Information fusion in order-2 fuzzy environments: A matrix transformation perspective

Order-2 information granules, as a representation of multi-layer structured information, have recently rekindled discussions. It is usually generated by abstracting order-1 information granules. When the dependence relationship and corresponding membership function of the order-1 information granules (reference information granules) are known, Pedrycz et al. used a method based on gradient optimization to complete the aggregation of the order-2 information granules. In this paper, we discuss a more specific scenario: not only the dependencies between reference information granules are captured, but also the order-1 information granules can be expressed as specific fuzzy information distributions. For this, we propose a fusion scheme of order-2 fuzzy sets based on matrix transformation called CQRP. To our knowledge, it is the first method that completely integrates the structural information of the order-2 environment into the fusion of order-2 fuzzy sets. In the process, we also creatively proposed the attraction and exclusion of structural information, deepening the understanding of structural information. Through sufficient comparison and analysis, we prove that it makes fuller use of information in the order-2 environment and is more reasonable and effective in tasks such as classification and identification.