A framework for analysis of extended fuzzy logic

Farnaz SABAHI; M.-R. AKBARZADEH-T

doi:10.1631/jzus.C1300217

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A framework for analysis of extended fuzzy logic

Computer & Automation | Updated：2022-05-19

- A framework for analysis of extended fuzzy logic
- 一种分析扩展模糊逻辑的架构
- Frontiers of Information Technology & Electronic Engineering Vol. 15, Issue 7, Pages: 584-591(2014)
- Affiliations：
  
  Center of Excellence on Soft Computing and Intelligent Information Processing, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
- Author bio：
  
  [ "SABAHI Farnaz, E-mail: farna.sabahi@stu-mail.um.ac.ir" ]
  [ "AKBARZADEH-T M.-R., E-mail:akbarzadeh@ieee.org" ]
- Funds：
- DOI：10.1631/jzus.C1300217
  CLC： TP273
- Received：15 August 2013，
  
  Revised：2016-;6-16，
  
  Published：2014-07
- Accepted：
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Farnaz SABAHI, M.-R. AKBARZADEH-T. A framework for analysis of extended fuzzy logic[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(7): 584-591.
DOI：

Farnaz SABAHI, M.-R. AKBARZADEH-T. A framework for analysis of extended fuzzy logic[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(7): 584-591. DOI： 10.1631/jzus.C1300217.

摘要

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。

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.

关键词

Keywords

references

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