In the decision analysis, due to the fuzziness, complexity and uncertainty of human thinking and objective things, decision-makers often cannot give accurate values when making judgements on things by pairwise comparison. Herrera et al. [1,2] noted the concept of using linguistic information to express evaluation results. The linguistic judgement matrix has become an important information form for decision-makers to compare objects. However, it is also important whether the linguistic judgement matrix is consistent before the decision-maker gives the judgement result. At present, the research in this field has attracted the extensive attention of scholars and achieved some results [3,4,5,6,7,8]. The number of illogical objects is found by constructing the directed graph, and then the satisfactory consistency degree of linguistic judgement is calculated ; this problem is solved by deriving the compatibility of matrix and weight matrix .
Many achievements on the consistency of linguistic judgement matrix have been obtained [9,10,11,12,13,14,15,16]. From the current research results, few scholars directly use the definition to determine the satisfactory consistency of the linguistic judgement matrix. Most scholars use graph theory knowledge or define a preference relation matrix to determine the satisfactory consistency of the linguistic judgement matrix. Whether the diagonal element of the reachable matrix is 0 was used to determine whether the linguistic judgement matrix has satisfactory consistency . A method for determining the satisfactory consistency of the linguistic judgement matrix was established by using the concepts of the derived matrix and preference relation matrix . The linguistic judgement matrix and graph theory were linked together to solve the problem of satisfactory consistency of linguistic judgement matrix with no difference between two objects . Fan  used the concept of the induced matrix to transform the linguistic judgement matrix into a quantitative matrix to solve this problem. However in these methods, multiple matrices are required to be multiplied. Based on the former, this paper also uses the preference relation matrix to analyse the satisfactory consistency of the linguistic judgement matrix, but it is different. It proposes the concepts of the equivalent scheme, row preference value, column preference value, and standard 0-1 permutation matrix. This paper also presents a method to determine the satisfactory consistency of the linguistic judgement matrix. The method not only solves the problem of satisfactory consistency but is also simple and effective.
However, only judging whether the linguistic judgement matrix is consistent cannot meet the requirements of decision-makers. In recent years, some achievements have been made in other aspects of the linguistic judgement matrix [17,18,19,20,21,22,23,24,25,26]. Definitions of the consistency, acceptable incompleteness and complete consistency of the linguistic judgement matrix are given as well as a method for ranking alternatives . A new proof method is given in reference . It proves that if the judgement matrices given by each decision-maker were acceptable, then their weighted geometric average judgement matrices were also acceptable. For uncertain linguistic multi-attribute decision-making problems with incomplete weight coefficients, an optimisation model was established by transforming uncertain linguistic information into trapezoidal fuzzy numbers to obtain scheme weight coefficients . The definition and properties of binary intuitionistic fuzzy language preference information are given, and a ranking method based on binary intuitionistic fuzzy language preference information is proposed . Pang  compared the preference information of individuals and groups and measured the influence of the preference information of individuals and groups on decision-making from three evaluation indicators of consistency, closeness and monotonicity. Hsu  used the direct and indirect pairwise comparison rules to construct a multi-criteria incomplete language preference relationship model to solve the problem of increasing solutions and decreasing consistency.
This paper discusses the method to determine and adjust the satisfactory consistency of the linguistic judgement matrix with strict preference relation between two objects. In this paper, the satisfactory consistency of the linguistic judgement matrix can be modified by using whether the 0-1 permutation preference relation matrix of the linguistic judgement matrix is an upper triangular matrix, and then the three objects for forming a circular circle of judgement results are found by using the cyclic matrix. Using the size of the row preference value to modify the cyclic circle, the 0-1 type permutation preference relation matrix with satisfactory consistency is obtained. Finally the linguistic judgement matrix with satisfactory consistency is obtained.
Orderliness: when Inverse operation neg: neg( Maximisation operation: if Minimisation operation: if
Inverse operation neg: neg(
Maximisation operation: if
Minimisation operation: if
[11,12] A linguistic judgement matrix on the finite object set
In the linguistic judgement matrix, if
According to the meaning of the objects in the linguistic term set, we can know that the objects in the linguistic judgement matrix have the following properties:
If If If
A preference relation matrix of the linguistic judgement matrix on the finite object set
In the preference relation matrix
A linguistic judgement matrix
In the last section, the definition of the linguistic judgement matrix is given, and the definitions of the equivalent scheme, the row preference value and the column preference value, and the preference relation matrix are proposed. On the basis of comparison of each object, the method to determine the satisfactory consistency of the linguistic judgement matrix is given, and the ranking method is also given.
