logic to emphasize the certainty of judgment while excluding uncertain identification from the logical category, from the objective point of view, such practice cut off the internal relations between judgment and identification, which is very unfavorable for the study of thinking or cognitive science and artificial intelligence. Matters reflect their state, movement and change process by means of their attributes and change process. Taking attributes and their change processes as the center, the method defines the criterion change operation in the criterion topological space, and further defines the basic information granules composed by attributes and criterions of matters, and provides the computing rules. The results show that this method can not only reflect the thinking process of the judgment with uncertain identification, but also express the transformation process amongst granules through the definition of qualitative mapping, so as to endow granular information processing with general sense in the process of thought expressing.