scholarly journals A Multimodal Retrieval and Ranking Method for Scientific Documents Based on HFS and XLNet

2022 ◽  
Vol 2022 ◽  
pp. 1-11
Author(s):  
Meichao Yan ◽  
Yu Wen ◽  
Qingxuan Shi ◽  
Xuedong Tian
Keyword(s):  
Fuzzy Set ◽  
Mathematical Expression ◽  
Ranking Method ◽  
Retrieval Models ◽  
Fuzzy Similarity ◽  
Mathematical Expressions ◽  
Multimodal Retrieval ◽  
Multimodal Information ◽  
Full Text Retrieval ◽  
Text Mode

Aiming at the defects of traditional full-text retrieval models in dealing with mathematical expressions, which are special objects different from ordinary texts, a multimodal retrieval and ranking method for scientific documents based on hesitant fuzzy sets (HFS) and XLNet is proposed. This method integrates multimodal information, such as mathematical expression images and context text, as keywords to realize the retrieval of scientific documents. In the image modal, the images of mathematical expressions are recognized, and the hesitancy fuzzy set theory is introduced to calculate the hesitancy fuzzy similarity between mathematical query expressions and the mathematical expressions in candidate scientific documents. Meanwhile, in the text mode, XLNet is used to generate word vectors of the mathematical expression context to obtain the similarity between the query text and the mathematical expression context of the candidate scientific documents. Finally, the multimodal evaluation is integrated, and the hesitation fuzzy set is constructed at the document level to obtain the final scores of the scientific documents and corresponding ranked output. The experimental results show that the recall and precision of this method are 0.774 and 0.663 on the NTCIR dataset, respectively, and the average normalized discounted cumulative gain (NDCG) value of the top-10 ranking results is 0.880 on the Chinese scientific document (CSD) dataset.

scholarly journals ANALISIS REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN MASALAH MATEMATIKA BERDASARKAN TAHAPAN KRULIK DAN RUDNICK DITINJAU DARI ADVERSITY QUOTIENT

KadikmA ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 25
Author(s):  
SETYA DEWI
Keyword(s):  
Data Analysis ◽  
Visual Representations ◽  
Mathematical Expression ◽  
Linear Program ◽  
Mathematical Representation ◽  
Verbal Representation ◽  
Mathematics Test ◽  
Mathematical Expressions ◽  
Collecting Methods ◽  
Verbal Representations

This research purpose to describe the mathematical representation abilities of students based on the Krulik and Rudnick stages in terms of students' AQ. This research type is qualitative descriptive research. The research location is in  SMAN Darussholah Singojuruh with the subjects of class XI MIPA 3 and XI MIPA 7 as many as 30 students. The data collecting methods used test and interview methods, with research instruments, such as Adversity Response Profile (ARP) questionnaire, mathematics test questions on linear program material, interview guidelines, and validation sheets. The subjects selected as interview respondents were two students from each level of AQ who had significant differences in ARP scores (scores between AQ Climber, Camper, and Quiter), as well as based on the timeliness and accuracy of students' answers. Based on the test result data analysis and interview data analysis, the following results were obtained, such as 1) Climber students could solve linear program questions based on Krulik and Rudnick stages coherently, and be able to used forms of verbal representations, visual representations, and mathematical expressions properly and correctly; 2) Camper students could solve linear program questions based on Krulik and Rudnick stages coherently but had not been able to use forms of verbal representations, visual representations, and mathematical expressions properly and correctly; 3) Quitter students had not been able to solve linear program questions based on Krulik and Rudnick stages correctly and had not been able to use their verbal representation, visual representation, and mathematical expression skills properly.  

Detecting and Normalizing Formulas in Electronic Literature Resources

2015 ◽  
Vol 740 ◽  
pp. 875-880
Author(s):  
Wei Xin Xu ◽  
Xue Dong Tian ◽  
Xin Fu Li
Keyword(s):  
Mathematical Expression ◽  
Electronic Literature ◽  
Unique Form ◽  
Format Conversion ◽  
Conversion Method ◽  
Mathematical Expressions ◽  
Matching Rules ◽  
Formula Recognition

Formulas exist in various kinds of documents with different formats. Extracting and normalizing them into a unique form are the precondition of mathematical retrieval. In this paper, an extraction and conversion method of formulas in Word documents is built for mathematical expression retrieval. Firstly, the mathematical expressions in Word documents are detected through the processing of OLE objects. Then, the matching rules of formula format conversion are defined. Finally, the extracted mathematical expressions in OMML format are converted into LaTeX format follow the defined rules and stored in a txt file. Furthermore, the formulas exist in MathType format are stored in bitmap documents and converted into LaTeX documents through formula recognition and reconstruction module. Experiments show the effectiveness of the designed approach.

