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Rule Based Fuzzy Cognitive Mapping:

Applications in EducationGuide : Prof. Abdul Kareem (M tech., PhD)

NAVEEN [4SF10EC062] SHREYAS A S [4SF11EC421] RAVI GHAEL [4SF10EC079] NAJASHREE [4SF10EC061]

Dept.of Electronics & Communication,SCEM

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CONTENT

• INTRODUCTION• HISTORY OF FUZZY LOGIC• LITERATURE REVIEW• FUZZY LOGIC• FUZZY LOGIC INFERENCE SYSTEM• RULE BASED FUZZY LOGIC APPLICATION IN EDUCATION• IMPLEMENTATION AND RESULT• CONCLUSION

Dept.of Electronics & Communication,SCEM

INTRODUCTION• Embeds human knowledge into working algorithms.• “Rule based fuzzy logic application in education”

FCMs in educational organization. Performance of students

o Activeness of student, o teaching materials,o Recency, o Forums on subject

the objective is to have the opportunity to revise and improve the education and assessment instruments

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HISTORY OF FUZZY LOGIC

• Bertrand Russell, a Polish logician named “Jan Lukasiewicz” started working on ‘multivalued logics’ .[1920]

• Zadeh is the father of the modern fuzzy logic.• Ebrahim Mamdani and S. Assilian. Published paper on “An

Experiment in Linguistic Synthesis with a Fuzzy Logic Controller” [1975].

• Fuzzy cognitive maps [FCMs] tool developed by Kosko,• Fuzzy Logic was developed by Dr. LotfiZadeh in 1960s

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LITERATURE REVIEW

• Cornell, there have been several studies conducted on the efficacy of using concept maps as teaching and learning tools.

• Novak reports that concept mapping plays an important role in facilitating the change of science teachers’

• Cornell that focused on conceptual changes in students over a 12 year period.

• Hebbian learning law .

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LITERATURE REVIEW

• investigate two categories of potential applications

1.They used FCMS in organizational context to promote investigation by participants of their individual

• First

FCMs have potential applications in intelligent tutoring systems

• Second

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Fuzzy logic

• Important tool in generic decision making• Applicable when model is unknown or impossible to obtain.FUZZY SETS• It is an extension of a crisp set.• values in the range of [0,1]

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CRISP V/S FUZZY

• Fuzzy logic is a system for representing uncertainty, or possibility.

• (a) crisp set boundary (b) fuzzy set boundary

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MEMBERSHIP FUNCTIONS

• A membership value between 0 and 1Different types of membership• triangular, • trapezoidal, • generalized bell shaped, • Gaussian curves, • polynomial curves, • sigmoid functions. 0

1

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FUZZY RULES

IF x is A THEN y is B• Linguistic variables : x, y• Linguistic values : A, B• Antecedent : “x is A”• Consequent : “y is B”

If the antecedent is true to some degree of membership, then the consequent is also true to that same degree

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TRUTH TABLES FOR AND, OR, AND NOT OPERATORS.

AND OR NOT• A B A∩B A B AUB A Ā 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1

μA∩B(x) = min [μA(x), μB(x)] ; μAUB(x) = max [μA(x), μB(x)] ; μĀ(x) = 1- μA(x)

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FUZZY LOGIC CONNECTIVES

• Fuzzy Conjunction, AVB max(A, B)“ Quality C is the conjunction of Quality A and B"• Fuzzy Disjunction, AB = C min(A, B)"Quality C is the disjunction of Quality A and B"

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FUZZY LOGIC INFERENCE SYSTEM

• Nonlinear mapping of the input data vector into a scalar output.

Fuzzification Inference Mechanism Defuzzification

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FUZZIFICATION

• It measure the values of the inputs variables • It comprises the process of transforming crisp values into

grades of membership for linguistic terms of fuzzy sets.

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INFERENCE MECHANISM

• membership functions • fuzzy logic operators • fuzzy if–then rules

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DEFUZZIFICATION

• Converts a fuzzy set into a crisp output• Properties of the application• Fuzzy output consists of the following steps:

1. Find the firing level of each rule,2. Find the output of each rule,3. Aggregate the individual rules outputs in order to

obtain the overall system output.

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DEFUZZIFICATION TECHNIQUES

• Centre of Gravity• Middle-of-Maxima(MOM) • Max-Criterion(Max-membership principle, Height Method)• Bisector of the Area • First (or last) of maxima• Largest of Maximum (LOM)• Smallest of Minimum (SOM)

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FUZZY INFERENCE METHOD

Fuzzy reasoning

Direct Methods

Mamdanis direct method

Takagi and Sugeno’s method

Tsukamoto methodIndirect

Methods

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MAMDANI FUZZY INFERENCE

• Step 1: Evaluate the antecedent for each rule.• Step 2: Obtain each rule's conclusion.• Step 3: Aggregate conclusions.• Step 4: Defuzzification.

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MAMDANI

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SUGENO• linear or constant. • If Input 1 = k1 and Input 2 = k2, input 3 = k3

then Output is z = ak1 + bk2 + ck3+d• For a zero-order Sugeno model, the output level z is

a constant (k1=k2 =k3=0).

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APPLICATION OF FUZZY LOGIC IN EDUCATION

• Growth of any institute• Performance of students• Three main factors

Students Attendance Teaching EffectivenessFacilities

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CONCEPT MAPPING

• Graphical representations : decision maker• Subjectivity. distributed

intelligence. structure activity; save mental work; avoid error.

