Survey on Soft Computing Based Approaches in ...

Survey on Soft Computing Based Approaches in Academic Performance Evaluation Jyotirmay Patel

Ramjeet Singh Yadav

Department of Computer Application Meerut Institute of Technology, Meerut, UP, India

Research Scholar Department of Computer Science and Engineering, Sharda University, Greater Noida, UP, INDIA

[email protected]

[email protected]

ABSTRACT In this paper, we have described six survey of evaluation academic performance based on soft computing techniques like fuzzy logic and fuzzy expert system. The problem partly can be traced back to the uncertainty in the opinion or the evaluator that cannot be expressed properly in the traditional one-value-based scoring. Fuzzy Expert System based evaluation methods can reduce the mentioned differences. In this paper after defining criteria set for the evaluation and comparison we do a survey on six soft computing inferences based student academic performance evaluation methods. This paper also explorer the drawback of Fuzzy Expert System based existing methods of academic performance evaluation. In this paper, we have proposed the Dynamic Fuzzy Expert System for academic performance evaluation. This method will remove the drawback of six existing methods describes in this paper.

Keywords Soft Computing Techniques, Fuzzy Logic, Student Evaluation, Rules Based System, Fuzzy Inference, and Fuzzy Expert Systems.

1. Introduction In case of the evaluation of students’ academic performance containing narrative responses quite often there is vagueness in the opinion of the evaluator that hardly can be fitted in the frames of the traditional evaluation techniques where a response is rated by a single crisp value. Therefore this area could be a very good application field for Fuzzy Set theory and Fuzzy Expert System based evaluation methods. Recently several Fuzzy Set theory and Fuzzy Expert Systems methods have been published in order to deal with this problem. They can be classified in three main categories: (i) methods applying Fuzzy Set theory inference, and (ii) methods applying “only” Fuzzy arithmetic (iii) methods applying Fuzzy Expert System. The advantage of the first approach is that the rules are easily readable and understandable. Their drawback is however that they usually require a tedious preparation work done by human expert graders. Besides, such a system is usually task/subject specific, i.e. minor modifications in the aspects can lead to a demand on a completely redefinition of the rule base (rigidity of the system). Another problem arises from the fact that rule based systems can only operate with a low number of fuzzy sets owing to the exponentially growing number of necessary rules in multidimensional cases if a full coverage of the input space should be ensured. The advantage of the second approach is its simplicity and easy adaptability. Besides it can operate with a higher resolution of the input space. However, as its disadvantage it should be mentioned the lack of the humanly

easy-to-interpret rules. The advantage of the third approach is its simplicity and easy adaptability. However, as its disadvantage it should be mentioned the lack of the humanly easy-to-interpret rules. In this paper, we have proposed Dynamic Fuzzy Expert System (DEFS) for academic performance evaluation. This Dynamic Fuzzy Expert System (DEFS) is based on fuzzy logic and clustering algorithm like fuzzy C-means clustering algorithm. This paper inspired by successful application of KMeans and Fuzzy C-Means clustering algorithm for solving academic performance evaluation problems. DEFS will remove the all drawback of six existing methods describes in this paper.

2. Criteria for Comparison of Computing Evaluation Methods

Soft

In this section, we introduce a set of criteria for fuzzy methods aiming the evaluation of the students’ academic performance. We consider these requirements as properties that help the reader to compare the overviewed methods. The criteria are the followings. i. The method should not increase the time needed for the assessment compared to the traditional evaluation techniques. ii. The method should help the graders to express the vagueness in their opinion. iii. The method should be transparent and easy to understand for both parties involved in the assessment process, i.e. the students and the graders. iv. The method should ensure a fair grading. v. The method should allow the teacher to express the final result in form of a total score or percentage as well as in form of grades using a mapping between them. vi. The method should be easy implementable in software development terms. vii. The method should be compatible with the traditional scoring system.

3. Soft Computing Methods

Student

Evaluation

The soft computing techniques as compared to hard computing techniques are more powerful in providing feasible solutions to the problems that deal with uncertainties and vagueness. There are several approaches to soft computing techniques. Some of them, like Fuzzy Logic (FL), Genetic Algorithm (GA), and Fuzzy C-Means clustering algorithm, have gained impertinence because of their problem potential. The fuzzy logic, handles, imprecision, and uncertainty in a natural manner by providing a human oriented knowledge

representation is possible, but it is weak in self learning and generalization of rules.

