Properties and Data-driven Design of Perceptual Reasoning Method Based Linguistic Dynamic Systems

The linguistic dynamic systems (LDSs) based on type-1 fuzzy sets can provide a powerful tool for modeling, analysis, evaluation and control of complex systems. However, as pointed out in earlier studies, it is much more reasonable to take type-2 fuzzy sets to model the existing uncertainties of linguistic words. In this paper, the LDS based on type-2 fuzzy sets is studied, and its reasoning process is realized through the perceptual reasoning method. The properties of the perceptual reasoning method based LDS (PR-LDS) are explored. These properties demonstrated that the output of PR-LDS is intuitive and the computation complexity can be reduced when the consequent type-2 fuzzy numbers in the rule base satisfy some conditions. Further, a data driven method for the design of the PR-LDS is provided. At last, the effectiveness and rationality of the proposed data-driven method are verified by an example.