Teaching Effectiveness

Student attendance

Performance

Rule Based Fuzzy cognitive map structure

Facilities

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FUZZY MEMBERSHIP FUNCTIONS AND LINGUISTIC VARIABLES

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Teaching EffectivenessStudent attendance

Linguistic variables fuzzy setMembership function

INPUTS

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FUZZY MEMBERSHIP FUNCTIONS AND LINGUISTIC VARIABLES

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Linguistic variables

Facilities

INPUTS

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FUZZY MEMBERSHIP FUNCTIONS & FUZZY LINGUISTIC VARIABLES

• OUTPUTS• Performance

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Grade

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FUZZY SET OF INPUT VARIABLES 1. Student Attendance

Fuzzy variable Degree of Membership

Medium -20 – 40

Good 20 – 80

Very good 60 – 100

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FUZZY SET OF INPUT VARIABLES 2. Teaching effectiveness

Fuzzy variable Degree of Membership

Less Effective -40 – 40

Effective 20 – 80

High Effective 60 – 100

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FUZZY SET OF INPUT VARIABLES 3. Facilities

Fuzzy variable Degree of Membership

Low -40 – 40

Medium 20 – 80

Good 60 – 100

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FUZZY SET OF OUTPUT VARIABLES Performance

Fuzzy variable Degree of Membership

Poor -30 – 30

Medium 0 – 60

Good 30 – 90

Very Good 60 –120

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RULES FORMATION• Rule 1: If Student Attendance is Medium and Teaching Effectiveness is Less Effective and Facilities is Medium then Performance of Students is Poor.Rule 2: If Student Attendance is Good and Teaching Effectiveness is Less Effective and Facilities is Medium then Performance of Students is Medium.• Rule 3: If Student Attendance is Very Good and Teaching Effectiveness is Less Effective and Facilities is Medium then Performance of Students is Medium.

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MAMDANI RULE

• μA∩B(x) = min [μA(x), μB(x)]

attendance Effectiveness facilities Performance

0.25

Result

Apply AND Operator

Fuzzy inputs Fuzzy output

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MAMDANI RULE

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CENTROID METHOD

50.87%

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IMPLIMENTATION

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FUZZY LOGIC EDITER

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MEMBERSHIP FUNCTIONS AND LINGUISTIC VARIABLES EDITOR

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MEMBERSHIP FUNCTIONS AND LINGUISTIC VARIABLES EDITOR

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ADDING RULES

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FUZZY RULE OPTIMIZATION

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SURFACE VIEWER OF ACADEMIC PERFORMANCE EVALUATION

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SIMULINKRUN

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PLOT THE GRAPHS

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RESULTFinal Value Output (%)

Student Attendance Teaching Effectiveness Facilities Performance

0 0 0 9.667

25 10 50 12.25

85 35 70 58.2

60 60 25 39.13

95 80 70 83.37

39 48 62 60

10 75 83 39.13

44 50 50 60

78 20 35 29.86

100 100 100 87

Performance of Students for Different Input Values

Step time =0

Initial value =0

Sample time =0

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ADVANTAGES

Easier to design

FCMs capture more information in the relationships between concepts.

FCMs are dynamic. FCMs express hidden relationships.

FCMs are combinable.

FCMs are tunable.  

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DISADVANTAGES

• The rules for it are not very direct.

• Many experts have proposed rules over the years for this, but there are many of them. It would be impossible to follow all of these rules, since they tend to vary from researcher to researcher.

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CONCLUSION

• This paper has discussed the potential usefulness of fuzzy cognitive mapping in educational organization settings.

• The development of graphical tools to facilitate conceptual change is an important endeavour for educational technologists and facilitators of systemic change.

• By combining the capability of fuzzy logic to represent soft knowledge domains with dynamic modelling capabilities.

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REFERENCES

[1]. Jason R. Cole, Kay A. Persichitte “Fuzzy Cognitive Mapping: Applications in Education” Nashoba Regional School District, 50 Mechanic St., Bolton, Massachusetts 01740, Ed Tech/McKee 518, University of Northern Colorado, Greeley, Colorado 80639.[2]. NeeteshSaxena, KajalKaushalSaxena “Fuzzy Logic Based Students Performance Analysis Model forEducational Institutions”,IMS Engg. College, Ghaziabad (UP), India.[3]. Timothy J. Ross “Fuzzy Logic with Engineering Applications” ,Third Edition, University Of New Mexico, USA.[4]. Kosko B. Fuzzy cognitive maps. Int J Man-Mach Stud 1986. Gardner H. The unschooled mind: How children learn and how schools should teach.

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THANK YOU

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• If attendance is (very_less) and obtained_marks is (good) then performance is (very_poor).

• If attendance is (good) and obtained_marks is (good) then performance is (fine).

• . If attendance is (very_good) and obtained_marks is (very_good) then performance is (excellent).

.

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.

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• If attendance is (very_less) and obtained_marks is (good) then performance is (very_poor).

• If attendance is (good) and obtained_marks is (good) then performance is (fine).

• . If attendance is (very_good) and obtained_marks is (very_good) then performance is (excellent).

.

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• If attendance is (very_less) and obtained_marks is (good) then performance is (very_poor).

• If attendance is (good) and obtained_marks is (good) then performance is (fine).

• . If attendance is (very_good) and obtained_marks is (very_good) then performance is (excellent).

.

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• Methodology for Measuring the Quality of Education Using Fuzzy Logic

Sergio Valdés-Pasarón, Bogart Yail Márquez, and Juan Manuel Ocegueda-Hernández Baja California Autonomous UniversityCalzada Universidad 14418, Tijuana, Baja California, México{svaldes,bmarquez,jmocegueda}@uabc.edu.mx

.