For example: if
According to the example above_St can be concluded that the 0-1 permutation preference relation matrix of the preference relation matrix is not unique.
For example, the following matrices are the standard 0-1 permutation matrices:
First, we prove the necessity. According to definition 2.5, if Then,
From equation (2), it can be concluded that,
First, we prove the necessity. According to definition 2.5, if
From equation (2), it can be concluded that,
The corresponding 0-1 permutation preference relation matrix is
It can be seen from the above that when the linguistic judgement matrix has satisfactory consistency, its 0-1 permutation preference relation matrix is the standard 0-1 permutation matrix.
Second, we prove the sufficiency. Let
Suppose the object
From the above proof, it can be concluded that the 0-1 permutation preference relation matrix is an upper triangular matrix when Step 1: Write the corresponding preference relation matrix according to the linguistic judgement matrix; Step 2: Write the 0-1 permutation preference relation matrix according to the preference relation matrix; Step 3: Judge whether the 0-1 permutation preference relation matrix is the standard 0-1 permutation matrix; Step 4: If it is an upper triangular matrix, it has a strict preference relationship; otherwise, proceed to the next step; Step 5: If it is a standard 0-1 permutation matrix, Step 6: Judge the end.
Step 1: Write the corresponding preference relation matrix according to the linguistic judgement matrix;
Step 2: Write the 0-1 permutation preference relation matrix according to the preference relation matrix;
Step 3: Judge whether the 0-1 permutation preference relation matrix is the standard 0-1 permutation matrix;
Step 4: If it is an upper triangular matrix, it has a strict preference relationship; otherwise, proceed to the next step;
Step 5: If it is a standard 0-1 permutation matrix,
Step 6: Judge the end.
According to the above judgement method, we can judge whether a linguistic judgement matrix has satisfactory consistency or not. At the same time, we can also get a ranking method of objects. The specific steps are as follows:
Step 1: Judge whether the linguistic judgement matrix given by the decision-maker has satisfactory consistency; Step 2: If there is no satisfactory consistency, it will be returned to the decision-maker for adjustment until satisfactory consistency is obtained; Step 3: If there is satisfactory consistency, write the 0-1 permutation preference relation matrix of the linguistic judgement matrix, that is, the standard 0-1 permutation matrix; Step 4: Judge the advantages and disadvantages of the scheme according to the standard 0-1 type permutation matrix; Step 5: Get the sequence of advantages and disadvantages of the object.
Step 1: Judge whether the linguistic judgement matrix given by the decision-maker has satisfactory consistency;
Step 2: If there is no satisfactory consistency, it will be returned to the decision-maker for adjustment until satisfactory consistency is obtained;
Step 3: If there is satisfactory consistency, write the 0-1 permutation preference relation matrix of the linguistic judgement matrix, that is, the standard 0-1 permutation matrix;
Step 4: Judge the advantages and disadvantages of the scheme according to the standard 0-1 type permutation matrix;
Step 5: Get the sequence of advantages and disadvantages of the object.
Following Definition 3.2 and Theorem 3.1, the conclusion can be easily derived.
The secondary sub-formulas of the 0-1 permutation preference relation matrix of linguistic judgement matrix are called the cyclic circle matrix, if they have the following form:
The cyclic circle matrix is the secondary sub-formula of the 0-1 permutation preference relation matrix, which is not necessarily true in reverse. There is only one element of the cyclic circle matrix in the main diagonal of the 0-1 permutation preference relation matrix, and the comparison relationship between the objects and the original linguistic judgement matrix remains unchanged. The comparison result of the three objects constituting the cyclic circle matrix is cyclic, and the cyclic circle matrix composed of the three objects can be the above four forms.
First, we prove the sufficiency. If there is a cyclic circle matrix in the 0-1 permutation preference relation matrix of the linguistic judgement matrix, it shows that the comparison results of the three objects are a cycle circle. Therefore, the comparison results of the objects are not transitive, and the linguistic judgement matrix is not of satisfactory consistency. Second, we prove the necessity. According to theorem 1, the linguistic judgement matrix has strict preference relation between two objects, then its 0-1 permutation preference relation matrix
First, we prove the sufficiency. If there is a cyclic circle matrix in the 0-1 permutation preference relation matrix of the linguistic judgement matrix, it shows that the comparison results of the three objects are a cycle circle. Therefore, the comparison results of the objects are not transitive, and the linguistic judgement matrix is not of satisfactory consistency.