3.1. Modeling Academic Performance Evaluation Using Soft Computing Techniques: A Fuzzy Logic Approach Ramjeet Singh Yadav, et al. (2011) presented a method to deal with the modeling academic performance evaluation using fuzzy logic. Academic performance evaluation with fuzzy expert system comprised with three steps: i. Fuzzification of inputs semester examination results and output performance value. ii. Determine of application rules and inference method. iii. Defuzzification of performance value.

3.1.1. Fuzzification of Semester Examination Results and Performance Value Fuzzification of semester examinations was carried out using input variables and their membership functions of fuzzy sets. Each student has two semester results both of which from input variables of the fuzzy logic based expert system. Each input variable has five triangular membership functions. The fuzzy sets of the input and output variable are given in Table1 and Table-2 respectively. Table-1: Fuzzy Set of input variable Linguistic variable Interval Very Low (VL) (0, 0, 25) Low (L) (0, 25, 50) Average (A) (25, 50, 75) High (H) (50, 75, 100) Very High (VH) (75, 100, 100)

3.1.2. Experimental Results Ramjeet Singh Yadav, et al. (2011), has proposed fuzzy expert system was tested with 20 student’s marks. Table-2 shows the semester scores and calculated students performance value. Table-2: Semester Score and Calculated Performance Value S.No. Semsester-1 SemesterPerformance Value 2 Fuzzy-1 Fuzzy-2 1. 40 65 0.530 0.627 2. 20 35 0.243 0.243 3. 50 65 0.654 0.750 4. 10 20 0.203 0.203 5. 45 65 0.576 0.676 6. 65 45 0.576 0.625 7. 34 60 0.462 0.530 8. 48 55 0.533 0.758 9. 56 90 0.759 0.759 10. 74 70 0.735 0.440 11. 45 50 0.440 0.575 12. 89 100 0.908 0.908 13. 100 100 0.920 0.920 14. 65 35 0.500 0.387 15. 48 50 0.473 0.473 16. 45 55 0.500 0.490 17. 55 25 0.310 0.310 18. 84 80 0765 0.778 19. 63 65 0.639 0.753 20. 28 30 0.310 0.241

Both inputs had same triangular membership functions. In the above Table-1, students 5 and 6 have same performance value. We conclude that the level of intelligence of both students is same. This is a fallacious conclusion since we find from the above Table-1 that the student 5 has improved consistently while student 6 has deteriorated consistently. This is the drawback of this fuzzy expert system proposed in this method. Here, also pointed out that the problem of in this method is that fuzzy membership value is fixed by the expert domain. Solve such type of problem by the Fuzzy C-Means algorithm.

3.2. Evaluation of Teacher’s Performance Evaluation Using Fuzzy Logic Techniques Sirigiri Pavani, et al. (2012) presented a method to deal with the evaluation of teacher’s academic performance evaluation using fuzzy logic techniques. The descriptions of this method are given below.

3.2.1. Fuzzification of Semester Examination Results and Performance Value Fuzzification of input parameters of teacher’s performance was carried out using input variables and their membership functions of fuzzy sets are given below in Table-3. Table-3: Fuzzy Set of input variables Input Name linguistic Range Variable Input1 Knowledge Bad 01-50 Good 25-75 Very Good 50-100 Input2 Speed Erratic 01-50 Delivery Manageable 25-75 Optimum 50-100 Input3 Representation Abstract 01-50 Better 25-50 Relevant 50-100 Input4 Over All Very 01-50 Impression Unimpression Impression 25-75 Very 50-100 Impression The fuzzy sets of output (performance value) variable are shown in Table-4. Input

Table-4: Fuzzy set of output variable of Teacher’s Performance Output1 Performance Linguistic Range Variable Output Performance Poor 01-40 Good 40-80 Excellent 90-100

3.2.2. Experimental Results As per the input, output parameters fuzzified and rule base is generated by applying my own reasoning as an expert person to observe or taking decision to evaluate the performance of teacher. For the simplicity of discussion only the trapezoidal fuzzified are presented here for fuzzification of a real-valued variable is done with intuition, experience and analysis of the rues and conditions associated with input data variables. Here, there are 34 numbers of rule generated using ‘AND’ and ‘OR’ operator. Some rules are below: i. If (knowledge is bad) then (performance) is poor.

ii.

