CN111985793A - Online student evaluation and education method - Google Patents

Online student evaluation and education method Download PDF

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CN111985793A
CN111985793A CN202010757025.1A CN202010757025A CN111985793A CN 111985793 A CN111985793 A CN 111985793A CN 202010757025 A CN202010757025 A CN 202010757025A CN 111985793 A CN111985793 A CN 111985793A
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张孝琪
桂云苗
龚本刚
张云丰
安国强
高一凌
武圣
孙勤
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Anhui Polytechnic University
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Abstract

One or more embodiments of the present specification provide a student online assessment and education method, including generating a plurality of aspects of evaluation indexes, and dividing each aspect of evaluation indexes into a plurality of evaluation grades to obtain an evaluation index system; acquiring original data according to the obtained evaluation index system, and calculating the probability of each evaluation grade of each evaluation index to obtain the distribution probability; calculating the maximum utility score and the minimum utility score of the teacher to be evaluated under incomplete information according to the distribution probability to obtain utility score data; calculating the regret value under the decision of each teacher by adopting a minimum maximum regret value method according to the obtained utility score data; and sequencing the teaching level of the teacher from small to large according to the remorse value. The evaluation index value is simple, has good operability, does not need to determine the attribute weight in advance, fully considers the complex nonlinear relation existing between indexes, and can better process the condition that the evaluation index has data missing or data fuzzy.

Description

Online student evaluation and education method
Technical Field
One or more embodiments of the specification relate to the technical field of online evaluation and education, in particular to an online evaluation and education method for students.
Background
The student evaluation work is that college students objectively evaluate the course teaching work of a teacher in a certain period according to a certain evaluation standard and a teaching practical situation in a teaching affair system, and the quality of the course teaching of the teacher is fed back to a certain degree. Because the assessment is carried out on the internet, the student commenting and teaching activities can acquire real data and have the characteristics of convenience, timeliness and the like. Colleges and universities collect and evaluate the data through the online educational administration system to supervise the teaching quality, and then improve the teaching quality. The online evaluation and teaching of students become an important way for most colleges to assess and evaluate the teaching quality of teachers.
At present, a plurality of scholars develop researches on the aspects of student evaluation and education system construction, index system construction, evaluation method and the like. However, the applicant has found that the prior art has at least the following problems:
firstly, the theoretical performance of some evaluation methods is strong, the evaluation index value is too complex, and the actual operability of college students in evaluation needs to be improved; secondly, the proposed method is mostly a linear decision method, and the complex nonlinear relation existing among indexes is not considered; and thirdly, the existing evaluation method cannot process the condition that the evaluation index has data missing or data fuzziness.
Disclosure of Invention
In view of this, one or more embodiments of the present disclosure are directed to providing a student online assessment and education method, so as to solve the problems that some assessment methods are highly theoretical, the evaluation index value is too complex, the actual operability of the college students in performing the evaluation needs to be improved, most of the proposed methods are linear decision methods, the complex nonlinear relationship existing between the indexes is not considered, and the data is processed in a fuzzy or missing manner.
In view of the above, one or more embodiments of the present specification provide a student online review and education method, including:
generating evaluation indexes of multiple aspects, and dividing the evaluation indexes of each aspect into multiple evaluation grades to obtain an evaluation index system;
acquiring original data according to the obtained evaluation index system, and calculating the probability of each evaluation grade of each evaluation index to obtain the distribution probability;
calculating the maximum utility score and the minimum utility score of the teacher to be evaluated under incomplete information according to the distribution probability to obtain utility score data;
calculating the regret value under the decision of each teacher by adopting a minimum maximum regret value method according to the obtained utility score data;
and sequencing the teaching level of the teacher from small to large according to the remorse value.
