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Front. Inform. Technol. Electron. Eng.  2014, Vol. 15 Issue (7): 584-591    DOI: 10.1631/jzus.C1300217
    
A framework for analysis of extended fuzzy logic
Farnaz Sabahi, M.-R. Akbarzadeh-T
Center of Excellence on Soft Computing and Intelligent Information Processing, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
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Abstract  We address a framework for the analysis of 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.

Key words： Extended fuzzy logic      Fuzzy logic      f-Transformation      S-answer      Validity     
Received: 15 August 2013      Published: 10 July 2014
CLC:  TP273  
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Farnaz Sabahi
M.-R. Akbarzadeh-T
Cite this article:

Farnaz Sabahi, M.-R. Akbarzadeh-T. A framework for analysis of extended fuzzy logic. Front. Inform. Technol. Electron. Eng., 2014, 15(7): 584-591.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1300217     OR     http://www.zjujournals.com/xueshu/fitee/Y2014/V15/I7/584


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。

关键词： 扩展模糊逻辑,  模糊逻辑,  f变换,  S解,  有效性 
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