If (knowledge is good) and (speed of delivery is manageable) and (presentation is relevant) then (performance is good). If (knowledge is very good) and (speed of delivery is manageable) and presentation is relevant) then (performance is good). If (knowledge is very good) and (speed of delivery is optimum) and (presentation is relevant) and (overall impression is high impressible) then (performance is excellent). The experimental results of this method are given in Table-5.

iii.

iv.

Presentation

Over All Impression

Explanation

06.0

12.9

18

15.9

20.3

20.4

2. 3. 4.

07.0 32.6 44.7

12.2 35.6 38.6

24.5 28.0 40.2

9.85 37.0 31.1

22.0 31.1 38.6

33.7 40.4 56.2

5. 6. 7.

40.2 53.8 64.4

47.7 41.7 58.3

52.2 53.5 62.8

41.1 55.2 64.4

55.0 61.4 64.4

67.2 68.3 70.4

Triangular

Speed of Delivery

1.

S.No.

Knowledge

Table-5: Input Variables and Teacher’s Performance Value Input Output (Performance)

and are entitled “IF-THEN” rules. From the discussion with the academic experts some rules are formulated from their practical and past experiences. Here, we pointed out that the drawback of this proposed study, there is need of academic expert for the generation of fuzzy rule and membership function. Step-4:Fuzzy Output (Overall Performance) and Defuzzification (Performance)): The output variable is the overall performance of the teacher, which has five linguistic variables. The degree of membership function is given by equation (1): 𝜇𝐹 𝑥 = 𝑀𝑎𝑥 𝑀𝑖𝑛 𝜇𝐴 𝑓1 , 𝜇𝐵 𝑓2 , … … … … … . , 𝑘 = 1, 2, 3, 4, … … … . 𝑟 (1) This expression determines an output membership function value for each active rule. When one rule is active an AND operation is applied between inputs. The linguistic variables of output variable are shown in Table-7.

3.3.2. Numerical Results and Discussion

8. 68.8 76.5 70.5 75.0 72.0 76.1 9. 78.5 81.1 70.5 70.0 84.1 83.8 10. 97.7 87.6 97.7 96.2 96.2 95.0 From the Table-5, the inference process when knowledge = 97.7, speed of delivery = 87.6, presentation = 97.7, overall impression = 96.2 and explanation = 96.2 then performance = 95. Here, we pointed out that the membership value of input variable and output variables are fixed by expert domain. In this method, there is no fixed set of procedure for the fuzzification. This is another drawback. Such type of problems solved by the fuzzy C-Means Clustering Algorithm

3.3. Soft Computing Model for Academic Performance of Teachers Using Fuzzy Logic O.K. Chaudhari, et al. (2012) presented a method to deal with the evaluation of teacher’s academic performance evaluation using fuzzy logic. The descriptions of this method are given below.

3.3.1. Fuzzy Expert System for Academic Performance Evaluation Steps involved in the Fuzzy Expert System are as follows: Step-1:(Crisp Value (Data)): Teachers self-appraisal forms are filled in by respective teachers with sub activity which then recommended by the head of the department and head of the institution. The crisp data is tabulated from these forms (Table-7). Step-2: (Fuzzification (Fuzzy Input Value)): The input variables (elements) are then divided into linguistic variablesexcellent, very good, good, average and poor. O.K. Chaudhari, et al. (2012) has used the trapezoidal membership function for converting the crisp set into fuzzy set. Step-3:(Fuzzy Rule and Interference Mechanism): The rules determine input and output membership functions that will be used in inference process. These rules are linguistics