Optionally, the generating the evaluation indexes of the multiple aspects, and dividing the evaluation index of each aspect into multiple evaluation grades to obtain an evaluation index system includes:
generating 7 evaluation indexes respectively Ci(i ═ 1,2,. 7); each evaluation index is divided into 5 evaluation grades Hn(n＝1，2，...，5)，(H1，H2，H3，H4，H5) (fail, pass, medium, good, excellent), the corresponding evaluation grade was assigned (u (H)1)，u(H2)，u(H3)，u(H4)，u(H5))＝(50,65,75,85,95)。
The method for evaluating and teaching students on line according to claim 1, wherein the obtaining of raw data according to the obtained evaluation index system, calculating the probability of each evaluation level of each evaluation index, and obtaining the distribution probability comprises:
obtaining information of a teacher to be evaluated to obtain the teacher I to be evaluatedj(j＝1，2，.., M) is an evaluation object;
obtaining the ith evaluation index in an evaluation index system and recording as fi(i＝1，2，...，L)；
Generating w as the attribute weight corresponding to the ith evaluation indexi(i ═ 1,2,. cndot., L), and
Figure BDA0002611920320000021
due to the complexity of obtaining the attribute weight of the evaluation index, under the environment of uncertain decision, the evaluation index is recorded by the number of intervals, namely
Figure BDA0002611920320000022
Capturing user evaluation data, wherein the user evaluation data comprises: the number of the evaluated persons, the number of the unevaluated persons, and the total number of the evaluated persons at each evaluation level of each evaluation index.
And acquiring the distribution probability of the evaluation of the teacher to be evaluated on each evaluation level in each evaluation index according to the user evaluation data.
Optionally, the distribution probability of the evaluation of the teacher to be evaluated on each evaluation level in each evaluation index is obtained according to the user evaluation data; wherein, the distribution probability comprises:
calculating teacher I to be evaluatedjIn the evaluation index CiTo obtain an evaluation rating of Hn(n ═ 1, 2.., 5.) probability of being evaluated βn,i(Ij)，βn,i(Ij) Is at the evaluation index CiUpper evaluation rating HnDivided by the total rater number.
According to the user evaluation data, calculating a teacher I to be evaluatedjIn the evaluation index CiAbove, an evaluation rating of H was not obtainednUnannotated probability β of (1, 2.., 5)H，i(Ij). Wherein
Figure BDA0002611920320000031
Optionally, the calculating, according to the distribution probability, a maximum utility score and a minimum utility score of the teacher to be evaluated under the incomplete information to obtain utility score data includes:
according to the distribution probability, calculating the evaluation index C of the teacher to be evaluatediUpper evaluation rating HnBasic probability distribution mn，i。
Optionally, the basic probability distribution mn，iThe calculation method is as follows:
mn，i＝mi(Hn)＝wi(βn，i(Ij))；i＝1，2，…，L；j＝1，2，…，M
Figure BDA00026119203200000315
Figure BDA0002611920320000032
wherein m isi(Hn) Evaluation index C of teacher to be evaluatediUpper evaluation rating HnA base probability mass of;
Figure BDA0002611920320000033
indicating probability values that are not assigned to the evaluation levels due to the attribute weights,
Figure BDA0002611920320000034
the probability value is a probability value that is not assigned to each evaluation level due to the presence of an unexcited state of the evaluation index.
Alternatively, according to the m obtainedi(Hn)，
Figure BDA0002611920320000035
And
Figure BDA0002611920320000036
calculating probability values of the teachers to be evaluated in different grades to obtain grade scores of the teachers to be evaluated;
Figure BDA0002611920320000037
Figure BDA0002611920320000038
Figure BDA0002611920320000039
Figure BDA00026119203200000310
Figure BDA00026119203200000311
Figure BDA00026119203200000312
wherein m isnIs expressed as the combination of each evaluation index and assigned to the evaluation grade HnThe joint probability mass of (a);
Figure BDA00026119203200000313
expressed as the unassigned joint probability mass due to the attribute weights,
Figure BDA00026119203200000314
the evaluation index is expressed as an unassigned joint probability mass due to the presence of an unanimous case. k represents a measure of the degree of evidence conflict for each evaluation index, βnIndicating that the whole of each teacher to be evaluated is evaluated to the evaluation level HnProbability of (a) ofHRepresenting the uncertainty of the overall evaluation. Beta is anAnd betan+βHThe expression was evaluated to an evaluation level HnThe probability interval of (3).
Optionally, the maximum evaluation value, the minimum evaluation value and the mean value of each teacher to be evaluated are calculated according to the obtained grade scores.