Second, we prove the necessity. According to theorem 1, the linguistic judgement matrix has strict preference relation between two objects, then its 0-1 permutation preference relation matrix
Discussing circular circle matrix of
Discussing the cyclic circle matrix of
It is discussed that there is an element of 1 in the lower semi-triangular matrix, and the corresponding element is 0 in the upper triangular matrix of the 0-1 permutation preference relation matrix. Since 1 of the lower triangular matrix and 0 of the corresponding upper semi-triangular matrix are the results of the same pair of scheme comparison, the 0 element in the upper triangular matrix is no longer discussed. Theorem 2 is proved.
From Theorem 2, we get a method to judge whether the linguistic judgement matrix has satisfactory consistency. At the same time, we also find out the circle composed of three objects. If we modify the circle formed, we can get the order of the objects. Now, we give the criteria of correcting the circulation circle:
If the row preference values of the three objects are not equal, the one with the smallest row preference value is regarded as the worst object among the three objects; If the row preference values of two objects are equal and less than that of the other object, the object corresponding to the row with element 1 in the lower triangular matrix is recorded as the worst object; If the row preference values of the three objects are equal, the sum of the subscripts of the linguistic phrases in the linguistic judgement matrix is compared, and the one with the smallest subscript sum is regarded as the worst object among the three objects; if the sum of subscripts is equal, according to the comparison results with the optimal object, the worst one is marked as the worst one.
If the row preference values of the three objects are not equal, the one with the smallest row preference value is regarded as the worst object among the three objects;
If the row preference values of two objects are equal and less than that of the other object, the object corresponding to the row with element 1 in the lower triangular matrix is recorded as the worst object;
If the row preference values of the three objects are equal, the sum of the subscripts of the linguistic phrases in the linguistic judgement matrix is compared, and the one with the smallest subscript sum is regarded as the worst object among the three objects; if the sum of subscripts is equal, according to the comparison results with the optimal object, the worst one is marked as the worst one.
After finding the worst object, if the cyclic circle is
The specific steps of judgement and correction are given as follows:
Step 1: Give the preference relation matrix of linguistic judgement matrix; Step 2: 0-1 permutation preference relation matrix of linguistic judgement matrix is given; Step 3: Judge whether the 0-1 permutation preference relation matrix is an upper triangular matrix; if the linguistic judgement matrix has satisfactory consistency, the judgement ends, otherwise proceed to the next step; Step 4: Find the cyclic matrix in the 0-1 permutation matrix, and get the objects of forming the cyclic matrix; Step 5: According to the principle of modified cycle, the first cycle is modified to obtain the modified 0-1 permutation preference relation matrix; Step 6: Rearrange the 0-1 permutation preference relation matrix and turn to step 3; Step 7: According to the principle of determining the comparison results, the modified linguistic judgement matrix is obtained; Step 8: Get the ranking of the objects; Step 9: Judge the end.
Step 1: Give the preference relation matrix of linguistic judgement matrix;
Step 2: 0-1 permutation preference relation matrix of linguistic judgement matrix is given;
Step 3: Judge whether the 0-1 permutation preference relation matrix is an upper triangular matrix; if the linguistic judgement matrix has satisfactory consistency, the judgement ends, otherwise proceed to the next step;
Step 4: Find the cyclic matrix in the 0-1 permutation matrix, and get the objects of forming the cyclic matrix;
Step 5: According to the principle of modified cycle, the first cycle is modified to obtain the modified 0-1 permutation preference relation matrix;
Step 6: Rearrange the 0-1 permutation preference relation matrix and turn to step 3;
Step 7: According to the principle of determining the comparison results, the modified linguistic judgement matrix is obtained;
Step 8: Get the ranking of the objects;
Step 9: Judge the end.
