Fuzzy matrix refers to the matrix of fuzzy relation. If the set X has m elements and the set Y has n elements, the fuzzy relation from the set X to the set Y can be represented by a matrix. Let R=(rij)m*n and S=(sij)m*n be fuzzy matrices, then it can be obtained:

Is equal to: R = S ⇔ rij = sij

Contains: R ⊆ S ⇔ rij ≤ sij

Delivery: R∩S = (rij∧sij)m*n

And: R ∪ S=(rij ∨ sij)m*n

Complement (remainder): Rc=(1-rij)m*n

The multiplication operation of fuzzy matrix is similar to the ordinary matrix operation, but the difference is that the two terms are not multiplied first and then added, but small first and then large.

When determining the target weight, assuming that the ordered preference relation matrix conforms to complete homogeneity, then the ordering phasor is _{1}, _{2}, …, _{m}^{T}, Conform to the _{i}_{ik} β_{kj} β_{ji}_{ki} β_{jk} β_{ij}

In the meet

That is:

Assume that the indicator Ac exists

^{[1]}:

First, solitude/private quadrant and device tech support. In this quadrant, individuals will study in a closed or semi-closed space, and the planning and design of the overall spatial pattern pays more attention to the privacy of sound and vision, which can ensure that learners will not be interfered by the outside world. During the planning and design period, the technical support of the equipment selected is divided into the following points: firstly, attention should be paid to enhancing the sense of enclosing the space, and the temporary ownership of the learning space should be guaranteed in the system design; Secondly, the space color should be cold color, so as to help learners to engage in learning; Finally, provide Internet and power outlets^{[2]}.

Second, solitude public quadrant and technical device support. This quadrant should be considered from two situations. On the one hand, it belongs to studying alone in the formal learning environment such as self-study room or reading room. This design continues the learning atmosphere of the traditional library reading room. The selected equipment supports formal desks and chairs, and maintains the rules and regulations of a serious learning environment. On the other hand, students will study alone in informal learning environments such as stairs, corridors and halls. The learning space here is more free, which provides possibilities for those who like to study in crowds.

Third, shared/private quadrant and technical device support. This kind of environment design means that multiple learners choose a private space for communication on the basis of reservation or occupation. For example, in the group discussion room, group members can achieve the goal of active learning by communicating with each other. The equipment technical support of the actual quadrant is divided into the following points: First, choose the voice environment with high privacy to solve the noise problem; Secondly, to ensure that the internal space has privacy and closure, management system to ensure that learners have the ownership of this space temporarily; Finally, we should provide the black and white board and projector needed for communication and discussion, and the color selection should have a certain vitality^{[3]}.

Fourth, shared/common quadrant and device technical support. This kind of environment design requires multiple learners to study or engage in activities in an open public environment, which belongs to the leisure mode of sharing/private quadrant. From the practical point of view, it can not only be used for teacher-student interaction and student communication, but also can hold campus lectures, readers, salon and other activities.

According to the current operation of university libraries at home and abroad, it can be seen that the operation of the above four quadrants can usually be described, and the functional values shown in them are shown in the figure 2 below^{[4]}:

According to the study on the learning shared space of university library constructed above, the core content of the design and analysis of learning shared space is image retrieval algorithm. In this paper, related research is carried out from the bottom visual features to the top wing features, and the selected algorithm is verified and analyzed.

^{[5]}:

After the color histogram and color block are defined, the barycenter position of all color blocks shall be calculated and analyzed. The calculation formula of barycenter position of the KTH color block is as follows:

Wherein, k ∈ [1,36] represents 36 colors after quantization, p[ck] represents the center of gravity of each color block, and p represents the center of gravity set of color blocks contained in an image.

It is necessary to consume a lot of time and energy to calculate and analyze gray co-occurrence matrix by using HSV model formula, so this paper chooses four directions

In the above formula, P_{ij} only has half of the spatial information, but because the gray level co-occurrence matrix has symmetry, the structure diagram is shown FIG. 3 below, so all the distribution information can be obtained through flipping and stacking. The specific formula is:

As the most representative shape feature extraction method, the actual calculation formula is as follows:

For curves, if the ruler change factor is alpha, then the scale must change the perimeter, and the change factor corresponds to alpha. And that gives us

The support vector machine (SVM) image classification method was proposed by Vapnik, and its core idea is to construct a hyperplane as a decision surface to maximize the distance edge between positive and negative examples, as shown in the following figure 4^{[6]}:

This paper focuses on obtaining the matrix algorithm according to the transitivity of fuzzy similarity matrix so as to ensure the semantic information transfer between images in the learning shared space constructed by university library is more convenient and rapid. Suppose the given sample is X={x1, x2… Xn}, and fit _{i}^{n}_{i}_{i}_{1}, _{i}_{2},…, _{im}

First, the similarity coefficient formula of the index:

In the above formula, accord with

This condition.