In order to test the above proposed model by using fuzzy expert system and rules defined in the this study the data from one of the reputed engineering college have been used. From the input data the output variable overall performance of teacher is determined by direct method and also by using the fuzzy model developed in the study. Last two columns of Table-6 show the values of teachers’ performance by direct method and fuzzy expert system respectively. Table-6: Teachers Overall Performance (Crisp and Fuzzy) S.No. Input Variables Output Value F1 F2 F3 F4 F5 F6 Direct Fuzzy 1. 86 85 70 12 13 33 86 80 2. 85 92 90 12 14 34 92 90 3. 95 98 60 09 08 26 73 80 4. 80 95 73 10 15 32 87 80 5. 89 75 60 09 08 33 77 73 6. 94 80 60 12 10 34 84 80 7. 75 80 75 12 04 28 72 71 8. 67 75 75 09 08 33 76 76 9. 70 85 75 09 13 25 74 76 10. 85 90 90 12 08 25 77 89 11. 93 100 75 10 08 28 78 80 12. 82 80 70 09 08 30 75 75 13. 83 91 70 12 00 35 76 70 14. 80 95 73 12 00 21 63 70 15. 71 89 83 12 00 21 63 72 16. 83 90 82 12 00 26 69 76 17. 97 90 95 12 01 34 81 80 18. 75 97 90 10 02 17 61 70 19. 85 96 84 12 08 34 86 84 20. 71 95 76 10 03 23 65 72 21. 73 95 94 06 04 19 60 70 22. 70 94 85 12 09 18 68 80 23. 76 89 75 12 00 24 65 71 24. 72 95 80 12 00 23 65 74 25. 79 99 84 12 00 17 61 70 26. 86 96 90 12 00 14 59 70 27. 95 95 85 12 00 28 72 80 28. 81 96 72 10 00 26 67 70 29. 83 98 85 12 01 30 75 80 30. 79 93 73 11 02 25 68 70 31. 70 100 77 09 01 28 67 71 O.K. Chaudhari et al. (2012) observed that the difference in the direct value and the values determined by using fuzzy model. This is due to the weightage given on some important

related to teaching learning process and overall development of the institute while framing the rules. Here, we observed that the membership function values of input variable and output variables for academic performance of teachers are fixed and decided by the expert domain. This is the drawback of the proposed fuzzy expert system. In this method, we also observed that this proposed fuzzy expert system cannot group or cluster the teachers’ performance. Such type of problem can solve by the fuzzy C-means clustering algorithm.

3.4. Using Fuzzy Numbers in Educational Grading System Chiu-Keung Law (1996) presented a method for using fuzzy numbers in educational grading system. They also discussed a method to build the membership functions of several linguistic values with different weights. The description this method is given below.

3.4.1. Fuzzy Numbers of Educational Grading System Generally, Chiu-Keung Law (1996) has assigned the linguistic values A, B, C, D, and F to describe a student’s performance. It is important that the criteria of the performance of the ideal population (students who take the same course in the same school or district) be set before students take an examination. Thus, the criteria cannot be influenced by how well the subjects in the samples (students in a particular class) do on examination. They try to make the linguistic values A, B, C, D and F into corresponding reasonable normal fuzzy numbers 𝐴, 𝐵, 𝐶, 𝐷 𝑎𝑛𝑑 𝐹 with trapezoidal (or triangular) membership functions.

3.4.2. Advantage of the Fuzzy Educational Grading System As national Council of Teachers of Mathematics reported, only adding scores on examination will not give a full picture of what students know. The challenge for teacher is to try different ways of grading, scoring, and reporting to determine the best ways to describe students’ knowledge of mathematics. They list the raw scores of 10 students and their corresponding grade in Table-7. Table-7: The raw scores of 10 students and their corresponding grade S.N S S S S S Tot Fuzzy Gra o. 1 2 3 4 5 al Performa de nce Value 1. 1 1 2 2 3 100 0.8878 A 0 5 0 5 0 2. 1 1 2 2 9 94 08562 A 4 9 4 8 4 3. 0 1 1 2 2 86 0.7978 B 8 2 5 4 7 4. 0 1 1 2 0 59 0.5671 B 5 1 7 1 5 5. 0 1 1 0 1 45 0.4386 C 2 1 9 2 1 6. 0 0 0 1 0 27 0.3274 C 0 8 1 5 3 7. 0 0 0 1 0 26 0.2945 D 2 3 9 2 0 8. 0 0 0 0 0 15 0.1734 D 4 3 2 4 2 9. 0 0 0 0 0 04 0.0980 F 1 0 2 0 1

10.

