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Data Analysis and Knowledge Discovery  2020, Vol. 4 Issue (7): 118-126    DOI: 10.11925/infotech.2096-3467.2019.1294
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Retrieving Mathematical Expressions Based on Hesitant Fuzzy Weight
Xu Yicong,Tian Xuedong(),Li Xinfu,Yang Fang,Shi Qingxuan
School of Cyber Security and Computer, Hebei University, Baoding 071002, China
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Abstract  

[Objective] This paper proposes a retrieval method for mathematical expressions, aiming to find items matching the queries from a large collection of math expressions.[Methods] Firstly, we extracted characteristic subformulas of each single mathematical expression and introduced the theory of hesitant fuzzy sets(HFSs) to compute their weights. Secondly, we added the weight values of all subformulas belonging to the same expression as the similarity scores between the index and query. Finally, we ranked retrieved results with the similarity scores.[Results] The proposed method had higher retrieval efficiency and better results than traditional methods, with the highest NDCG value reached 0.88.[Limitations] Our method did not fully address the semantics of mathematical expressions.[Conclusions] The proposed method could retrieve the needed mathematical expressions more accurately.
Key words： Mathematical Expressions Retrieval      HFSs      Weight of Subformula      Similarity Score     
Received: 02 December 2019      Published: 25 July 2020
ZTFLH:  TP393 G250  
Corresponding Authors: Tian Xuedong     E-mail: xuedong_tian@126.com
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Yicong Xu
Xuedong Tian
Xinfu Li
Fang Yang
Qingxuan Shi

Cite this article:

Xu Yicong,Tian Xuedong,Li Xinfu,Yang Fang,Shi Qingxuan. Retrieving Mathematical Expressions Based on Hesitant Fuzzy Weight. Data Analysis and Knowledge Discovery, 2020, 4(7): 118-126.

URL:

https://manu44.magtech.com.cn/Jwk_infotech_wk3/EN/10.11925/infotech.2096-3467.2019.1294     OR     https://manu44.magtech.com.cn/Jwk_infotech_wk3/EN/Y2020/V4/I7/118

The Process of Mathematical Expression Retrieval
subf md5-subf {ul,un,ulevel}
$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ B91DA5EC3DE8F0E3 {1.000,1.000,1.000}
$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ 82E1ED17885C94AD {0.941,0.857,1.000}
$-b \pm \sqrt{b^{2}-4 a c}$ EE207D7D9882D3AB {0.588,0.714,0.796}
$\sqrt{b^{2}-4 a c}$ 9099FE6F46BF69A5 {0.441,0.600,0.796}
$b^{2}-4 a c$ 965B906F4467622C {0.265,0.286,0.693}
$b^{2}$ F9DD6D7A16C781A2 {0.147,0.143,0.693}
-b A55F0819B2F990F6 {0.059,0.143,0.796}
Expression Information Description
Characteristic Subformula Inverted Index Structure
Mathematical Expression Retrieval and Matching Process
实验环境 配置
CPU型号 Intel(R)Core(TM) i7-7700, 3.6GHz
内存 8GB
操作系统 Microsoft Windows10
主要开发工具 Visual Studio2017, C#
模式 C/S
Development Environment
文档数量(篇) 数学表达式数量(个) 索引总大小(MB) 建立耗时
(ms)
1 024 1 908 0.47 0.501
10 240 115 797 24.92 15.411
20 480 251 018 55.13 32.603
31 741 391 955 82.96 79.957
Index File Size
索引中数学表达式数量(个) 索引文件大小(MB) 索引建立耗时
(ms)
1 000
10 000
100 000
138 539		 0.13
3.78
48.21
74.99		 0.070
1.641
26.540
33.909
Index File Size of Literature[6]
Retrieval Time of Different Methods
NDCG Value Comparison
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