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Fuzzy Petri Nets of Education
Jaroslav Knybel – Univesity of Ostrava
University of Ostrava
Necessity of Simulation
creation of new study programs optional and selection courses orientation of students
Student input information recommended way of passing the
studies
University of Ostrava
Fuzzy Petri Nets
Graphic visualization of simulation Petri Nets Open-ended input information - „some“, „lot“,
„small“, „middle“
Use Fuzzy
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Clasic Petri Nets
Place Transition Edge Token
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Clasic Petri Nets
Example – two processes and one joint source
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Classical logic
Transition from one status to second one using IF THEN rules
Conjunction in antecedent Disjunction in antecedent
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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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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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Petri nets with inhibitors
PN+inhibitive edge E.g.: The transition will happen if it doesn’t
contain token
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Logic in Petr nets with inhibitors
Conjunction in antecedent
Disjuction in antecedent
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Fuzzy Petri net
IF THEN rules
IF d1 THEN d2 - IF d1 AND d2 THEN d3 - IF d1 OR d2 THEN d3 -
213 ,min t
213 ,max t
12 t
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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
University of Ostrava
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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Grafical illustration
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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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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)
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Conclusion
Creation of simulator Incorporation into the current systems Extension of PN for Fuzzy modeling
application