Evaluation of Rolling Bearing Vibration Using Fuzzy Set Theory and Chaos Theory

2012 ◽  
Vol 424-425 ◽  
pp. 338-341 ◽  
Author(s):  
Xiao Chao Sun ◽  
Xin Tao Xia ◽  
Yan Bin Liu ◽  
Lei Lei Gao
Keyword(s):  
Phase Space ◽  
Set Theory ◽  
Fuzzy Set ◽  
Chaos Theory ◽  
Fuzzy Set Theory ◽  
Rolling Bearing ◽  
Similarity Coefficient ◽  
Vibration Acceleration ◽  
Fuzzy Similarity ◽  
Bearing Vibration

The optimal fuzzy similarity coefficient based on the phase space is proposed to evaluate the rolling bearing vibration acceleration generated by wear on the surface of the ring raceway. The phase space of the time series of the rolling bearing vibration acceleration is reconstructed via the chaos theory, the fuzzy similarity relation between the phase trajectories is established by the fuzzy set theory, and then the optimal fuzzy similarity coefficient is obtained through a reasonable choice of the embedding dimension and the delay. Experimental investigation shows that with the increase of the fault diameter, the optimal fuzzy similarity coefficient decreases nonlinearly

MATHEMATICAL REPRESENTATION OF A CHINESE CHARACTER AND ITS APPLICATIONS

2002 ◽  
Vol 16 (06) ◽  
pp. 735-747 ◽  
Author(s):  
XINGMING SUN ◽  
HUOWANG CHEN ◽  
LIHUA YANG ◽  
Y. Y. TANG
Keyword(s):  
Chinese Character ◽  
Mathematical Expression ◽  
Mathematical Representation ◽  
Chinese Characters ◽  
Chinese Information Processing ◽  
Mathematical Expressions ◽  
Library Network ◽  
Novel Method ◽  
Network Transmission ◽  
The Common

In this paper, a novel method to express Chinese characters mathematically is presented based on the knowledge of the structure of Chinese characters. Each Chinese character can be denoted by a mathematical expression in which the operands are components of Chinese characters and the operators are the location relations between the components. Five hundred five components are selected and 6 operators are defined to express all the Chinese characters successfully. These mathematical expressions of Chinese characters are simple, natural, and can be operated like the common mathematical expression of numbers. It makes Chinese information processing much simpler than before. This theory has been applied successfully in fonts automation, Chinese information transmission among different platforms and different operating systems on Internet, and knowledge discovery of the structure of Chinese characters. It can also be applied extensively to many areas such as typesetting, advertising, packing design, virtual library, network transmission, pattern recognition and Chinese mobile communication.

FUZZY SIMILARITY AND MEASURE OF SIMILARITY WITH LUKASIEWICZ IMPLICATOR

2008 ◽  
Vol 04 (02) ◽  
pp. 191-206 ◽  
Author(s):  
ISMAT BEG ◽  
SAMINA ASHRAF
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Measure ◽  
Fuzzy Similarity ◽  
Measure Of Similarity ◽  
Universe Of Discourse ◽  
Fuzzy Subsets

Given a universe of discourse X. A fuzzy similarity mapping ST,Inc : F(X) × F(X) → F(X) is defined, where F(X) denotes the set of all fuzzy subsets of X. Mapping ST,Inc maps two fuzzy sets A and B to a fuzzy set ST,Inc(A,B) in X called their fuzzy set of similarity. A measure of similarity between A and B is then obtained by applying the composite of fuzzy measure and fuzzy similarity mapping on the pair (A,B). Several properties of fuzzy set of similarity and the measure of fuzzy similarity are obtained within the framework of Lukasiewicz fuzzy implicator and its respective t-norm and t-conorm. Many examples of measure of similarity are also constructed.

