a data-driven fuzzy rule-based approach for studentacademic performance evaluation

Fuzzy Rule-Based System„ Fuzzy set Theory „ Fuzzy membership functions „ Fuzzy logical operators „ Fuzzy IF-THEN rules... Fuzzy Membership Functions„ measure linguistic variable „ A ling

A Data-Driven Fuzzy Rule-Based Approach for Student

Academic Performance Evaluation

Ernest Wu Paper Reading

Assessment Components (method)

„ Series of tests and quizzes

„ Portfolios

„ Formal written examinations

„ Individual Assignments and Coursework

„ Group work

„ Observation

„ Theses and publishable materials

„ Posters and oral presentation

„ Single letter-grade (A, B, C, D, E, F)

„ Nominal score (1, 2, …, 10)

„ Single numerical score (100 percent)

„ Linguistic terms ("Pass" and "Fail“)

„ GPA (0.00~4.00)

目前來說，使用數值資料表示法來作進一步統計計算比較普遍。

層的方式，將它們匯總起來。

來就是大概，因此使用fuzzy concepts可以面對這種 狀況。

的詞彙比較不能處理，若能使用自然語言將會讓衡量 更有彈性。

新增的衡量方式

Fuzzy Rule-Based System

„ Fuzzy set Theory

„ Fuzzy membership functions

„ Fuzzy logical operators

„ Fuzzy IF-THEN rules

Fuzzy set theory

„ 傳統set theory—everything is precise

„ Fuzzy set theory

Fuzzy Membership Functions

„ measure linguistic variable

„ A linguistic variable is defined as a variable whose values

are words or sentences in a natural or synthetic language

„ choosing or generating an appropriate fuzzy membership function to represent a linguistic term is very important.

Fuzzy Logical Operators

„ Traditional logical operators

‰ Complement Æ negation

‰ Intersection Æ conjunction

‰ Union Æ disjunction

Fuzzy Logical Operators(2)

„ Fuzzy Negation:

„ Fuzzy Conjunction (t-norm):

„ Fuzzy Disjunction (t-conorm):

Min-Max operators have been used widely probably because of their simplicity.

Fuzzy IF-THEN Rules

„ “IF x is A THEN y is B" where A and B are fuzzy sets

„ fuzzy IF-THEN rules are production rules whose antecedents, consequences or both are fuzzy

„ linguistic fuzzy model

‰ Mamdani-type FRBS

‰ Takagi-Sugeno-Kang (TSK) type FRBS

Fuzzy IF-THEN Rules(2)

Mamdani-type FRBS

Demonstration

Traditional decision tree- training set

No Strong

High Mild

Rain

Yes Weak

Normal Hot

Overcast

Yes Strong

High Mild

Overcast

Yes Strong

Normal Mild

Sunny

Yes Weak

Normal Mild

Rain

Yes Weak

Normal Cool

Sunny

No Weak

High Mild

Sunny

Yes Strong

Normal Cool

Overcast

No Strong

Normal Cool

Rain

Yes Weak

Normal Cool

Rain

Yes Weak

High Mild

Rain

Yes Weak

High Hot

Overcast

No Strong

High Hot

Sunny

No Weak

High Hot

Sunny

play ball Wind

Humidity Temperature

Outlook

Traditional decision tree- generate tree

„ Outlook = Overcast: Yes (4.0)

Traditional decision tree- testing

„ Outlook: Sunny, Humidity: Normal

„ Decision:

‰ Yes CF = 1.00 [ 0.50 - 1.00 ]

Traditional decision tree- generate rules

Data Driven FRBS with WSBA method

Training Dataset

Testing Set

Labels used for each linguistic term

Step 1: Divide dataset into subgroups

„ The training dataset was divided into three

subgroups according to the classification outcomes.

Step 2: Define fuzzy partition

„ The fuzzy partition is pre-defined according to the criterion of evaluation It will be used to

transform crisp values into fuzzy values

Step 3: Calculate fuzzy subsethood values

„ Calculate fuzzy subsethood values for each linguistic term in each subgroup

Step 4: Calculate weights for each linguistic term

„ Calculate weights for each linguistic term

using subsethood values calculated in Step 3

Step 5: Create rule

„ Rule 1: The Final Grade is Poor (X)

0.43B2) AND Final Exam is (C1 OR 0.04C2) THEN the Final Grade is Poor

„ Rule 2: The Final Grade is Average (Y)

(0.27B1 OR B2 OR 0.59B3) AND Final Exam is (0.68C1 OR C2 OR 0.21C3) THEN the Final Grade is Average

„ Rule 3: The Final Grade is Good (Z)

B3) AND Final Exam is (C3) THEN the Final Grade is Good

Testing the ruleset for classification tasks

„ For testing the ruleset trained using SAP-1 for classification

of student performance, the SAP-2 dataset is used.

Data Driven FRBS—Steps

Subsethood-Based Rule Generation

Algorithm (SBA)

„ handle classification problems.

„ classify training data into subgroups according to

the underlying classification results

„ calculate fuzzy subsethood values for every variable

in each subgroup

„ create rules

Subsethood-Based Rule Generation

Algorithm (SBA) (2)

Fuzzy rules dependent on the fuzzy subsethood values and a prespecified threshold value

α ∈ [0, 1] Any variables that have a subsethood value that is greater than or equal to α will automatically be chosen as an antecedent for the fuzzy rules.

Weighted Subsethood-based Rule Generation Algorithm (WSBA)

Conclusion of this paper

„ The development of WSBA, which is based

on fuzzy subsethood values, offers simplicity

by generating default fuzzy rules without the need to use any threshold value This is quite useful in the area of educational evaluation

„ http://designer.mech.yzu.edu.tw/papers/kevin87/ch2.doc

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