The study on the anxiety level of college students in emergencies based on fuzzy rough set over two universes

Abstract

In 2020, the spread of the COVID-19 epidemic has attracted global attention. As a large-scale group that is receiving higher education, college students also show greater mood swings. How to reduce the psychological harm of anxiety to college students is a problem that needs to be solved urgently. Based on this, this paper proposes an evaluation model for the anxiety level of college students in different regions under the influence of COVID-19. First of all, the general influence index of college student’s anxiety level is obtained by correlation analysis. Secondly, the logical OR of the double quantization variable precision fuzzy set model and the degree fuzzy rough set model is used to establish the evaluation model of the anxiety level of college students under the influence of COVID-19. Finally, used big data, the idea of fuzzy upper and lower approximation, combined with the principle of maximum membership in fuzzy set theory, achieved the quantitative ranking of the anxiety levels of college students in different areas. The research shows that when the accuracy of decision-making is 45%, the anxiety level of the township college students group and the provincial capital or municipality college students group is higher. When the accuracy of decision-making is 65%, the anxiety level of the provincial capital or municipality college students group is higher than others.

Keywords

Fuzzy rough set two universes COVID-19 college students anxiety level

1 Introduction

Novel coronavirus infected pneumonia (Corona Virus Disease 2019, referred to as “new coronary pneumonia”), which was widely infected in December 2019 in Wuhan, Hubei Province, China, aroused global attention. On January 30, 2020, the World Health Organization (WHO) designated the disease (COVID-19) caused by the new coronavirus as a health emergency of international concern [1]. On January 27, the “Notice of the Ministry of Education on the Postponement of the 2020 Spring Semester” emphasized that the universities appropriately postpone the start of the 2020 spring semester [2]. In March 2020, a survey conducted by the Shanghai Mental Health Center on the psychological stress and emotional status of more than 50,000 ordinary people in China, showed about 35.00% of the respondents suffer from psychological distress and have obvious emotional stress reactions. Among them, the respondents belong to mild to moderate distress about 29.29%, and the respondents experienced severe psychological distress about 5.14%. As a social group that has attracted much attention, college students have special psychological characteristics that make them more likely to show uncontrollable anxiety and panic in the face of health emergencies [3]. Therefore, attach importance to the emotional guidance of college students, face up to the psychological needs of college students to vent their emotions, and rationally channel the emotional fluctuations of college students, which has become an important task for the prevention and control of the COVID-19 epidemic.

For emergencies, due to the tight time and the comprehensive influence of various subjective factors, the governments and universities have very limited information. The information obtained has basic characteristics of inaccuracy and incompleteness. Therefore, there is a one-sided judgment on the anxiety level of college students. The rough set is a non-parametric new mathematical theory for dealing with uncertain problems. Its ideological foundation and the means to deal with uncertain problems provide us with a new perspective for the quantitative description, expression of uncertain objects and quantitative calculation and analysis. In 1982, Polish scholar Pawlak first proposed rough sets [4], as a non-classical quantitative mathematical tool for dealing with uncertain objects, and became a relatively new soft computing method. In recent years, rough set theory has been continuously improved and applied to many disciplines [5], such as clinical medicine [6], power grid [7], fault prediction [8], management decision-making [9]. However, with the rapid development of society, uncertainties such as ambiguity and hesitation of data have become increasingly prominent, and Pawlak rough sets have shown insufficient. In 1990, Dubois and Prade gave the concept of fuzzy rough sets, which accelerated the research process of uncertain problems [10]. Also, because the fuzzy rough set on a single domain may limit the expert’s description of decision information, two or more universes can solve practical problems more effectively, their research objects are two or more different but with the universe of fuzzy relations [11]. Therefore, the fuzzy rough set model based on two universes has been deeply studied and is widely used in many practical problems. In the sense of Shafer’s compatible view, Canadian scholar Yao proposed the concept of double universe rough set [12]. In recent years, two universes fuzzy rough sets have been widely used in logistics and transportation [13], emergency decision-making [14 –16], medical diagnosis [17 –19], and many other fields. It has become another important tool for dealing with uncertainty mathematics. Yao et al. [20] first proposed a rough set model on two universes. Pei and Xu [21] conducted a detailed study on rough sets and their properties on two universes. Elmonsef et al. [11] compared the three types of rough fuzzy sets on two general sets. Sun and Ma [22] studied fuzzy rough set models and related applications in two different universes. Yang et al. [23] proposed a fuzzy probability rough set model on two universes and applied the model to clinical diagnosis cases. Zhang et al. [24] proposed a hesitating fuzzy rough set model on two universes.

With the continuous development of the digital economy, AI applications have gradually become popular. The uncertainty of the decision-making environment is also increasing. As a new method to deal with complex problems in uncertain environments, soft computing has been mentioned in many different research fields. Such as, Ahmed Mostafa Khalil et al. [25] based on fuzzy soft sets to develop a new fuzzy expert system that can be used to predict lung cancer disease. A.S. Nawar et al. [26] build some new different types of j-covering approximations based rough sets and application of the new types of covering-based rough sets to the rheumatic fever is given. M.Ei Sayed et al. [27] to introduce a new approach to modify and generalize soft rough sets and apply it to COVID-19 medical diagnosis to determine whether it is infected. Based on intuitionistic fuzzy sets, Zhang al. [28] proposed medical image fusion based on intuitionistic fuzzy sets and brightness enhancement. Results show that this method can improve the quality of medical image fusion. Ahmed Mostafa Khalil et al. [29] proposed a Possibility m-polar fuzzy soft sets and construct an algorithm using this to solve the decision-making problems. Ahmed Mostafa Khalil et al. [30] presented the notion of the interval-valued picture fuzzy soft set theory and use this to solve the decision-making problems. Haresh Kumar Sharma et.al [31] proposed a new technique to select the best forecasting model using rough set approach and it provides an alternative way to select the best forecasting model for time series forecasting. To overcome the shortcomings of the traditional probabilistic hesitant fuzzy element ranging method, Fang et al. [32] proposed an improved probabilistic hesitant fuzzy element ranging method, and took the army combat plan combat fuzzy optimization as an example to demonstrate the feasibility and effectiveness of the method. Muhammad Riaz et al. [48] established a multi-criteria decision-making algorithm with aggregation operators based on SMS topology, which was used to select the best biopesticide and the best textile company. In summary, it mainly involves clinical medical treatment [25 –28], management decision [29 , 33], model prediction [32], emergency management [34 –36], power grid [37], military management [32] and many other fields. However, for the emotional guidance of college students under the influence of the COVID-19 epidemic, there are relatively little researches in this field due to problems such as the difficulty of defining evaluation indicators, incomplete and uncertain information.

