Properties and Data-driven Design of Perceptual Reasoning Method Based Linguistic Dynamic Systems
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摘要: 采用一型模糊集合的语言动力系统为复杂系统的建模、分析、评估及控制提供了一种有效工具.但正如已有二型模糊理论中指出的,在对具有强不确定性的语言词建模时采用二型模糊集合更为合理,因此,研究了采用二型模糊集合的语言动力系统,其推理过程基于感知推理方法来实现.首先,给出了基于感知推理方法的语言动力系统的一些基本性质,相关性质表明:基于感知推理方法的语言动力系统的输出词具有直观性,且当规则后件中的二型模糊集合满足一定条件时,该语言动力系统的运算复杂性将会大大简化.进一步,提出了基于感知推理方法的语言动力系统的数据驱动设计方案,该数据驱动方案采用粗糙集方法进行规则提取.最后,通过具体仿真实验验证了所提数据驱动方法的有效性及合理性.Abstract: 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.
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Key words:
- Computing with words /
- linguistic dynamic system /
- type-2 fuzzy /
- perceptual reasoning
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