0 0 0 0 0 00 0.0781 F 0 0 0 0 0 From Table-7, although the highest and lowest degrees of membership are 0.8878 and 0.0781 known that the ideal percentage of receiving grades A and grade B are 15% and 10%. It is important to emphasize that this approach not only apply to an individual, but also a group of individuals. Here, we observed that the membership function values of input variable and output variables for academic performance (grading System) of students are fixed and decided by the expert domain (educational domain). This is the drawback of the proposed fuzzy numbers grading system for students’ academic performance.

3.5. An Evaluation of Students Performance in Oral Presentation Using Fuzzy Approach Wan Suhan Wan Daud, et al. (2011) presented a method for evaluating students academic performance using fuzzy logic approach. They pointed that the evaluation of students’ performance is a process of making judgment on a student based on several elements such as examinations, assignment, test, quiz, research work and so on. They have used the following methodology for evaluating students’ performance: Step-1 (Normalized the Marks): The mark obtained by each student has to be converted to the normalized values. Normalized value is referred to a range of [0, 1]. It can be obtained by dividing the mark for each criterion with the total mark. The normalized value will be the input value of this evaluation. Table-8 shows the examples marks and the normalized values obtained by a student for all the criteria. Table-8: An example of mark and normalized value Criteria Total Mark Normalized Mark Obtained Mark Introduction and 15 11.67 0.78 Objective(C1) Research(C2) 20 15.33 0.77 System 15 12.00 0.80 Implementation(C3) Results(C4) 15 12.67 0.84 Conclusion(C5) 10 08.00 0.80 Organization(C6) 05 03.67 0.73 Creativity(C7) 05 03.00 0.60 Visual Aids(C8) 05 03.12 0.62 Stage Presence(C9) 05 04.17 0.83 Report with the 05 03.50 0.70 panels(C10) The graph of membership function is developed in order to execute the fuzzification process. In this process, the input value is mapped into the graph of membership function to obtain the fuzzy membership value of that particular input value. Each membership value will represent the level of satisfaction. Table-9 shows 12 satisfaction levels that have been proposed in this study.

Table-9: Standard Satisfaction Level and the Corresponding Degree of Satisfaction Satisfaction Laves Degree of Maximum Satisfaction Degrees of Satisfaction Exceptional(E) 80-100(0.8-1.0) 1.00 Excellent(EX) 75-79(0.750.79 0.79) Very Good(VG) 70-74(0.700.74 0.74) Fairly Good(FG) 65-69(0.650.69 0.69) Marginally Good(MG) 60-64(0.600.64 0.64) Competent(C) 55-59(0.550.59 0.59) Fairly Competent(FC) 50-54(0.500.54 0.54) Marginally 45-49(0.450.49 Competent(MC) 0.49) Bad(B) 40-44(0.400.44 0.44) Fairly Bad(FB) 35-39(0.350.39 0.39) Marginally Bad(MB) 30-34(0.300.34 0.34) Fail(B) 00-29(0.000.29 0.29) Step-2: Calculate the Degree of satisfaction by formula given below: 𝐷 𝐶𝑗 =

𝑦1 ∗𝑇 𝑋1 +𝑦2 ∗𝑇 𝑋2 +⋯+𝑦12 ∗𝑇 𝑋12 𝑦1 +𝑦2 +⋯…….+𝑦12

(2) Where yi = degree of membership value for each satisfaction level, i = 1, 2, 3,……,12. Step-3: Compute the Final Mark. The final mark for kth student by the formula given below: 𝑤 ∗𝐷 𝐶1 +𝑤 2 ∗𝐷 𝐶2 +⋯………..+𝑤 10 ∗𝐷 𝐶10 𝐹 𝑆𝑘 = 1 𝑤 1 +𝑤 2 +⋯……+𝑤 10

(3) Where wi = the total marks of ith criteria for i = 1,2, ……..,10. The result obtained is put into the fuzzy grade sheet (Table10) in the appropriate columns.