Based on this, this paper applies rough set theory to the problem of quantifying the anxiety level of college students affected by health emergencies, and tries to use the unique advantages of rough set theory in processing incomplete and inaccurate data to give a new emotional evaluation model for similar emergencies. The main idea is to obtain a general influence index of the anxiety level of college students through correlation analysis. On this basis, the logical OR of the double quantization variable precision fuzzy set model and the degree fuzzy rough are used to establish an evaluation model for the anxiety level of college students under the influence of COVID-19. Combined with the idea of fuzzy upper and lower approximation and the principle of maximum membership degree in fuzzy set theory, the quantitative ranking of the anxiety level of college students in different regions is realized. The analysis of the anxiety level model and method of college students in emergencies based on the two universes fuzzy rough set, on the one hand, provides a quantitative description for the evaluation of the anxiety level of college students under the influence of new coronary pneumonia, and on the other hand, it can also provide relevant government departments and universities provide accurate decision-making reference for college students mental health education.

The rest of this article is arranged as follows. The second part of this article introduces the research methods and data preparation. The third part takes the COVID-19 epidemic as an example, constructs the evaluation model of the anxiety level of college students under the influence of COVID-19, and realizes the anxiety level of college students in different regions quantitative ranking. The last part gives conclusions and future research prospects.

2 Data processing and research methods

2.1 Data Sources

This study designed a risk perception and psychological evaluation system for college students from the COVID-19 epidemic. The system consists of three parts, namely demographic characteristics (a total of 6 questions including current status, gender, educational background, area, type of area, and school province), the risk perception part and emotional state part of college students to the COVID-19 (the risk perception part including the perceived severity of the epidemic, the degree of concern about the epidemic, the degree of threat to oneself, the possibility of infection, the degree of negative impact on life, the degree of impact on learning, and the degree of perception of prevention and control measures. The emotional state part including the degree of anxiety, the degree of panic, the degree of irritability, the degree of suspected illness, the degree of anger, and the degree of complaint), the behavioral intentions of college students for COVID-19. The mood scale is mainly based on the Likert seven-point scale, which is designed with reference to the “Depression-Anxiety-Stress Scale Simplified Chinese Version (DASS-21)”. The system has completed preliminary research on the risk perception of the COVID-19 epidemic by some college students through social software such as WeChat and QQ. On the basis of extensive consultation with domestic risk perception, disaster social psychology, and social psychologists, it has finally formed a nationwide epidemic risk perception and psychological evaluation system for college students. The total number of people surveyed was 17586, including 7705 men and 9881 women. There are 565 associates (including higher vocational colleges), 12550 undergraduates, 4394 postgraduates, and 77 doctoral candidates. Excluding invalid questionnaires, a total of 16925 valid feedback questionnaires were received, with an effective rate of 96.24%. According to the type of area where the research subjects were located during the epidemic, they were divided into rural areas, township areas, county towns, prefecture-level cities, provincial capitals or municipalities. The specific percentage is shown in Table 1.

Table 1
Number of area types of college students

Area type Number Percentage

(person) (%)

Rural areas 6779 41.25

Township areas 3262 41.25

County towns 4430 41.25

Prefecture-level cities 1851 41.25

Provincial capitals or municipalities 1264 41.25

Total 17586 100.0

Area type	Number	Percentage
Rural areas	6779	41.25
Township areas	3262	41.25
County towns	4430	41.25
Prefecture-level cities	1851	41.25
Provincial capitals or municipalities	1264	41.25
Total	17586	100.0

2.2 Impact index selection

Recently, a variety of new or recurring infectious diseases have caused a serious threat to the global society, such as the outbreak of SARS in 2003 [38 –40], and the outbreak of H1N1 influenza in 2009 [41, 42]. When such incidents occur, due to their high degree of suddenness and unpredictability, people’s sense of security drops sharply, and it is easy to produce negative emotions. At the same time, the special psychological characteristics of college students make them often show uncontrollable anxiety and panic when facing emergencies. Due to their special psychological characteristics, college students will inevitably show uncontrollable anxiety when facing emergencies. Therefore, on the basis of the research of domestic and foreign scholars, based on the data of the “college students COVID-19 epidemic risk perception and psychological evaluation system”, use SPSS software to carry out correlation analysis and combined with reality, this article intends to select the 7 types of impact indicators in Table 2 as the general impact indicators of the anxiety level of college students under the influence of the COVID-19 epidemic.

Table 2
Influencing indicators of college student’s anxiety level

Serial number Impact index

1 The severity of the epidemic in the region

2 The degree of attention to the development of the epidemic

3 Self-evaluation of the threat of the epidemic to life and health

4 Self-evaluation of the impact of the epidemic on learning

5 Local government’s prevention and control measures against the epidemic

6 Self-evaluation of anxiety

7 Whether to spread unconfirmed gossip

Serial number	Impact index
1	The severity of the epidemic in the region
2	The degree of attention to the development of the epidemic
3	Self-evaluation of the threat of the epidemic to life and health
4	Self-evaluation of the impact of the epidemic on learning
5	Local government’s prevention and control measures against the epidemic
6	Self-evaluation of anxiety
7	Whether to spread unconfirmed gossip

2.3 Research method

In this section, we will review the theory of rough set and the main rough set models used in this article. Such as Pawlak rough set, rough set over two universes, fuzzy rough set, quantitative fuzzy rough sets over two universes and so on.

Let U be a non-empty finite universe and R is an equivalence relation on U, then the relational system (U, R) is called an approximation space.