Figure BDA0002611920320000041
Figure BDA0002611920320000042
uavg(Ij)＝0.5*(umax(Ij)+umin(Ij)) (3)
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
And (4) taking the average utility score in the formula (3) as an optimization target, constructing a nonlinear pair optimization model, and calculating the maximum average utility score and the minimum average utility score of the teacher to be evaluated under incomplete information.
Max/Minuavg(Ij)＝0.5*(umax(Ij)+umin(Ij))
Figure BDA0002611920320000043
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
From the above description, it can be seen that the online evaluation and teaching method for students provided in one or more embodiments of the present specification realizes effective ranking of teaching levels of each teacher by establishing an evaluation and teaching index system and constructing a new online evaluation and teaching model based on an evidence reasoning method. Case demonstration analysis shows that the method has simple evaluation index value, good operability, no need of determining attribute weight in advance, full consideration of complex nonlinear relation existing between indexes, and good capability of processing the condition of data loss or data fuzziness existing in the evaluation index.
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In order to more clearly illustrate one or more embodiments or prior art solutions of the present specification, the drawings that are needed in the description of the embodiments or prior art will be briefly described below, and it is obvious that the drawings in the following description are only one or more embodiments of the present specification, and that other drawings may be obtained by those skilled in the art without inventive effort from these drawings.
Fig. 1 is a flow chart of a method for evaluating and teaching students on line according to one or more embodiments of the present disclosure.
Detailed Description
To make the objects, technical solutions and advantages of the present disclosure more apparent, the present disclosure is further described in detail below with reference to specific embodiments.
It is to be noted that unless otherwise defined, technical or scientific terms used in one or more embodiments of the present specification should have the ordinary meaning as understood by those of ordinary skill in the art to which this disclosure belongs. The use of "first," "second," and similar terms in one or more embodiments of the specification is not intended to indicate any order, quantity, or importance, but rather is used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that the element or item listed before the word covers the element or item listed after the word and its equivalents, but does not exclude other elements or items. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.
As one embodiment of the present invention, as shown in the figure, a student online education assessment method includes:
generating evaluation indexes of multiple aspects, and dividing the evaluation indexes of each aspect into multiple evaluation grades to obtain an evaluation index system;
the step can also include generating 7 evaluation indexes, each Ci(i ═ 1,2,. 7); each evaluation index is divided into 5 evaluation grades Hn(n＝1，2，...，5)，(H1，H2，H3，H4，H5) (fail, pass, medium, good, excellent), the corresponding evaluation grade was assigned (u (H)1)，u(H2)，u(H3)，u(H4)，u(H5))＝(50,65,75,85,95)。
Step 002, obtaining original data according to the obtained evaluation index system, and calculating the probability of each evaluation grade of each evaluation index to obtain distribution probability;
the step may further include:
obtaining information of a teacher to be evaluated to obtain the teacher I to be evaluatedj(j ═ 1, 2.. times, M) as an evaluation target;
obtaining the ith evaluation index in an evaluation index system and recording as fi(i＝1，2，...，L)，；
Generating w as the attribute weight corresponding to the ith evaluation indexi(i ═ 1,2,. cndot., L), and
Figure BDA0002611920320000061
due to the complexity of obtaining the attribute weight of the evaluation index, under the environment of uncertain decision, the evaluation index is recorded by the number of intervals, namely
Figure BDA0002611920320000062
Capturing user evaluation data, wherein the user evaluation data comprises: the number of the evaluated persons, the number of the unevaluated persons, and the total number of the evaluated persons at each evaluation level of each evaluation index.
And acquiring the distribution probability of the evaluation of the teacher to be evaluated on each evaluation level in each evaluation index according to the user evaluation data. Wherein, the distribution probability comprises:
calculating teacher I to be evaluatedjIn the evaluation index CiTo obtain an evaluation rating of Hn(n ═ 1, 2.., 5.) probability of being evaluated βn，i(Ij)，βn，i(Ij) Is at the evaluation index CiUpper evaluation rating HnDivided by the total rater number.
According to the user evaluation data, calculating a teacher I to be evaluatedjIn the evaluation index CiAbove, an evaluation rating of H was not obtainednUnannotated probability β of (1, 2.., 5)H，i(Ij). Wherein
Figure BDA0002611920320000063
And step 003, calculating the maximum utility score and the minimum utility score of the teacher to be evaluated under the incomplete information according to the distribution probability to obtain utility score data.