Degree of Sat.

0.4 0.6 0 0.770 0.62 0.38 0 0.759 0 0.81 0.19 0.830 0.50 0.50 0 0.765 0 0 1 1.000 0.83 0 0 0.732 0 0 0 0.600 0 0 0 0.619 0 0.2 0.8 0.958 0.2 0 0 0.700

ET

0 0 0 0 0 .17 0 0 0 0.8

EX

VG

C1 0 0 0 0 0 0 0 C2 0 0 0 0 0 0 0 C3 0 0 0 0 0 0 0 C4 0 0 0 0 0 0 0 C5 0 0 0 0 0 0 0 C6 0 0 0 0 0 0 0 C7 0 0 0 0 0 0.8 0.2 C8 0 0 0 0 0 0.43 0.57 C9 0 0 0 0 0 0 0 C10 0 0 0 0 0 0 0 The Final Mark of student-1 = 0.7869

FG

MG

CT

FC

MC

MB

F

FB

Criteria

Table-10: Fuzzy Grade Sheet with Contain the overall Fuzzy marks of Student-1 Fuzzy Membership Value

Table-11 shows the results for 10 students obtained from fuzzy and non-fuzzy method St. Non-Fuzzy Method Fuzzy Evaluation Method Final Linguistic Final Linguistic Term Mark Term Mark 1. 77 Excellent 0.79 Very Good at 0.17, Excellent at 0.83 2. 89 Exceptional 0.90 Exceptional at 1.0 3. 71 Very good 0.73 Fairly Good at 0.18, Very Good at 0.82 4. 56 Competent 0.59 Competent at 1.0 5. 69 Fairly Good 0.71 Fairly Good at 0.6, Very Good at 0.4 6. 75 Excellent 0.80 Excellent at 0.81, Exceptional at 0.19 7. 73 Very Good 0.77 Very Good at 0.4, Excellent at 0.6 8. 83 Exceptional 0.87 Exceptional at 1.0 9. 51 Fairly 0.54 Fairly Competent at Competent 1.0 10. 68 Fairly Good 0.71 Fairly Good at 0.6, Very Good at 0.4 The Table-11 shows the fuzzy marks obtained are higher than the non-fuzzy marks. Here, we pointed out that the student-1 has the performance of Very Good at 0.17 and also Excellent at 0.83. This is the drawback of the proposed method. We also pointed out that membership function is fixed and decided by the expert domain.

3.6. Fuzzy Logic Based Evaluation Performance of Students in Colleges

of

Mamatha S. Upadhya (2012) presented a method for evaluation of students’ performance based on fuzzy logic. The description of this method is given below.

3.6.1. Details about the Set Applied The proposed fuzzy system is dealt with, the range of possible values for the input and output variables are determined. These (in language of fuzzy set theory) are the membership function (input variables vs. the degree of membership function) used to map the real world measurement values to the fuzzy values. Values of the input variables are considered in term of percentage. The membership function input and output variables are given in Table-12, 13, 14 and 15. Table-12: Fuzzy membership Function for the input Variable (Student Attendance) Linguistic variable Interval Medium (0, 0, 40) Good (20, 50, 80) Very Good (60, 100, 100) Table-13: Fuzzy membership Function for the input Variable (Teaching Effectiveness) Linguistic variable Interval Less Effective (0, 0, 40) Effective (20, 50, 80) Highly Effective (60, 100, 100) Table-14: Fuzzy membership Function for the input Variable (Facilities) Linguistic variable Interval Medium (0, 0, 40) Good (20, 50, 80)

Very Good (60, 100, 100) Table-15: Fuzzy membership Function for the Output Variable (Student Performance) Linguistic variable Interval Poor (0, 0, 30) Medium (0, 30, 60) Good (30, 60, 90) Very Good (60, 100, 100) The rules framed for this study is provided below:  If student attendance is medium and teaching effectiveness is Less Effective and Facilities is medium then performance of student is poor.  If student attendance is good and teaching effectiveness is less effective and Facilities is medium then performance of student is Medium.  If student attendance is very good and teaching less effectiveness is less effective and Facilities is medium then performance of student is medium.