Definition 2.1. let (U, R) be the Pawlak approximation space, and R is an equivalence relation on U, for the basic collection X ⊆ U, the lower and upper approximations are respectively:

$\underline{R} (X) = {x \subseteq U | [x]_{R} \subseteq X},$ (1) $\bar{R} (X) = {x \subseteq U | [x]_{R} \cap X \neq \emptyset} .$ (2) For any Y ⊆ U, the lower and upper approximations of Y with respect to the approximation space are that R must belong to the set: $\underline{apr} (Y) = {x \subseteq U | R (X) \subseteq X},$ (3) $\bar{apr} (Y) = {x \subseteq U | R (X) \cap X \neq \emptyset} .$ (4) Simply put, the lower approximation is based on the set of elements in U that must belong to the set X according to the relation R, the upper approximation is based on the set of elements in U that may belong to the set X according to the relation R. Pawlak rough set limits the objects in discussion to the same universe. However,two or more universe are often involved in application practice in many fields. Next, we briefly introduce the basic concepts of two universe rough sets. Definition 2.2. [45] let U, V be two universe, and R is the compatible relationship defined on U and V. The (U, V, R) tripleis called the two universe of approximation space. For any Y ⊆ U, the lower and upper approximations of Y with respect to the approximate space are respectively defined as: $\underline{apr} (Y) = {x \subseteq U | F (X) \subseteq Y},$ (5) $\bar{apr} (Y) = {x \subseteq U | F (X) \cap Y \neq \emptyset} .$ (6) Among them, $(\underline{apr} (Y), \bar{apr} (Y))$ is generalixed rough set or two universe rough set. Samely, the ordered binary operator $(\underline{apr}, \bar{apr})$ is called an interval structure. Definition 2.3. [46] A fuzzy set A on the universe U is represented by a membership function A on U, where A (x) represents the degree to which the element belongs to the fuzzy set A. Definition 2.4. [47] let (F (U, R)) be the Pawlak approximation space, and U is universe, R is the fuzzy relationship on U, approximation operator $\underline{R}$ , $\bar{R} : F (U) \to F (U) \times F (U)$ , for ∀A ∈ F (U) , ∀ x ∈ F (U) , ∀ x ∈ U, defined as: $\underline{R} (A) (x) = inf_{y \in U} \max {A (y), 1 - R (x, y)},$ (7) $\bar{R} (A) (x) = sup_{y \in U} \min {A (y), R (x, y)} .$ (8) Obviously, the upper and lower approximation $\underline{R} (A), \bar{R} (A)$ of A with respect to R is still a fuzzzy set. Definition 2.5. Let U and V are two non-empty finite domains. For any Y ⊆ V, in the dual domain rough set model of the logical OR of precision and degree, the lower and upper approximation are respectively (0 ≤ β < 0.5, k is a positive integer)

$\begin{matrix} {\underline{apr}}_{β \lor k} (Y) = {x \subseteq U | c ({[x]}_{R}, Y) \leq β, \\ | [x]_{R} | - | [x]_{R} \cap Y | \leq k}, \end{matrix}$ (9) $\begin{matrix} {\bar{apr}}_{β \lor k} (Y) = {x \subseteq U | c ({[x]}_{R}, Y) < 1 - β, \\ | {[x]}_{R} \cap Y | > k} . \end{matrix}$ (10)

The rough set consisting of the approximation operator ${\underline{apr}}_{β \lor k} (Y)$ and the definition ${\bar{apr}}_{β \lor k} (Y)$ is called two universe rough sets based on double quantization, where $c ({[x]}_{R}, Y) = 1 - \frac{| {[x]}_{R} \cap Y |}{| {[x]}_{R} |}$ is called the equivalence class [x] _R with respect to the wrong classification rate of the set X.

Based on the basic concept of fuzzy information system, we will study the variable precision fuzzy rough set and the degree fuzzy rough set under the fuzzy system, and combine the two through logic or.

Definition 2.6. Let $(U, V, {\tilde{R}}_{α})$ is the fuzzy compatible approximation space of the two universes, for any fuzzy set A (A ∈ F (V)), where 0 ≤ β < 0.5, then A with respect to ${\tilde{R}}_{α}$ and β under fuzzy set ${\underline{A}}_{{\tilde{R}}_{α}^{β}}$ and β upper fuzzy set ${\bar{A}}_{{\tilde{R}}_{α}^{β}}$ are respectively defined as

$\begin{matrix} {\underline{A}}_{{\tilde{R}}_{α}^{β}} (x) = \min {A (y) | c ({\tilde{R}}_{α} (x), A) \leq β, \\ y \in {\tilde{R}}_{α} (x), x \in U}, \end{matrix}$ (11) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{α}^{β}} (x) = \max {A (y) | c ({\tilde{R}}_{α} (x), A) < 1 - β, \\ y \in {\tilde{R}}_{α} (x), x \in U} . \end{matrix}$ (12)

The rough set defined by the approximation operators ${\underline{A}}_{{\tilde{R}}_{α}^{β}}$ and ${\bar{A}}_{{\tilde{R}}_{α}^{β}}$ is called a variable precision fuzzy rough set based on fuzzy compatibility relations under the two universes, where $c ({\tilde{R}}_{α} (x), A) = 1 - \frac{\sum_{y \in {\tilde{R}}_{α} (x)} A (y)}{| {\tilde{R}}_{α} (x) |}$ is called the wrong classification rate of fuzzy compatibility class $\tilde{R_{α}}$ on fuzzy set A.

Definition 2.7. Let $(U, V, {\tilde{R}}_{α})$ is the fuzzy compatible approximation space of the two universes, for any fuzzy set A (A ∈ F (V)), k is a non-negative integer, and the lower fuzzy set ${\underline{A}}_{{\tilde{R}}_{α}^{k}}$ and β upper fuzzy set ${\bar{A}}_{{\tilde{R}}_{α}^{k}}$ of the definition A according to the degree K are respectively defined as:

$\begin{matrix} {\underline{A}}_{{\tilde{R}}_{α}^{k}} (x) = \min {A (y) | | {\tilde{R}}_{α} (x) | \\ - \sum_{y \in {\tilde{R}}_{α} (x)} A (y) \leq k, x \in U}, \end{matrix}$ (13) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{α}^{k}} (x) = \max {A (y) | \sum_{y \in {\tilde{R}}_{α} (x)} \\ A (y) > y, x \in U} . \end{matrix}$ (14)

The rough set defined by the approximation operators ${\underline{A}}_{{\tilde{R}}_{α}^{k}}$ and ${\bar{A}}_{{\tilde{R}}_{α}^{k}}$ is called the degree fuzzy rough set based on the fuzzy compatibility relation in the two universes. The dual quantization fuzzy rough set model based on two universes mainly adopts the logic or information integration construction of the dual quantization variable precision fuzzy rough set model and the degree fuzzy rough set model.

Definition 2.8. [11 , 46] Let $(U, V, {\tilde{R}}_{α})$ is the fuzzy compatible approximation space of the two universes, for any fuzzy set A (A ∈ F (V)), where 0 ≤ β < 0.5 and k are non-negative integers, the fuzzy set [26, 27].

