基于区间值相似度的模糊推理算法

doi:10.12263/DZXB.20211085

电子学报 ›› 2022, Vol. 50 ›› Issue (11): 2738-2745.DOI: 10.12263/DZXB.20211085

基于区间值相似度的模糊推理算法

史宏艳, 罗敏霞

中国计量大学理学院，浙江杭州 310018

收稿日期:2021-08-13 修回日期:2022-01-10 出版日期:2022-11-25
- 作者简介:
- 史宏艳女, 1995年生于山西太原，硕士研究生，研究方向为区间值模糊推理算法.E-mail: S1908070108@cjlu.edu.cn
  罗敏霞（通讯作者）女， 1964年生于山西运城，教授、博士、硕士生导师，担任中国人工智能学会人工智能基础专业委员会常务委员；中国逻辑学会非经典逻辑与计算专委会委员；国际信息研究学会中国分会人工智能专业委员会专家委员.主要研究方向为计算机科学中的非经典逻辑、模糊推理算法与图像处理等. 先后在国际国内专业领域的期刊上发表论文120余篇，出版专著2部，教材1部.
- 基金资助:
- 国家自然科学基金 (12171445)

Fuzzy Inference Method Based on Interval-Valued Similarity Measure

SHI Hong-yan, LUO Min-xia

College of Sciences，China Jiliang University，Hangzhou，Zhejiang 310018，China

Received:2021-08-13 Revised:2022-01-10 Online:2022-11-25 Published:2022-11-19

摘要/Abstract

摘要：

模糊推理最基本的模型是模糊假言推理和模糊反驳推理. 本文是在区间值模糊集层面解决区间值模糊假言推理和区间值模糊反驳推理问题，给出基于区间值相似度的模糊推理算法. 首先，基于区间值 $t$ -可表示三角范数诱导的区间值剩余蕴涵,给出一种区间值相似度；其次，研究基于区间值相似度的模糊推理算法，给出算法解的表示形式；证明基于区间值相似度的模糊推理算法具有还原性；最后，研究基于区间值相似度的广义模糊推理算法. 本文提出的基于区间值相似度的模糊推理算法可应用于模式识别与多属性决策等领域.

关键词: 区间值模糊集, 区间值三角范数, 区间值剩余蕴涵, 区间值相似度, $t$ -可表示三角范数, 模糊推理算法

Abstract:

The basic models of fuzzy reasoning are fuzzy modus ponens and fuzzy modus tollens. The paper studies the problems of interval-valued fuzzy modus ponens and interval-valued fuzzy modus tollens at the level of interval-valued fuzzy sets, and propose fuzzy reasoning algorithms based on interval-valued similarity measure. Based on the interval-valued residuated implication induced by left-continuous interval-valued t-representable triangular norm, the interval-valued similarity measure is given. The fuzzy reasoning algorithms based on interval-valued similarity are further studied, and the representation of the algorithm solutions are given. Meanwhile, the fuzzy reasoning algorithms based on interval-valued similarity are proved to be reductive. Finally, the generalized fuzzy reasoning algorithms based on interval-valued similarity measure are studied. The fuzzy reasoning algorithms based on interval-valued similarity measure can be applied to the fields of pattern recognition and multi-attribute decision-making.

Key words: interval-valued fuzzy set, interval-valued triangular norm, interval-valued residuated implication, interval-valued similarity, $t$ -representable triangular norm, fuzzy reasoning algorithm

中图分类号:

O141.1

史宏艳, 罗敏霞. 基于区间值相似度的模糊推理算法[J]. 电子学报, 2022, 50(11): 2738-2745.

SHI Hong-yan, LUO Min-xia. Fuzzy Inference Method Based on Interval-Valued Similarity Measure[J]. Acta Electronica Sinica, 2022, 50(11): 2738-2745.

图/表 4

表1 A,A*和B的数据

	$x 1$	$x 2$	$x 3$
$A$	$[0.49,0.70]$	$[0.44,0.62]$	$[0.51,0.73]$
$A *$	$[0.15,0.40]$	$[0.30,0.55]$	$[0.10,0.35]$
	$y 1$	$y 2$	$y 3$
$B$	$[0.51,0.74]$	$[0.62,0.81]$	$[0.65,0.76]$

表1 A,A*和B的数据

	$x 1$	$x 2$	$x 3$
$A$	$[0.49,0.70]$	$[0.44,0.62]$	$[0.51,0.73]$
$A *$	$[0.15,0.40]$	$[0.30,0.55]$	$[0.10,0.35]$
	$y 1$	$y 2$	$y 3$
$B$	$[0.51,0.74]$	$[0.62,0.81]$	$[0.65,0.76]$

表2 区间值五蕴涵算法与区间值相似度算法的解(FMP)

方法		$y 1$	$y 2$	$y 3$
五蕴涵算法	$B *$	$[1.00,1.00]$	$[1.00,1.00]$	$[1.00,1.00]$
本文算法	$B *$	$[0.00,0.40]$	$[0.45,0.55]$	$[0.00,0.35]$

表2 区间值五蕴涵算法与区间值相似度算法的解(FMP)

方法		$y 1$	$y 2$	$y 3$
五蕴涵算法	$B *$	$[1.00,1.00]$	$[1.00,1.00]$	$[1.00,1.00]$
本文算法	$B *$	$[0.00,0.40]$	$[0.45,0.55]$	$[0.00,0.35]$

表3 A,A',A*,A'*和B,B'的数据

	$x 1$		$x 2$
$A$	$[0.49,0.70]$	$A'$	$[0.49,0.70]$
$A *$	$[0.15,0.40]$	$A' *$	$[0.95,0.99]$
	$y 1$		$y 2$
$B$	$[0.51,0.74]$	$B'$	$[0.51,0.74]$

表3 A,A',A*,A'*和B,B'的数据

	$x 1$		$x 2$
$A$	$[0.49,0.70]$	$A'$	$[0.49,0.70]$
$A *$	$[0.15,0.40]$	$A' *$	$[0.95,0.99]$
	$y 1$		$y 2$
$B$	$[0.51,0.74]$	$B'$	$[0.51,0.74]$

表4 区间值相似度模糊推理算法的解B*,B'*

	$B *$	$B' *$
$R (T 1, T 2) 1$	$[0.00,0.23]$	$[0.49,0.70]$
$R (T 1, T 2) 2$	$[0.02,0.40]$	$[0.49,0.74]$

表4 区间值相似度模糊推理算法的解B*,B'*

	$B *$	$B' *$
$R (T 1, T 2) 1$	$[0.00,0.23]$	$[0.49,0.70]$
$R (T 1, T 2) 2$	$[0.02,0.40]$	$[0.49,0.74]$

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基于区间值相似度的模糊推理算法

Fuzzy Inference Method Based on Interval-Valued Similarity Measure

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