4. Proposed Dynamic Fuzzy Expert System (DEFS) For Academic Performance Evaluation We have proposed Dynamic Fuzzy Expert System (DEFS) for student academic performance evaluation. This proposed Dynamic Fuzzy Expert System (DEFS) consists of Fuzzy Logic, Fuzzy C-means clustering algorithm and Regression analysis model. The Fuzzy C-Means clustering algorithm is used for classify input space into different classes or clusters and regression analysis model used for output estimation of the input data.

3.6.2. Defuzzification At last, the crisp value of the ‘Performance of Students’ is obtained as an answer. This is done by defuzzifying the fuzzy output. There are many defuzzification methods available in the literature but most commonly used are centroid and maximum defuzzification methods. The criteria used to select suitable defuzzification method are very difficult. In this proposed, centroid defuzzification method is used, which is given by: 𝐷𝑒𝑓𝑢𝑧𝑧𝑖𝑓𝑖𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 =

𝜇 𝐴 𝑥 𝑥 𝑑𝑥 𝜇 𝐴 𝑥 𝑑𝑥

(4) Where A is the output fuzzy set and 𝜇𝐴 𝑥 is the membership function.

3.6.3. Results and Discussion With the input values and using the above model, the inputs are fuzzified and then by using simple if-else rules and other simple fuzzy set operations, the output fuzzy function is obtained and using the criteria, the output value for performance of students is obtained. The fuzzy output for few different input values is provided in Table-16.

Table-16: Performance of students for Different Input Values S.N Student Teaching Faciliti Performan o. Attendan Effectivene es ce of ce ss Students 1. 40 60 50 60.00 2. 80 60 70 64.54 3. 80 90 70 84.70 4. 30 90 40 47.20 5. 90 90 30 72.76 6. 35 45 65 53.80 7. 65 45 35 53.80 In the above Table-16, student 6 and 7 belong to same class (cluster). We conclude that the level of intelligence of both students is same. This is a fallacious conclusion since we find from the above Table-16 that the student 6 has improved consistently while student 7 has deteriorated consistently. This is the drawback of proposed fuzzy model for student academic performance. Solve such type of problem by the Fuzzy CMeans algorithm.

4.1. Dynamic Fuzzy Expert System (DFES) The world of information is surrounded by uncertainty and imprecision. The human reasoning process can handle inexact, uncertain, and vague concepts in an appropriate manner. Usually, the human thinking, reasoning, and perception process cannot be expressed precisely. These types of experiences can rarely express or measured using statistical or probability theory. Fuzzy logic provides a framework to model uncertainty, the human way of thinking, reasoning, and the perception process. Fuzzy system was introduced by Zadeh (1965). A fuzzy expert system is simply an expert system that uses a collection of fuzzy membership functions and rules, instead of Boolean logic, to reason about data (Schneider et al. 1996). The rules in a fuzzy expert system are usually of a form similar to the following: If A is Low and B is High then X = Medium. Where A and B are input variables, X is an output variable. Here low, high and medium are fuzzy sets defined on A, B and X respectively. The antecedent (the rule’s premise) describes to what degree the rule applies, while the rule’s consequent assigns a membership function to each of one or more output variables. Let X is a space of objects and x be a generic element of X. A classical set 𝐴, 𝐴 ⊆ 𝑋, is defined as a collection of elements objects, such that x can either belong or not belong to the set. A Fuzzy set A in X is defined as a set of ordered pairs: 𝐴 = 𝑥, 𝜇𝐴 𝑥 , 𝑥 𝜖 𝑋 , where 𝜇𝐴 𝑥 is called the membership function (MF) for the fuzzy set A. The MF maps each element of X to a membership grade (or membership value) between zero and one. Figure-1 shows the basic architecture of proposed fuzzy expert system for modeling academic performance evaluation. The main components of proposed dynamic fuzzy expert system are: a fuzzification interface, a fuzzy rule-base (knowledge base), an inference engine (decision making logic), and a defuzzification interface. i. Fuzzification Interface: The input variables are fuzzified by the Fuzzy C-Means clustering algorithm. ii. Fuzzy Rule Base (Knowledge Base): Fuzzy if-then rules and fuzzy reasoning are the backbone of fuzzy expert systems, which are the most important modeling tools based on fuzzy set theory. The rule base is characterized in the form of if-then rules in which the antecedents and