$\begin{matrix} {\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x) = \min {A (y) | c ({\tilde{R}}_{α} (x), A) \leq β, \\ | {\tilde{R}}_{α} (x) | - \sum_{y \in {\tilde{R}}_{α} (x)} A (y) \leq k, x \in U}, \end{matrix}$ (15) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x) = \max {A (y) | c ({\tilde{R}}_{α} (x), A) < 1 - β, \\ \sum_{y \in {\tilde{R}}_{α} (x)} A (y) > y, x \in U} . \end{matrix}$ (16)

Respectively called fuzzy set A, the accuracy of the information system is 1 - β, and the degree of logic is k or the lower approximate set and the upper approximate set of ${\tilde{R}}_{α}$ . Where $c ({\tilde{R}}_{α} (x), A) = 1 - \frac{\sum_{y \in {\tilde{R}}_{α} (x)} A (y)}{| {\tilde{R}}_{α} (x) |}$ is called the fuzzy compatibility class ${\tilde{R}}_{α}$ misclassification rate of fuzzy set A. Obviously the approximation operators ${\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k}$ and ${\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k}$ are binary quantized fuzzy relations from F (V) to F (U), that is, the lower approximation ${\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x)$ and the upper approximation ${\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x)$ are two fuzzy sets on the universe U, if for any x ∈ U, ${\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k} = {\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k}$ , then it is said that A is definable with respect to $(U, V, {\tilde{R}}_{α})$ , otherwise, it is said that A is a fuzzy rough set on the universe U and V.

3 Analysis on the anxiety level of college students based on the quantitative fuzzy rough sets of two universes

This section will use the two universes quantitative fuzzy rough set model to quantitatively rank the anxiety levels of the five affected college student groups. The specific process is shown in Fig. 1.

Fig. 1

Flow chart for quantifying anxiety levels

3.1 Construction of an evaluation model for college students anxiety level under the influence of COVID-19

Set the universe U = {x₁, x₂, x₃, x₄, x₅} is the five affected college student groups divided by the type of region after the occurrence of the COVID-19, which are rural areas students, college areas students, counties students, prefecture-level cities students, and provincial capitals or municipalities students; Universe V = {y₁, y₂, y₃, y₄, y₅, y₆, y₇} is the 7 general impact indicators that affect the anxiety level. These are the severity of the epidemic in the region, the degree of attention to the development of the epidemic, self-evaluation of the threat of the epidemic to life and health, self-evaluation of the impact of the epidemic on learning, local government’s prevention and control measures against the epidemic, self-evaluation of anxiety, and whether to spread unconfirmed gossip. The anxiety level of college students in each region can be expressed by describing the values of 7 general impact indicators under the influence of the epidemic, namely, the correlation degree $\tilde{R} (x_{i}, y_{j}) (i = 1, 2, 3 . . ., 5, j = 1, 2, 3 . . ., 7)$ . Essentially, it is a quantitative numerical description of the different characteristic attributes of the anxiety level of college students after the outbreak of the COVID-19. That is, the vague expression of actual features. Therefore, the nature of correlation: membership degree of different influence attributes of college students in different regions about their anxiety levels under the influence of this epidemic. Obviously, $0 \leq \tilde{R} (x_{i}, y_{j}) \leq 1$ , and $\tilde{R} (x_{i}, y_{j}) \in F (U \times V)$ . The general impact index y_j (j = 1, 2, 3 . . . , 5)that is generally affected by the COVID-19 can be regarded as a profit-based indicators, that is, the larger the correlation measure $\tilde{R} (x_{i}, y_{j})$ , the more obvious y_j in the college student group $\tilde{R} (x_{i}, y_{j}) (i = 1, 2, 3 . . ., 5)$ under the influence of the epidemic. If y₁represents the severity of the epidemic in the area, then $\tilde{R} (x_{i}, y_{j})$ represents the quantitative description of the level of anxiety of the affected college student group x_i about the severity of the epidemic, the larger the $\tilde{R} (x_{i}, y_{j})$ the more severe the epidemic, the more anxious the college student group.

Let A ∈ F (V)is the collection of data and correlation analysis through the “College Students COVID-19 Epidemic Risk Perception and Psychological Evaluation System” after the occurrence of epidemic, obtained a data set of general impact indicators on the anxiety level of college students, and this information is fuzzy information about the quantitative description of the basic influence indicators of the anxiety level of college students in different regions. So A the fuzzy set that affects V on the universe of index set. When calculating the level of anxiety among college students, first, determine the credibility level of the information obtained according to your own judgment or the opinions of the expert group α (0 < α ≤ 1), that is, the credibility of the obtained information.

For the five affected college student group x_i ∈ U, 0 < α ≤ 1 divided by the area type, there is a distinct subset ${\tilde{R}}_{α} (x_{i}) \subseteq V$ on the universe V, this constructs the two universes quantitative fuzzy approximation space $(U, V, {\tilde{R}}_{α})$ of the anxiety level of college students under the influence of COVID-19, then the upper and lower approximations of $(U, V, {\tilde{R}}_{α})$ of fuzzy set A ∈ F (V) reflecting the anxiety level of college students are.

$\begin{matrix} {\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x) = \min {A (y) | c ({\tilde{R}}_{α} (x), A) \leq β, \\ | {\tilde{R}}_{α} (x) | - \sum_{y \in {\tilde{R}}_{α} (x)} A (y) \leq k, x \in U}, \end{matrix}$ (17) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x) = \max {A (y) | c ({\tilde{R}}_{α} (x), A) < 1 - β, \\ \sum_{y \in {\tilde{R}}_{α} (x)} A (y) > y, x \in U} . \end{matrix}$ (18)

It can be seen from the above formula that ${\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k}$ and ${\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k}$ are the fuzzy sets on the anxiety level set U of the affected university students group divided according to the type of area after the occurrence of COVID-19, from this.

According to the upper and lower approximation of $(U, V, {\tilde{R}}_{α})$ and the decision accuracy α (0 < α ≤ 1) of fuzzy set A ∈ F (V) of the anxiety level of college students, the following rules are given. Let $(U, V, {\tilde{R}}_{α})$ be the fuzzy compatible approximation space of the two universes. For any fuzzy set A ∈ F (V) and decision accuracy α (0 < α ≤ 1) then $δ (x_{i}) = T_{L} ({\underline{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x_{i}), {\bar{A}}_{{\tilde{R}}_{α}}^{β \lor k} (x_{i}))$ , that is, under the condition that the confidence level is α, the index function of all affected college student groups x_i divided by their located. Among them, according to the definition of the index function of the anxiety level of different college students under the influence of COVID-19 epidemics, 0 ≤ δ (x_i) ≤1, ∀ x_i ∈ U, i = 1, 2, . . . , m . can be obtained, which can be used to quantify the anxiety level of college students, the larger the δ (x_i), the higher the anxiety level.