The step may further include: according to the distribution probability, calculating the evaluation index C of the teacher to be evaluatediUpper evaluation rating HnBasic probability distribution mn，iWherein:
mn，i＝mi(Hn)＝wi(βn，i(Ij))；i＝1，2，…，L；j＝1，2，…，M
Figure BDA0002611920320000064
Figure BDA0002611920320000065
wherein m isi(Hn) Evaluation index C of teacher to be evaluatediUpper evaluation rating HnA base probability mass of;
Figure BDA0002611920320000066
indicating no score due to attribute weightA probability value assigned to each evaluation level,
Figure BDA0002611920320000067
the probability value is a probability value that is not assigned to each evaluation level due to the presence of an unexcited state of the evaluation index.
According to the obtained mi(Hn)，
Figure BDA0002611920320000068
And
Figure BDA0002611920320000069
calculating probability values of the teachers to be evaluated in different grades to obtain grade scores of the teachers to be evaluated;
Figure BDA0002611920320000071
Figure BDA0002611920320000072
Figure BDA0002611920320000073
Figure BDA0002611920320000074
Figure BDA0002611920320000075
Figure BDA0002611920320000076
wherein m isnIs expressed as the combination of each evaluation index and assigned to the evaluation grade HnThe joint probability mass of (a);
Figure BDA0002611920320000077
expressed as the unassigned joint probability mass due to the attribute weights,
Figure BDA0002611920320000078
the evaluation index is expressed as an unassigned joint probability mass due to the presence of an unanimous case. k represents a measure of the degree of evidence conflict for each evaluation index, βnIndicating that the whole of each teacher to be evaluated is evaluated to the evaluation level HnProbability of (a) ofHRepresenting the uncertainty of the overall evaluation. Beta is anAnd betan+βHThe expression was evaluated to an evaluation level HnThe probability interval of (3).
And calculating the maximum evaluation value, the minimum evaluation value and the mean value of each teacher to be evaluated according to the obtained grade scores.
Figure BDA0002611920320000079
Figure BDA00026119203200000710
uavg(Ij)＝0.5*(umax(Ij)+umin(Ij)) (3)
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
Assuming that the weights are known, the average utility score can be calculated through the formulas (1-3), so that the evaluation and the ranking of teachers in colleges and universities are realized. In practice, the interval weight is used as a constraint condition, the average utility score in the formula (3) is used as an optimization target, a nonlinear pairwise optimization model is constructed, and the maximum average utility score and the minimum average utility score of each teacher to be evaluated under incomplete information are calculated.
Max/Min uavg(Ij)＝0.5*(umax(Ij)+umin(Ij))
Figure BDA00026119203200000711
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
Step 004: and calculating the regret value under the decision of each teacher by adopting a minimum maximum regret value method according to the obtained utility score data.
Step 005: and sequencing the teaching level of the teacher from small to large according to the remorse value.
The invention is exemplified by the following teaching level demonstration evaluation using a public repair course of a college as an example, in which 234 students have selected the course and 4 teachers I1，I2，I3，I4And giving lessons together. On-line evaluation and teaching index system 7 attributes C1，C2，C3，C4，C5，C6，C7The attribute index weight value range under the incomplete information is expressed as (w)1，w2，w3，w4，w5，w6，w7)∈{[0.05，0.2]；[0.05，0.2]；[0.05，0.35]；[0.05，0.5]；[0.05，0.45]；[0.05，0.2]；[0.05，0.37]}. The online education rating is evaluated by 5 grades, and the corresponding grade score is (50, 65, 75, 85, 95). Next, the teaching levels of 4 teachers were evaluated using the above evaluation procedure, and the calculation procedure used Mtalab 2016(b) software.