consequents involve linguistic variables. In this paper, we use very high, high, average, low and very low as linguistic variable. The collection of these rules forms the rule base for the fuzzy logic system. In this proposed dynamic fuzzy expert system, we have used the following rules for finding the knowledge base:  If student belong to very high then 𝑌1 = 𝑎1 + 𝑏1 𝑋  If student belong to high then 𝑌2 = 𝑎2 + 𝑏2 𝑋  If student belong to average then 𝑌3 = 𝑎3 + 𝑏3 𝑋  If student belong to low then 𝑌4 = 𝑎4 + 𝑏4 𝑋  If student belong to very low then 𝑌5 = 𝑎5 + 𝑏5 𝑋 Where X is the students’ mark obtained in semester1 examination. 𝑎1 , 𝑎2 , 𝑎3 , 𝑎4 , 𝑎5 𝑎𝑟𝑒 𝑏1 , 𝑏2 , 𝑏3 , 𝑏4 , 𝑏5 are constant determine by the method of regression analysis model. iii Inference Engine (Decision Making Logic): Using suitable inference procedure, the truth value for the antecedent of each rule is computed and applied to the consequent part of each rule. Here, we have used the regression analysis model for decision making. This results in one fuzzy subset to be assigned to each output variable for each rule. Again, by using suitable composition procedure, all the fuzzy subsets to be assigned to each output variable are combined together to form a single fuzzy subset for each output variable. iv Defuzzification Interface: Defuzzification means convert fuzzy output into crisp output. Here, we have used the height defuzzification technique for converting fuzzy output into crisp output (performance value of students). The defuzzification formula is given below: 𝑌= 𝜇 𝑉𝑒𝑟𝑦

𝐻𝑖𝑔 ℎ

𝑥 ×𝑌1 +𝜇 𝐻𝑖𝑔 ℎ 𝑥 ×𝑌2 +𝜇 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑥 ×𝑌3 +𝜇 𝐿𝑜𝑤 𝑥 ×𝑌4 +𝜇 𝑉𝑒𝑟𝑦

𝜇 𝑉𝑒𝑟𝑦

𝐻𝑖𝑔 ℎ

𝑥 +𝜇 𝐻𝑖𝑔 ℎ 𝑥 +𝜇 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑥 +𝜇 𝐿𝑜𝑤 𝑥 +𝜇 𝑉𝑒𝑟𝑦

𝐿𝑜𝑤

𝐿𝑜𝑤

𝑥 ×𝑌5

𝑥

(5) With the help of equation (5), we can convert the fuzzy output into crisp output (performance value of a student). The proposed Dynamic Fuzzy Expert System will successfully implement for modeling students and teachers for academic performance evaluation. In this proposed system, there is no need of the expert for defining fuzzy inference rule and fuzzy membership functions because this Dynamic Fuzzy Expert System based on Fuzzy C-Means clustering algorithms.

5. Conclusion Soft computing student evaluation methods can be a very useful tool supporting the evaluator in handling the uncertainty that is often present in the opinion of the evaluator in cases when fuzzy inference based solutions the evaluation process is not fully defined, i.e. when it cannot be fully automated. Fuzzy inference based solutions offer a transparency owing to the humanly interpretable character of the rule base. However, their disadvantage is their rigidity and the implicit weighting. A small change in the aspects or in the weighting could require a completely redefinition of the underlying rule base. Besides, owing to the implicit weighting the importance of the different aspects is not clear visible. We can summarize that none of the overviewed methods fulfils all the previously defined criteria. The lack of the compatibility with the traditional methods proved to be a common drawback of them, which probably could be solved using automatic

fuzzy rule base identification methods. The proposed Dynamic Fuzzy Expert System will automatically convert the crisp data into fuzzy set and also calculates the total marks of a student for academic performance. Thus, we can say that the proposed Dynamic Fuzzy Expert System will remove drawback of six existing methods describes in this papers.

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