3.2 Correlation calculation

It can be seen from the model that universe U = {x₁, x₂, x₃, x₄, x₅}is the five affected college students group after the occurrence of COVID-19 according to the type of area. Universe V = {y₁, y₂, y₃, y₄, y₅, y₆, y₇} is 7 general indicators that affect anxiety levels. The anxiety level of college students in each region can be represented by 7 general impact indicators that characterize the impact of the epidemic, namely the correlation $\tilde{R} (x_{i}, y_{j}) (i = 1, 2, 3 . . ., 5, j = 1, 2, 3 . . ., 7)$ . In this experiment, the correlation is determined by the ratio of the number of general indicators to the total number of college students in different regions, and this value is obtained from the data statistics of the questionnaire system. The specific values are given in Table 3.

Table 3
Correlation

U/V y ₁ y ₂ y ₃ y ₄ y ₅ y ₆ y ₇

x ₁ 0.1392 0.0130 0.0772 0.1258 0.0224 0.1157 0.0155

x ₂ 0.5269 0.0491 0.2924 0.4762 0.0848 0.4382 0.0586

x ₃ 0.2737 0.0255 0.1519 0.2473 0.0440 0.2276 0.0305

x ₄ 0.3593 0.0335 0.1994 0.3249 0.0578 0.2988 0.0400

x ₅ 0.5261 0.0491 0.2919 0.4755 0.0847 0.4375 0.0585

U/V	y ₁	y ₂	y ₃	y ₄	y ₅	y ₆	y ₇
x ₁	0.1392	0.0130	0.0772	0.1258	0.0224	0.1157	0.0155
x ₂	0.5269	0.0491	0.2924	0.4762	0.0848	0.4382	0.0586
x ₃	0.2737	0.0255	0.1519	0.2473	0.0440	0.2276	0.0305
x ₄	0.3593	0.0335	0.1994	0.3249	0.0578	0.2988	0.0400
x ₅	0.5261	0.0491	0.2919	0.4755	0.0847	0.4375	0.0585

3.3 Quantitative ranking of anxiety levels

Suppose A is a collection of characteristic information about the COVID-19 epidemic. According to the incomplete information obtained, a set of numerical values reflecting the main characteristic indicators that affect the anxiety level of college students under the COVID-19 epidemic can be given. As mentioned above, A is the fuzzy set on the universe of V, and its membership degree is (the membership degree is determined by referring to the existing definition of the fuzzy set of the same kind and determined by considering the actual subjective judgment)

$\begin{matrix} A = \frac{0.7}{y_{1}} + \frac{0.6}{y_{2}} + \frac{0.8}{y_{3}} + \frac{0.7}{y_{4}} + \frac{0.3}{y_{5}} + \frac{0.6}{y_{6}} + \frac{0.4}{y_{7}} \end{matrix}$ (19)

Firstly, we take the confidence level α = 0.25 and let β = 0.4, k = 1, then the fuzzy compatibility class on the universe U and V are ${\tilde{R}}_{0.25} (x_{i}) (i = 1, 2, . . ., 5)$ , ${\tilde{R}}_{0.25} (x_{1}) = {\emptyset}$ , ${\tilde{R}}_{0.25} (x_{2}) = {y_{1}, y_{3}, y_{4}, y_{6}}$ , ${\tilde{R}}_{0.25} (x_{3}) = {y_{1}}$ , ${\tilde{R}}_{0.25} (x_{4}) = {y_{1}, y_{4}, y_{6}}$ , ${\tilde{R}}_{0.25} (x_{5}) = {y_{1}, y_{3}, y_{4}, y_{6}}$ .

Table 4

Information Statistics Table

U	$\| {\tilde{R}}_{α} (x) \|$	$\sum_{y \in {\tilde{R}}_{α} (x)} A (y)$	$\frac{\sum y \in {\tilde{R}}_{α} (x) A (y)}{\| {\tilde{R}}_{α} (x) \|}$	$c ({\tilde{R}}_{α} (x), A)$	$\| {\tilde{R}}_{α} (x) \| - \sum y \in {\tilde{R}}_{α} (x) A (y)$
x ₁	0	0.0	–	–	0.0
x ₂	4	2.8	0.7	0.3	1.2
x ₃	1	0.7	0.7	0.3	0.3
x ₄	3	2.0	0.67	0.33	1.0
x ₅	4	2.8	0.7	0.3	1.2

$\begin{matrix} {\underline{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0.6}{x_{2}} + \frac{0.7}{x_{3}} + \frac{0.6}{x_{4}} + \frac{0.6}{x_{5}}, \end{matrix}$ (20) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0.8}{x_{2}} + \frac{0.8}{x_{3}} + \frac{0.7}{x_{4}} + \frac{0.8}{x_{5}} . \end{matrix}$ (21)

Furthermore, the δ value of each group can be calculated. $\begin{matrix} δ (x_{i}) = T_{L} ({\underline{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1} (x_{1})}, {\bar{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1} (x_{1})} = \max {0, \\ {\underline{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1} (x_{1})} + {\bar{A}}_{{\tilde{R}}_{0.25}^{0.4 \lor 1} (x_{1})} - 1} = 0 \end{matrix}$ (22) then δ (x₁) =0, δ (x₂) =0.4, δ (x₃) =0.5, δ (x₄) =0.4, δ (x₅) =0.4. It can be seen from the above experiment that when the decision accuracy is 25% : δ (x₃) > δ (x₅) = δ (x₄) > δ (x₂) > δ (x₁).

That is, the order of anxiety level is: college students in county towns >college students in provincial capital capiyals or municipalities = college students in county towns = college students in township areas >college students in rural areas.

Secondly, taking the confidence level α = 0.45 and let β = 0.4, k = 1, then the fuzzy compatibility class on the universe U and V are ${\tilde{R}}_{0.45} (x_{i}) (i = 1, 2, . . ., 5)$ , ${\tilde{R}}_{0.45} (x_{1}) = {\emptyset}$ , ${\tilde{R}}_{0.45} (x_{2}) = {y_{1}, y_{4}}$ , ${\tilde{R}}_{0.45} (x_{3}) = {\emptyset}$ , ${\tilde{R}}_{0.45} (x_{4}) = {\emptyset}$ , ${\tilde{R}}_{0.45} (x_{5}) = {y_{1}, y_{4}}$ .