(1) And (5) counting the original data and calculating the probability on the index level. The original data is derived from the online educational administration system, and the statistical data on the level (including the number of unevaluated students on the level) is divided by the total number of the students evaluating the education to be converted into the statistical probability distribution on the level, and the results are as follows:
TABLE 1 teacher's evaluation of grades and probabilities on different attributes
Figure BDA0002611920320000081
TABLE 2 teacher's evaluation of the rank and probability on different attributes
Figure BDA0002611920320000082
Figure BDA0002611920320000091
TABLE 3 teacher's evaluation of the rank and probability on different attributes
Figure BDA0002611920320000092
TABLE 4 teacher's evaluation of the rank and probability on different attributes
Figure BDA0002611920320000093
(2) With I1For example, the process of solving the maximum and minimum utility scores is described. Because the target function is a nonlinear function, using the formula (1-3), calling fmincon function in Matlab software, where x0 is [ 1/7; 1/7, respectively; 1/7, respectively; 1/7, respectively; 1/7, respectively; 1/7, respectively; 1/7]An optimization is performed for the initial point of optimization and a minimum utility score 83.48 is calculated. The nonlinear optimization solution in the Matlab software is obtained as the minimum value, so that the negative sign is added in the objective function, and the maximum utility score is obtained by optimizing again, namely 87.41. And the like, and obtaining the maximum and minimum utility scores of other teachers under incomplete information. The details are shown in table 5 below:
table 54 teacher maximum and minimum utility scores
Figure BDA0002611920320000094
Figure BDA0002611920320000101
(3) And according to the steps, calculating the regret value under the decision by adopting a minimum maximum regret value method.
R(I1)＝max[max(85.78,88.55,84.91)-83.48,0]＝88.55-83.48＝5.07；
R(I2)＝max[max(87.41,88.55,84.91)-84.17,0]＝88.55-84.17＝4.36；
R(I3)＝max[max(87.41,85.78,84.91)-85.20,0]＝87.41-85.20＝2.21；
R(I4)＝max[max(87.41,85.78,88.55)-83.23,0]＝88.55-83.23＝5.32。
Obtaining 4 teacher teaching horizontal sequence I according to the minimum regret value3＞I2＞I1＞I4(">" indicates a preference).
It is to be appreciated that the method can be performed by any apparatus, device, platform, cluster of devices having computing and processing capabilities.
While the present disclosure has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic ram (dram)) may use the discussed embodiments.
It is intended that the one or more embodiments of the present specification embrace all such alternatives, modifications and variations as fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements, and the like that may be made without departing from the spirit and principles of one or more embodiments of the present disclosure are intended to be included within the scope of the present disclosure.

Claims (8)

1. A student online evaluation and education method is characterized by comprising the following steps:
generating evaluation indexes of multiple aspects, and dividing the evaluation indexes of each aspect into multiple evaluation grades to obtain an evaluation index system;
acquiring original data according to the obtained evaluation index system, and calculating the probability of each evaluation grade of each evaluation index to obtain the distribution probability;
calculating the maximum utility score and the minimum utility score of the teacher to be evaluated under incomplete information according to the distribution probability to obtain utility score data;
calculating the regret value under the decision of each teacher by adopting a minimum maximum regret value method according to the obtained utility score data;
and sequencing the teaching level of the teacher from small to large according to the remorse value.
2. The method as claimed in claim 1, wherein the generating of evaluation indexes of a plurality of aspects and dividing the evaluation indexes of each aspect into a plurality of evaluation grades to obtain an evaluation index system comprises:
generating 7 evaluation indexes respectively Ci(i ═ 1,2,. 7); each evaluation index is divided into 5 evaluation grades Hn(n＝1，2，...，5)，(H1，H2，H3，H4，H5) (fail, pass, medium, good, excellent), the corresponding evaluation grade was assigned (u (H)1)，u(H2)，u(H3)，u(H4)，u(H5))＝(50,65,75,85,95)。
3. The method for evaluating and teaching students on line according to claim 1, wherein the obtaining of raw data according to the obtained evaluation index system, calculating the probability of each evaluation level of each evaluation index, and obtaining the distribution probability comprises:
obtaining information of a teacher to be evaluated to obtain the teacher I to be evaluatedj(j ═ 1, 2.. times, M) as an evaluation target;
obtaining the ith evaluation index in an evaluation index system and recording as fi(i＝1，2，...，L)；
Generating w as the attribute weight corresponding to the ith evaluation indexi(i ═ 1,2,. cndot., L), and
Figure FDA0002611920310000011
due to the complexity of obtaining the attribute weight of the evaluation index, under the environment of uncertain decision, the evaluation index is recorded by the number of intervals, namely
Figure FDA0002611920310000012
Capturing user evaluation data, wherein the user evaluation data comprises: the number of the evaluated persons, the number of the unevaluated persons, and the total number of the evaluated persons at each evaluation level of each evaluation index.
