Mathematical Expression Retrieval Model Based On Hesitant Fuzzy Weight

The spatial hierarchy formed by the arrangement and combination of a variety of mathematical symbols serves as an important mark that distinguishes mathematical expressions from general texts.It makes the retrieval of mathematical expression become a difficult problem in the field of information retrieval.Therefore,it is urgent to develop retrieval theories and methods that can well adapt to the characteristics of mathematical expressions.Based on the analysis and induction of the characteristics of mathematical expressions,the key issues of feature extraction,index construction,and matching and ranking of mathematical expression retrieval models are studied.A mathematical expression retrieval method based on the characteristics of operators is designed.It is extended to make use of the advantages of hesitant fuzzy sets in solving multi-attribute and multi-membership classification problems,and a mathematical expression retrieval model based on hesitant fuzzy weights is proposed.First,the sub formula is extracted and its feature code is constructed.Then,the comprehensive hesitant fuzzy membership degree evaluation is conducted on the length,the operator number and the level of the sub formula,and the hesitant fuzzy weight value to each sub formula is assigned.Both the feature code and weight are added in the inverted index.In the retrieval process,the same parsing process for the target expression is done.Finally,the hesitant fuzzy similarity score is calculated by accumulating the weight values,and the retrieval results are output in an orderly manner to realize the mathematical expression retrieval.Experiments are carried out on a dataset of 31,742 scientific documents and 519588 LaTeX mathematical expressions obtained from the public data set in the field of mathematical information retrieval.The experimental results show that the retrieval time of the proposed method is within the acceptable range,and the maximum value of the ranking rationality index is 0.811,proving that the proposed model is able to retrieve mathematical expression reasonably.