Then the upper and lower approximation of fuzzy set A on the two universes quantitative fuzzy compatible approximation space $(U, V, {\tilde{R}}_{α})$ of the anxiety level of college students under the influence of COVID-19 are respectively (see Table 5). $\begin{matrix} {\underline{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0.7}{x_{2}} + \frac{0}{x_{3}} + \frac{0}{x_{4}} + \frac{0.7}{x_{5}}, \end{matrix}$ (23) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0.7}{x_{2}} + \frac{0}{x_{3}} + \frac{0}{x_{4}} + \frac{0.7}{x_{5}} . \end{matrix}$ (24)

Table 5

Information Statistics Table

U	$\| {\tilde{R}}_{α} (x) \|$	$\sum_{y \in {\tilde{R}}_{α} (x)} A (y)$	$\frac{\sum y \in {\tilde{R}}_{α} (x) A (y)}{\| {\tilde{R}}_{α} (x) \|}$	$c ({\tilde{R}}_{α} (x), A)$	$\| {\tilde{R}}_{α} (x) \| - \sum y \in {\tilde{R}}_{α} (x) A (y)$
x ₁	0	0.0	–	–	0.0
x ₂	2	1.4	0.7	0.3	0.6
x ₃	0	0.0	–	–	0.0
x ₄	1	0.0	–	–	1.0
x ₅	2	1.4	0.7	0.3	0.6

Furthermore, the δ value of each group can be calculated. $\begin{matrix} δ (x_{i}) = T_{L} ({\underline{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1} (x_{1})}, {\bar{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1} (x_{1})} = \max {0, \\ {\underline{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1} (x_{1})} + {\bar{A}}_{{\tilde{R}}_{0.45}^{0.4 \lor 1} (x_{1})} - 1} = 0 \end{matrix}$ (25) then δ (x₁) =0, δ (x₂) =0.4, δ (x₃) =0, δ (x₄) =0, δ (x₅) =0.4. It can be seen from the above experiment that when the decision accuracy is 45% : δ (x₂) = δ (x₅) > δ (x₄) = δ (x₃) = δ (x₁).

That is, the order of anxiety level is: college students in township areas = college students in provincial capital capitals or municipalities >college students in prefecture-level cities = college students in county towns = college students in rural areas.

Lastly, taking the confidence level α = 0.65 and let β = 0.4, k = 1, then the fuzzy compatibility class on the universe U and V are ${\tilde{R}}_{0.65} (x_{i}) (i = 1, 2, . . ., 5)$ , ${\tilde{R}}_{0.65} (x_{1}) = {\emptyset}$ , ${\tilde{R}}_{0.65} (x_{2}) = {\emptyset}$ , ${\tilde{R}}_{0.65} (x_{3}) = {\emptyset}$ , ${\tilde{R}}_{065} (x_{4}) = {\emptyset}$ , ${\tilde{R}}_{0.65} (x_{5}) = {y_{1}}$ .

Then the upper and lower approximation of fuzzy set A on the two universes quantitative fuzzy compatible approximation space $(U, V, {\tilde{R}}_{α})$ of the anxiety level of college students under the influence of COVID-19 are respectively (see Table 6). $\begin{matrix} {\underline{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0}{x_{2}} + \frac{0}{x_{3}} + \frac{0}{x_{4}} + \frac{0.7}{x_{5}}, \end{matrix}$ (26) $\begin{matrix} {\bar{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1}} = \frac{0}{x_{1}} + \frac{0}{x_{2}} + \frac{0}{x_{3}} + \frac{0}{x_{4}} + \frac{0.7}{x_{5}} . \end{matrix}$ (27)

Table 6

Information Statistics Table

U	$\| {\tilde{R}}_{α} (x) \|$	$\sum_{y \in {\tilde{R}}_{α} (x)} A (y)$	$\frac{\sum y \in {\tilde{R}}_{α} (x) A (y)}{\| {\tilde{R}}_{α} (x) \|}$	$c ({\tilde{R}}_{α} (x), A)$	$\| {\tilde{R}}_{α} (x) \| - \sum y \in {\tilde{R}}_{α} (x) A (y)$
x ₁	0	0.0	–	–	0.0
x ₂	0	0.0	–	–	0.0
x ₃	0	0.0	–	–	0.0
x ₄	0	0.0	–	–	0.0
x ₅	1	0.7	0.7	0.3	0.3

Furthermore, the δ value of each group can be calculated. $\begin{matrix} δ (x_{i}) = T_{L} ({\underline{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1} (x_{1})}, {\bar{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1} (x_{1})} = \max {0, \\ {\underline{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1} (x_{1})} + {\bar{A}}_{{\tilde{R}}_{0.65}^{0.4 \lor 1} (x_{1})} - 1} = 0 \end{matrix}$ (28)

then δ (x₁) =0, δ (x₂) =0, δ (x₃) =0, δ (x₄) =0, δ (x₅) =0.4. It can be seen from the above experiment that when the decision accuracy is 65% : δ (x₅) > δ (x₁) = δ (x₂) = δ (x₃) = δ (x₄).

That is, the order of anxiety level is: college students in provincial capital capitals or municipalities >college students in rural areas = college students in township areas = college students in county towns = college students in prefecture-level cities.

It can be seen from Fig. 2 that under different decision precisions, the decision results are different, indicating that as the confidence level increases, the decision results are more specific and accurate. Therefore, the choice of decision-making accuracy is generally determined by the decision-maker based on objective factors such as medical conditions and isolation measures, it can also be adjusted based on the duration of the epidemic or the accuracy of the data to make dynamic decisions. For example, when the accuracy of decision-making is 65%, the number of decision-making objects is 1, that is, the group of college students in provincial capitals or municipalities has the highest anxiety level. This conclusion is in line with reality. Due to the dense population and high mobility of people in provincial capitals or municipalities, the number of confirmed cases has increased sharply, the group of college students is relatively anxious. Therefore, it is recommended that relevant government departments and universities should give priority to the group of college students in the provincial capital or municipality when reducing the psychological harm of the epidemic to the group of college students.

