Fuzzy Petri Nets of Education

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Fuzzy Petri Nets of Education
Jaroslav Knybel Univesity of Ostrava
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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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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

• Lets 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

• Lets 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

• PNinhibitive edge
• E.g. The transition will happen if it doesnt
  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 -

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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

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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
• Lets 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 doesnt 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

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The end
Jaroslav Knybel jaroslav.knybel_at_osu.cz