In this paper, we give a method to judge whether the linguistic judgement matrix with the not equivalent object have satisfactory consistency. Then, for the linguistic judgement matrix with strict preference relation of pairwise objects, we give a method to determine the satisfactory consistency of the linguistic judgement matrix. We use whether the 0-1 permutation preference relation matrix is an upper triangular matrix to determine the satisfactory consistency of the linguistic judgement matrix. This method is simple and intuitive. It does not need to establish models and complex operations but only needs to make simple transformation of the matrix. Then, three objects of forming a cyclic circle are found by using the cyclic matrix, and the modified linguistic judgement matrix is obtained by giving the correction principle. However, the modified method is only applicable to the matrix with strict preference relationship, and there are some defects in the matrix with an equivalent scheme. Further research is needed.
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mechanism of regional ‘Artisan Workshop’ under big data environment Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises The analysis method of the impact of missing audit information on the securities investment decisions based on Logistic regression models Research on the innovation theory of college students’ ideological and political education under the background of big data Research on classification of e-commerce customers based on BP neural network Research on the problems and reform strategies of government statistics based on big data technology The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Adaptive fusion of multi-exposure images based on perceptron model Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Exploring the Path of Integrating Excellent Traditional Culture into Civic Education in Universities in the 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and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Grid data asset relationship and intelligent classification integrating knowledge graph and Internet of Things Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Analysis of digital humanistic knowledge production based on natural language processing Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering The Construction of Judgment Model for Cultivating Intelligent Accounting Professionals in Universities Based on Logarithmic Periodic Power Law Model Action of Aut( G) on the set of maximal subgroups of p-groups Digital Regeneration and Database Construction of Hunan Embroidery Needlework under the Perspective of Artificial Intelligence Research on the practice of innovation and entrepreneurship education in universities under the environment of big data Application of digital technology in environmental art design Research on loyalty prediction of e-commerce customer based on data mining Research on the evaluation system of tourism management classroom teaching based on multimedia big data analysis The application of ARCS motivation model in college oral English teaching Research on Innovation of Translation Teaching and Translation Strategies for College Students in Multimedia Background A multi-channel convolutional neural network based on attention mechanism fusion for facial expression recognition Exploring the development of cultural and creative tourism under the perspective of ecological theory of tourism destination management Modeling Analysis of User Consumption Data of Internet Culture Industry in the Context of Emerging Technologies Reference: An algorithm for recognizing the main melody of orchestral music based on artificial intelligence of music melody contour Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting The construction of a practical platform for party building and ideological and political education based on information fusion A study on the influence of the spread of Yangming Studies in Japan on the psychology of the Japanese people based on big data analysis Research on personalized recommendation algorithm for micromechanical sensors based on cloud model Research on the value of modern vernacular literature in contemporary rural construction based on ADDIE model Robust speech recognition based on deep learning for sports game review Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Model Construction of Influencing Factors of Physical Education Core Quality Cultivation Based on Multiple Linear Regression Application of Nonlinear Differential Equation in Electric Automation Control System Research on the operation and management mechanism of cross-border e-commerce shared practice training base Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Strategies for improving Chinese language proficiency based on artificial intelligence technology The success rate model of college students’ new entrepreneurship based on nonlinear differential equations Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Research on the application of marketing strategy of national fitness exercise and dance events in the construction of sports culture based on big data technology Decisions of competing supply chain with altruistic retailer under risk aversion Strategies for constructing mathematical models of nonlinear systems based on multiple linear regression models Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations Research on human resource management performance evaluation based on BP algorithm The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on urban energy Internet planning based on fuzzy comprehensive method Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the intelligent path of college students’ network ideological and political education based on big data mining technology Research on the application of PLC technology in electrical automation engineering Application of matrix multiplication in signal sensor image perception Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence VR-based computer maintenance practical training platform development design and application research Design and implementation of an integrated management system for discipline construction and postgraduate education in universities Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Research on educational resource recommendation system based on MRLG Rec Visual analysis of the trend of mental health changes among Chinese college students in the context of the normalisation of the new crown epidemic A study on the phenomenon of anaphoric correction in college students’ English conversation Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model Research on the innovation of collaborative education model of scientific research and teaching in colleges and universities based on the theory of process reengineering AtanK-A New SVM Kernel for Classification The innovative path of diversified vocal music education reform in colleges and universities under the advanced educational concepts of China and the West Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Rhino application in ceramic packaging design teaching Study of a linear-physical-programming-based approach for web service selection under uncertain service quality Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning Design and evaluation of intelligent teaching system on basic movements in PE Research on identifying psychological health problems of college students by logistic regression model based on data mining Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Retraction