Fig. 2

Number of decision objects under different confidence levels

From the experimental analysis, it can be seen that when the accuracy of decision-making is 65%, the anxiety level of the group of college students in the provincial capital or municipality is the highest. Provincial capital cities or municipalities have high population density and well-developed transportation, it is the Spring Festival and the population circulation is difficult to control. In addition, the overwhelming epidemic news is hotly discussed on various social media, which has led to a sharp increase in the anxiety level of college students. The model and method proposed in this article are an initial attempt to introduce two universe rough sets into the field of evaluation of the anxiety level of college students under the influence of the COVID-19 epidemic. The advantages of this model can integrate the influence of various factors and combine qualitative and quantitative indicators, avoiding the drawback of subjective assumptions of decision makers and more consistent with objective facts. On the one hand, the proposed model provides a quantitative description for evaluating the anxiety level of college students under the influence of COVID-19, on the other hand, it can also provide accurate decision-making reference for relevant government departments and universities on college students mental health education. In fact, due to the characteristics of decision-making itself, its decision-making process is highly dependent on the subjective experience of decision-makers and domain experts, such as the α, β, k in this article. Therefore, how to reduce the subjective experience and intuitive judgment as much as possible is a topic for further research in the future.

4 Conclusions and discussions

Based to analysis the essential characteristics of the factors affecting the anxiety level, this paper abstracts the level of college students anxiety into a two universes quantitative fuzzy decision-making problem, and proposes a two universe quantitative fuzzy rough set method for college students anxiety level. This method combines the risk perception and psychological evaluation system data of college students with the COVID-19 epidemic, realizes the quantitative description of the anxiety level of college students through a fuzzy set, then calculate the upper and lower approximation of the fuzzy set about the double universe of quantitative fuzzy compatibility approximation space, and give a quantitative ranking of the anxiety levels of different college students affected by COVID-19. The model proposed in this paper is a preliminary attempt to introduce the decision-making principle of two universe fuzzy rough sets into the anxiety level of college students.

The spread of COVID-19 has caused the world to face unprecedented challenges, at the same time as the spread of the epidemic, the negative emotions of college students have also increased. Therefore, while preventing the spread of the epidemic, we must also pay attention to emotional guidance, diversify the mood swings, and put forward some specific methods and suggestions to promote the mental health of college students to help college students correctly deal with health emergencies. In fact, with the advent of the era of big data, two universes information decision-making problems have appeared in many fields. Therefore, the model proposed in this paper can be widely used in many fields, such as risk management, military management, and bidding for complex construction projects. We hope that this method is expected to attract researchers working in these related fields.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China: Research on PublicEnvironmental Perception and spatial-temporal Behavior Based on Socially Aware Computing (No. 71764025).

References

Hui

D.S.

, Azhar

E.I.

, Madani

T.A.

, Ntoumi

, Kock

, Dar

, Ippolito

, Mchugh

T.D.

, Memish

Z.A.

and Drosten

, The continuing 2019-nCoV epidemic threat of novel coronaviruses to global health–The latest novel 2019 coronavirus outbreak in Wuhan, China, International Journal of Infectious Diseases 91 (2020), 264–266.

Jiang

M.M.

, Wang

, Wu

, Du

M.X.

, Fang

Z.M.

, Zhu

L.J.

, Chen

, Jin

Y.L.

and Yao

Y.S.

, Network usage and influencing factors of college students returning to school during the new crown pneumonia epidemic, China School Health 42 (2021), 260–263.

Wan

, Du

C.D.

, Xu

and Ou

L.Q.

, Analysis of the status quo of college students knowledge and response to public health emergencies, China School Health 34 (2013), 1371–1373.

Wang

Q.P.

, Zhang

D.H.

and Liang

, A NewType of Mathematics Tool-Rough Set Theory and Its Application, The Sixth Annual Conference of Decision Science Professional Committee of Chinese System Engineering Society Beijing, China, 2005, pp. 8.

Pawlak

and Skowron

, Rudiments of rough sets, Information Sciences 177 (2006).

Gao

and Cheng

, Overview of Rough Set Theory-Assisted Modern Medical Diagnosis Research Technology and Innovation (2019), 25–27+29.

Liu

, Li

J.S.

and Liu

A.J.

, Research on Superior Rough Set Classification System for Power System Fault Diagnosis Electrotechnical Technology (2018), 57–60.

Zhang

Y.P.

, Jiang

X.Y.

and Zhao

, Turnout fault prediction based on fusion of rough set and grey model, Journal of Railway Science and Engineering 16 (2019), 2331–2338.

and Liu

X.R.

, Application of Rough Set Theory in Emergency Response to Tourism Emergency, Technoeconomics 38 (2019), 78–87.

10.

Dubois

and Prade

, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (1990), 191–209.

11.

El-Monsef

M.E.A.

, El-Gayar

M.A.

and Aqeel

R.M.

, A comparison of three types of rough fuzzy sets based on two universal sets, International Journal of Machine Learning and Cybernetics 8 (2017).

12.

Yan

R.X.

, Zheng

J.G.

and Zhai

Y.M.

, Uncertainty Measurements of Dual Universe Rough Sets, Journal of Shanghai Jiaotong University 45 (2011), 1841–1845.

13.

Wang

X.R.

, Zhang

Y.Z.

and Zhang

Z.J.

, Selection of fast cargo transportation scheme based on two universe rough set, Computer application 1–7.

14.

X.Y.

and Sun

B.Z.

, Public health emergency decisionmaking model based on two universe quantitative fuzzy rough sets, Systems Science and Mathematics 39 (2019), 409–424.

15.

Sun

and Ma

, Fuzzy rough set over multi-universes and its application in decision making, Journal of Intelligent & Fuzzy Systems 32 (2016).

16.

Sun

, Zhou

and Lin

, Diversified binary relation-based fuzzy multigranulation rough set over two universes and application to multiple attribute group decision making, Information Fusion 55 (2020).

17.

, Sun

, Wang

and Jiang

, Double-quantitative decision rough set over two universes and application to African swine fever decision-making, Journal of Experimental & Theoretical Artificial Intelligence (2020), 1–17.

18.

Sun

and Ma

, Fuzzy rough set model on two different universes and its application, Applied Mathematical Modelling 35 (2010).

19.

Chauhan

and Singh

, A hybrid multi-criteria decision making method approach for selecting a sustainable location of healthcare waste disposal facility, Journal of Cleaner Production 139 (2016).

20.

Yao

Y.Y.

, Wong

S.K.M.

and Wang

L.S.

, A Non-numeric appoach to reasoning, International Journal of General Systems 23 (1995).

21.

Pei

Y.D.

and Xu

Z.-B.

, Rough Set Models on Two universes, International Journal of General Systems 33 (2004).

22.

