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Received: 2013-08-15

Revision Accepted: 2013-10-30

Crosschecked: 2014-06-16

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Journal of Zhejiang University SCIENCE C 2014 Vol.15 No.7 P.584-591

http://doi.org/10.1631/jzus.C1300217


A framework for analysis of extended fuzzy logic


Author(s):  Farnaz Sabahi, M.-R. Akbarzadeh-T

Affiliation(s):  Center of Excellence on Soft Computing and Intelligent Information Processing, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Corresponding email(s):   farna.sabahi@stu-mail.um.ac.ir, akbarzadeh@ieee.org

Key Words:  Extended fuzzy logic, Fuzzy logic, f-Transformation, S-answer, Validity


Farnaz Sabahi, M.-R. Akbarzadeh-T. A framework for analysis of extended fuzzy logic[J]. Journal of Zhejiang University Science C, 2014, 15(7): 584-591.

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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

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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