University of Ostrava Institute for Research and Applications of Fuzzy Modeling Logical Structure of Fuzzy IF-THEN Rules
University of Ostrava Institute for Research and Applications of Fuzzy Modeling Logical Structure of Fuzzy IF-THEN Rules
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发表时间：
2005
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通讯作者：
Vilém Novák;S. Lehmke
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作者：
Vilém Novák;S. Lehmke
本文为模糊IF-THEN规则操作提供了逻辑基础。我们的理论是足够广泛的，它不仅包括找到一个结论的手段，推理的组合规则，由于Lotfi A。Zadeh，而且还有其他种类的近似推理方法，例如基于感知的演绎，只要存在在形式逻辑系统中表征它们的可能性。与采用多值一阶逻辑变体的其他方法相比，这里提出的方法采用V. Novák的模糊类型理论，该理论具有足够的表达能力，可以以紧凑，优雅和合理的形式呈现基本概念和结果。在这里开发的有效的形式化表示，基于一个完整的逻辑系统，它是可能的，以重建许多著名的性能的CRI相关的模糊推理方法，虽然不是从分析的角度来看，通常提出的，但作为正式的派生的逻辑系统。作者有信心，最终所有相关的知识模糊推理方法的基础上模糊IF-THEN规则库将表示，形式化和支持的证据，在这里提出的有理有据的逻辑表示。这种方法的一个直接的积极后果是，突然之间，基于模糊IF-THEN规则的模糊推理方法的所有元素都是表示的“一等公民”：模糊IF-THEN规则库是一致的、完整的或独立的，有清晰的、逻辑上成立的定义。
This paper provides a logical basis for manipulation with fuzzy IF-THEN rules. Our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to Lotfi A. Zadeh but also other kinds of approximate reasoning methods, e.g. perception-based deduction, provided that there exists a possibility to characterize them within a formal logical system. In contrast with other approaches employing variants of multiple-valued first order logic, the approach presented here employs fuzzy type theory of V. Novák which has sufficient expressive power to present the essential concepts and results in a compact, elegant and justifiable form. Within the effectively formalized representation developed here, based on a complete logical system, it is possible to reconstruct numerous well-known properties of CRI-related fuzzy inference methods, albeit not from the analytic point of view as usually presented, but as formal derivations of the logical system employed. The authors are confident that eventually all relevant knowledge about fuzzy inference methods based on fuzzy IF-THEN rule bases will be represented, formalized and backed up by proof within the well-founded logical representation presented here. An immediate positive consequence of this approach is that suddenly all elements of a fuzzy inference method based on fuzzy IF-THEN rules are ‘first class citizens ́ of the representation: There are clear, logically founded definitions for fuzzy IF-THEN rule bases to be consistent, complete, or independent.