And acquiring the distribution probability of the evaluation of the teacher to be evaluated on each evaluation level in each evaluation index according to the user evaluation data.
4. The method for evaluating and teaching students on line according to claim 3, wherein the distribution probability of evaluation of a teacher to be evaluated at each evaluation level in each evaluation index is obtained according to the user evaluation data; wherein, the distribution probability comprises:
calculating teacher I to be evaluatedjIn the evaluation index CiTo obtain an evaluation rating of Hn(n ═ 1, 2.., 5.) probability of being evaluated βn，i(Ij)，βn，iThe value of (Ij) is in the evaluation index CiUpper evaluation rating HnDivided by the total rater number.
According to the user evaluation data, calculating a teacher I to be evaluatedjIn the evaluation index CiAbove, an evaluation rating of H was not obtainednUnannotated probability β of (1, 2.., 5)H，i(Ij). Wherein
Figure FDA0002611920310000021
5. The method for evaluating and teaching students on line according to claim 1, wherein the calculating of the maximum utility score and the minimum utility score of the teacher to be evaluated under incomplete information according to the distribution probability comprises:
according to the distribution probability, calculating the evaluation index C of the teacher to be evaluatediUpper evaluation rating HnBasic probability distribution mn，i。
6. The method as claimed in claim 5, wherein the basic probability distribution m isn，iThe calculation method is as follows:
mn，i＝mi(Hn)＝wi(βn，i(Ij))；i＝1，2，...，L；j＝1，2，...，M
Figure FDA0002611920310000022
Figure FDA0002611920310000023
wherein m isi(Hn) Evaluation index C of teacher to be evaluatediUpper evaluation rating HnA base probability mass of;
Figure FDA0002611920310000024
indicating probability values that are not assigned to the evaluation levels due to the attribute weights,
Figure FDA0002611920310000025
the probability value is a probability value that is not assigned to each evaluation level due to the presence of an unexcited state of the evaluation index.
7. The method as claimed in claim 6, wherein the method comprises obtaining mi(Hn)，
Figure FDA0002611920310000026
And
Figure FDA0002611920310000027
calculating probability values of the teachers to be evaluated in different grades to obtain grade scores of the teachers to be evaluated;
Figure FDA0002611920310000031
Figure FDA0002611920310000032
Figure FDA0002611920310000033
Figure FDA0002611920310000034
Figure FDA0002611920310000035
Figure FDA0002611920310000036
wherein m isnIs expressed as the combination of each evaluation index and assigned to the evaluation grade HnThe joint probability mass of (a);
Figure FDA0002611920310000037
expressed as the unassigned joint probability mass due to the attribute weights,
Figure FDA0002611920310000038
the evaluation index is expressed as an unassigned joint probability mass due to the presence of an unanimous case. k represents a measure of the degree of evidence conflict for each evaluation index, βnIndicating that the whole of each teacher to be evaluated is evaluated to the evaluation level HnProbability of (a) ofHRepresenting the uncertainty of the overall evaluation. Beta is anAnd betan+βHThe expression was evaluated to an evaluation level HnThe probability interval of (3).
8. The method as claimed in claim 7, wherein the maximum evaluation value, the minimum evaluation value and the mean value of the teachers to be evaluated are calculated based on the obtained ranking scores.
Figure FDA0002611920310000039
Figure FDA00026119203100000310
uavg(Ij)＝0.5*(umax(Ij)+umin(Ij)) (3)
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
And (4) taking the average utility score in the formula (3) as an optimization target, constructing a nonlinear pair optimization model, and calculating the maximum average utility score and the minimum average utility score of the teacher to be evaluated under incomplete information.
Max/Min uavg(Ij)＝0.5*(umax(Ij)+umin(Ij))
Figure FDA00026119203100000311
Wherein u ismax(Ij) Is the maximum evaluation value, umin(Ij) As a minimum evaluation value, uavg(Ij) Is the mean value.
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