基于犹豫模糊权重的数学表达式检索

Retrieving Mathematical Expressions Based on Hesitant Fuzzy Weight

【目的】从大量数学表达式中检索出与查询表达式相似的表达式,并对检索结果排序。【方法】提取单个数学表达式的特征子式,利用犹豫模糊集理论计算每个特征子式的权重值;将属于同一表达式的子式权重值进行累加,计算表达式间的相似度得分,按照分数从高到低的顺序排列检索结果。【结果】从时间和相似度的角度进行分析,本文方法检索效率较高,检索结果较准确,本文排序方法的NDCG值最高为0.88,表明该排序方法较合理。【局限】本文排序方法并非完全面向数学表达式语义检索。【结论】引入犹豫模糊集计算子式权重能够更准确地检索出具有相同结构特征的数学表达式。

[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.