A method for the formulation of Reynolds number functions

2000 ◽  
Vol 27 (4) ◽  
pp. 829-833 ◽  
Author(s):  
Ana Maria AF da Silva ◽  
Tirupati Bolisetti
Keyword(s):  
Reynolds Number ◽  
Sediment Transport ◽  
Flow Characteristics ◽  
Mathematical Expression ◽  
Open Channels ◽  
Strong Variation ◽  
Mathematical Expressions ◽  
Flow And Sediment Transport ◽  
Shields Curve ◽  
General Method

A general method for the formulation of flow characteristics which are functions of the Reynolds number of the system is presented. It is assumed that the flow characteristics exhibit a strong variation with the Reynolds number when the Reynolds number is "small," and that they become independent of it when the Reynolds number is "large." The method is illustrated by finding mathematical expressions for the experimentally determined "roughness" function curve and for the sediment transport initiation curve (Shields' curve), which are relevant for the analysis of flow and sediment transport in pipes and open channels. The two expressions thus obtained can be used in practice for computational purposes.Key words: Reynolds number functions, mathematical expression, roughness function, Shields' curve.

scholarly journals Significant Remote Sensing Vegetation Indices: A Review of Developments and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Jinru Xue ◽  
Baofeng Su
Keyword(s):  
Remote Sensing ◽  
Spectral Characteristics ◽  
Vegetation Indices ◽  
Growth Dynamics ◽  
Mathematical Expression ◽  
Advantages And Disadvantages ◽  
Light Spectra ◽  
Mathematical Expressions ◽  
Real World Applications ◽  
Application Requirements

Vegetation Indices (VIs) obtained from remote sensing based canopies are quite simple and effective algorithms for quantitative and qualitative evaluations of vegetation cover, vigor, and growth dynamics, among other applications. These indices have been widely implemented within RS applications using different airborne and satellite platforms with recent advances using Unmanned Aerial Vehicles (UAV). Up to date, there is no unified mathematical expression that defines all VIs due to the complexity of different light spectra combinations, instrumentation, platforms, and resolutions used. Therefore, customized algorithms have been developed and tested against a variety of applications according to specific mathematical expressions that combine visible light radiation, mainly green spectra region, from vegetation, and nonvisible spectra to obtain proxy quantifications of the vegetation surface. In the real-world applications, optimization VIs are usually tailored to the specific application requirements coupled with appropriate validation tools and methodologies in the ground. The present study introduces the spectral characteristics of vegetation and summarizes the development of VIs and the advantages and disadvantages from different indices developed. This paper reviews more than 100 VIs, discussing their specific applicability and representativeness according to the vegetation of interest, environment, and implementation precision. Predictably, research, and development of VIs, which are based on hyperspectral and UAV platforms, would have a wide applicability in different areas.

Processing of Queries with Fuzzy Similarity Domains

2015 ◽  
pp. 88-128
Author(s):  
Soraya O. Carrasquel ◽  
Ricardo R. Monascal ◽  
Rosseline Rodríguez ◽  
Leonid Tineo
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Data Model ◽  
Formal Semantics ◽  
Query Languages ◽  
User Preferences ◽  
Similarity Relation ◽  
Fuzzy Similarity ◽  
Type 3

There are some data models and query languages based on the application of fuzzy set theory. Their goal is to provide more flexible DBMS that allow the expression of user preferences in querying as well as imprecision in data. In this sense, the FuzzyEER data model proposes four kinds of fuzzy attributes. One of them, named Type 3, consists of a set of labels provided of a similarity relation. An extension of SQL, named FSQL, allows the expression and use of fuzzy attributes. Nevertheless, FSQL does not allow using fuzzy attributes in some clauses based on data ordering, due to semantics problem. This chapter presents a solution for this problem in case of Type 3 fuzzy attributes. Main contribution consists in how to process queries involving such attributes by means of an extension to an existing RDBMS. Formal semantics, grammar, catalogue definition and translation schemas are contained in this chapter.

scholarly journals A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method

Symmetry ◽  
2016 ◽  
Vol 8 (12) ◽  
pp. 153 ◽  
Author(s):  
Xiaodi Liu ◽  
Zengwen Wang ◽  
Shitao Zhang
Keyword(s):  
Fuzzy Set ◽  
Ranking Method ◽  
Hesitant Fuzzy Set
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