Second, cosine formula of included Angle:

Third, correlation coefficient formula:

In the above formula, accord with

This requirement.

Fourth, calculation formula of maximum and minimum values:

Fifth, calculation method of arithmetic mean and minimum value:

Sixth, calculation method of geometric mean and minimum value:

The fuzzy semantic correlation matrix constructed in this paper meets the following requirements:

Where, N represents the number of images contained in the image library, R (I, j) represents the direct similarity between images and images, which directly presents the similarity relationship between them. The feedback algorithm proposed in this paper is implemented in the image library classification, so it can be considered that each type of image has a certain degree of similarity. In the fuzzy semantic correlation matrix, it is assumed that the more similar two images are, the closer the corresponding weight value is to 1, and vice versa, the closer to 0. Therefore, the similarity weight value R (I, j) between images and images should meet the following conditions, where the following table represents the initialization results between the first 10 images:

0 ≤

The initialization result of the matrix

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

2 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

3 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

4 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

6 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

7 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 |

8 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 |

9 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 |

10 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 |

First, the feedback algorithm based on FSRM. This feedback algorithm is divided into two modules. On the one hand, it refers to the training stage, which is mainly to retrieve and feedback the images in the image library, so as to adjust the weight value between images in FSRM. On the other hand, it refers to the query stage, which is mainly to retrieve and feedback the images in the non-image library, so as to obtain clearer retrieval results and adjust the weight value of FSRM scientifically.

Secondly, the learning algorithm based on FSRM. During the study, implicit semantic information is considered to ensure that semantic information can be spread quickly in FSRM.

The similarity of images can be defined as follows:

In the above formula, T represents the threshold value and conforms to 1> T> 0.5 this condition. In this study, T was regarded as 0.7, and subsequent studies were used for verification analysis.

Finally, the long - term learning algorithm based on FSRM. For image retrieval, the similarity of the underlying visual features has a certain objectivity, but for more complex images, it is difficult to intuitively judge the semantic information contained in them, so a certain learning mechanism should be used to obtain them. After long-term study of fuzzy semantic correlation matrix, the weight value contained in FSRM can intuitively present the speech information between images.

For the above study, the standardized Corel image library was selected for verification analysis, which contained 1000 JPG images with a size of 384×256, divided into 10 categories in total, and each category contained 100 images. By inviting 10 users to use the system that models the learning shared space for university libraries, each user will make two searches for all image classes, and each search can be fed back one to five times according to the actual situation. In each feedback, they should combine their own requirements and put forward evaluation on the retrieval results. The actual experiment is divided into the following points:

First, the performance of SVM classification algorithm should be compared and analyzed. Combined with the comparative analysis of the classification effect of Su Shi in FIG. 5 and FIG. 6 below, it is found that the classification method proposed in this paper is superior in time performance, and the accuracy of the two is consistent^{[7]}.

Second, analyze the value range of threshold T, and the specific results are shown in Figure 7 below. The final results show that with the decrease of feedback times, the change of threshold has little influence on the actual accuracy. When the number of feedback reaches a certain range, higher accuracy can be obtained with different thresholds. Under the condition of average feedback number, the accuracy of threshold 0.7 is higher than that of other values.

Thirdly, the effectiveness of the learning algorithm is analyzed. The following figure represents the curve changes of accuracy with and without learning under different feedback times. As shown in Figure 8, comparative analysis shows that learning with definite feedback times has a stronger effect than no learning; In the continuous increase of feedback times, the accuracy of both learning and no learning will increase. After a certain number of feedbacks, the accuracy curves of learning and wu learning tend to be stationary. In other words, feedback algorithms can obtain stronger retrieval results after limited user feedback.

Fourth, compare the algorithm in this paper with the FSRM retrieval algorithm, as shown in Figure 9 below:

Combined with the above analysis, it is found that the relevant feedback algorithm based on FSRM selected in this paper is stronger than the FSRM retrieval algorithm in terms of feedback performance. The reason is that the correlation feedback algorithm simply classifies the images in the image library to reduce the number and complexity of FSRM calculations. The application time of the correlation algorithm is also reduced, thus improving the retrieval performance^{[8]}.

To sum up, in order to build a high-quality learning shared space for university libraries during the period of educational innovation, researchers propose to optimize module functions from multiple perspectives. Combined with the fuzzy matrix model, this paper conducts a comparative study on the image retrieval algorithm in the system, and the final results prove that the correlation feedback algorithm based on FSRM is stronger than the FSRM retrieval algorithm, and both the retrieval performance and computational efficiency have been further improved.

#### The initialization result of the matrix

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

2 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

3 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

4 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

6 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

7 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 |

8 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 |

9 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 |

10 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 |

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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 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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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model