Sun

and Ma

, Fuzzy rough set model on two different universes and its application, Applied Mathematical Modelling 36 (2012).

23.

Yang

H-L.

, Liao

, Wang

and Wang

, Fuzzy probabilistic rough set model on two universes and its applications, International Journal of Approximate Reasoning 54 (2013).

24.

Zhang

, Shu

and Liao

, Hesitant fuzzy rough set over two universes and its application in decision making, Soft Computing 21 (2017).

25.

Khalil

A.M.

, Li

S.-G.

, Lin

, Li

H.-X.

and Ma

S.-G.

, A new expert system in prediction of lung cancer disease based on fuzzy soft sets, Soft Computing (2020).

26.

Nawar

A.S.

, EI Bably

M.K.

and Fattah

E.A.A.E.

, Certain types of coverings based rough sets with application, Journal of Intelligent & Fuzzy Systems 39 (2020).

27.

Sayed

M.Ei.

, Gawad

Abdul

, A.Q. Ai Qubati

M.Ei.

and Ei-Bably

M.k.

, Soft pre-rough sets and its applications in decision making, Mathematical Biosciences and Engineering 17(5) (2020).

28.

Zhang

L.F.

, Zhang

Y.F.

, Wang

and Li

Z.Y.

, Medical image fusion based on intuitionistic fuzzy sets and brightness enhancement, Computer applications, 1–13.

29.

Mostafa

K.A.

, Gang

L.S.

, Xia

L.H.

and Quan

M.S.

, Possibility m-polar fuzzy soft sets and its application in decision-making problems, Journal of Intelligent & Fuzzy Systems 37 (2019).

30.

Khalil

A.M.

, Li

S.-G.

, Garg

, Li

and Ma

, New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications, IEEE Access 7 (2019), 51236–51253.

31.

Sharma

H.K.

, Kumari

and Kar

, A rough set theory application in forecasting models, Decision Making: Applications in Management and Engineering 3 (2020), 1–21.

32.

Fang

, Han

and Wen

C.H.

, Probabilistic hesitant fuzzy multi-attribute group decision-making method based on a new distance measure, Control and Decision, 1–8.

33.

C.H.

, Qu

G.H.

, Qu

W.H.

, Zhou

H.S.

and Zhang

, Dual hesitant fuzzy multi-attribute green behavior decision-making method considering information source correlation, Systems Science and Mathematics 40 (2020), 1224–1241.

34.

Sun

, Zhang

, Wang

and Zhang

, Diversified multiple attribute group decision-making based on multigranulation soft fuzzy rough set and TODIM method, Computational and Applied Mathematics 39 (2020).

35.

Wang

Y.Y.

and Sun

B.Q.

, Multi-period distribution optimization model for various types of emergency supplies under fuzzy information, Chinese Management Science 28 (2020), 40–51.

36.

Sun

, Zhou

and Lin

, Diversified binary relation-based fuzzy multigranulation rough set over two universes and application to multiple attribute group decision making, Information Fusion 55 (2020).

37.

Z.J.

, Hao

X.M.

, Liang

J.F.

, Li

and Lang

, Evaluation of Lightning Protection Ability Based on Interval Intuitionistic Fuzzy Sets, Electric Porcelain Lightning Arrester (2021), 56–62.

38.

Lau

E.H.

, Hsiung

C.A.

, Cowling

B.J.

, Chen

C.-H.

, Ho

L.-M.

, Tsang

, Chang

C.-W.

, Donnelly

C.A.

, Leung

G.M.

, A comparative epidemiologic analysis of SARS in Hong Kong, Beijing and Taiwan, BioMed Central (2010).

39.

Lam

K.F.

, Deshpande

J.V.

, Lau

E.H.Y.

, Naik-Nimbalkar

U.V.

, Yip

P.S.F.

and Xu

, A Test for Constant Fatality Rate of an Emerging Epidemic: With Applications to Severe Acute Respiratory Syndrome in Hong Kong and Beijing, Biometrics 64 (2008).

40.

W.H. Organization, Update 49-SARS case fatality ratio, incubation period, World Health Organization, Geneva, Switzerland (2003).

41.

Presanis

, Pebody

, Paterson

, Tom

, Birrell

, Charlett

, Lipsitch

and De Angelis

, Changes in severity of pandemic A/H1N1 influenza in England: a Bayesian evidence synthesis, Bmj 343 (2011), d5408.

42.

Nishiura

, The relationship between the cumulative numbers of cases and deaths reveals the confirmed case fatality ratio of a novel influenza A (H1N1) virus, Jpn J Infect Dis 63 (2020), 154–156.

43.

Sun

B.Z.

and Hu

X.Y.

, Quantitative Rough Set Models and Applications on Two Universe, Computer Engineering and Applications 53 (2017), 50–55+99.

44.

Tian

X.L.

, Li

Z.G.

, Wang

G.P.

, Cui

X.B.

, Research on the Simulation and Evaluation System of Aviation Ground-to-Air Missile Penetration Tactics, Military Operations Research and Systems Engineering (2005), 32–36.

45.

Rough Sets in Knowledge Discovery: Methodology and Applications, Physica-Verlag 1998.

46.

Sun

B.Z.

, Ma

W.M.

and Zhao

H.Y.

, Emergency decisionmaking model and method based on two universe fuzzy rough sets, Operations Research and Management 23 (2014), 41–48.

47.

Zhang

W.X.

, Wu

Z.W.

, Liang

J.Y.

, Rough Set Theory and Method, Beijing: Science Press (2001).

48.

Riaz

, Cagman

, Wali

and Mushtaq

, Certain properties of soft multi-set topology with applications in multicriteria decision making, Decision Making: Applications in Management and Engineering 3 (2020), 70–96.

The study on the anxiety level of college students in emergencies based on fuzzy rough set over two universes

Abstract

Keywords

1 Introduction

2 Data processing and research methods

2.1 Data Sources

Table 1 Number of area types of college students Area type Number Percentage (person) (%) Rural areas 6779 41.25 Township areas 3262 41.25 County towns 4430 41.25 Prefecture-level cities 1851 41.25 Provincial capitals or municipalities 1264 41.25 Total 17586 100.0

Footnotes

Acknowledgments

References

Table 1
Number of area types of college students

Area type Number Percentage

(person) (%)

Rural areas 6779 41.25

Township areas 3262 41.25

County towns 4430 41.25

Prefecture-level cities 1851 41.25

Provincial capitals or municipalities 1264 41.25

Total 17586 100.0