1. Fuzzy Petri Nets of Education
Jaroslav Knybel – Univesity of Ostrava

2. Necessity of Simulation
creation of new study programs
optional and selection courses
orientation of students
Student
input information
recommended way of passing the studies
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3. Fuzzy Petri Nets Use Fuzzy Graphic visualization of simulation
Open-ended input information - „some“, „lot“, „small“, „middle“
Use Fuzzy
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4. Clasic Petri Nets
Place
Transition
Edge
Token
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5. Clasic Petri Nets Example – two processes and one joint source
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6. Classical logic
Transition from one status to second one using IF THEN rules
Conjunction in antecedent
Disjunction in antecedent
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7. Conjunction in antecedent
Let’s say that statement C is true only in case that statements A and B are true. Then transcript in Petri nets the will be following µ(t):AB→C
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8. Disjuction in antecedent
Let’s say C is true when A or B is true.
Problem – this is a different net (token will be in A and B, so only one will get through)
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9. Petri nets with inhibitors
PN+inhibitive edge
E.g.: The transition will happen if it doesn’t contain token
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10. Logic in Petr nets with inhibitors
Conjunction in antecedent
Disjuction in antecedent
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11. Fuzzy Petri net IF THEN rules IF d1 THEN d2 - IF d1 AND d2 THEN d3 -
IF d1 OR d2 THEN d3 -
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12. Model of transition through studies
Mandatory, optional, selective subjects
Various orientations of studies
Initial knowledge of student
Required orientation of student
Volition of suitable subjects
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13. IF THEN rules
IF (p6) programming (at least) THEN (p7) subject „Basics of programming“
IF (p0) programming (basics) AND (p1) object programming (at least) THENsubject „the Introduction into the object programming (p2)“
IF Introduction into the object programming (good) OR Introduction into database systems (partly) THEN (p5) language UML
IF (p3) specialization of database (a lot) THEN (p4) subject Introduction into the database systems
IF Introduction into the database systems (well) THEN Relational database
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14. Grafical illustration
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15. Simulation
T0 = 0.84
T1 = 0.89
T2 = 0.71
T3 = 0.97
Let`s choose initial values P0, P1, P3, P6.
P0 = 0.71
P1 = 0.58
P3 = 0.92
P6 = 0.58
Output
P2 = 0.49
P4 = 0.82
P7 = 0.41
P5 = 0.80
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16. Simulators
Any independent software doesn’t exist for simulation of FPN.
CPN simulator – colourful Petri nets (simulators where it is possible to set up property of statuses and even of transitions)
University of Ostrava

17. Conclusion Creation of simulator
Incorporation into the current systems
Extension of PN for Fuzzy modeling application
University of Ostrava

18. The end Jaroslav Knybel – jaroslav.knybel@osu.cz
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