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Abstract: We address a framework for the analysis of fuzzy logic%29&ck%5B%5D=abstract&ck%5B%5D=keyword'>extended fuzzy logic (FLe) and elaborate mainly the key characteristics of FLe by proving several qualification theorems and proposing a new mathematical tool named the A-granule. Specifically, we reveal that within FLe a solution in the presence of incomplete information approaches the one gained by complete information. It is also proved that the answers and their validities have a structural isomorphism within the same context. This relationship is then used to prove the representation theorem that addresses the rationality of FLe-based reasoning. As a consequence of the developed theoretical description of FLe, we assert that in order to solve a problem, having complete information is not a critical need; however, with more information, the answers achieved become more specific. Furthermore, reasoning based on FLe has the advantage of being computationally less expensive in the analysis of a given problem and is faster.

一种分析扩展模糊逻辑的架构

研究目的：模糊逻辑的结论蕴含可证明为有效这一必要条件，而许多实际应用并不满足此条件。扩展模糊逻辑是在模糊逻辑基础上考虑有效性以满足此条件。目前扩展模糊逻辑理论描述相关工作很少。本文提出一种分析扩展模糊逻辑的架构，给出基于扩展模糊逻辑推理的数学描述。
创新要点：首次给出基于扩展模糊逻辑推理的数学描述。引入A-基粒（A-granule）的概念---A-基粒是保留f变换（f-transform）全部特性的最小基粒。
方法提亮：通过定理证明以及提出A-基粒概念，详细介绍了扩展模糊逻辑的关键特性。
重要结论：在扩展模糊逻辑中，不完整信息下的解接近完整信息下的解。在相同背景下，两种情形下的解与其有效性同构。由本文给出的扩展模糊逻辑理论描述可以明确，完整信息并非解决问题之必需，不过信息越充分，越能得到确切解。基于扩展模糊逻辑的推理，计算量小，速度快。
扩展模糊逻辑；模糊逻辑；f变换；S解；有效性

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