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Fuzzy graph and relation

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Fuzzy graph and relation. Outline. Graph and fuzzy graph Characteristics of fuzzy relations Types of fuzzy relations. Graph and fuzzy graph. Graph. Graph and fuzzy graph. Fuzzy graph. ~. ~. V : is fuzzy node. Graph and fuzzy graph. Fuzzy graph and fuzzy relation.

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Fuzzy graph and relation

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  1. Fuzzy graph and relation

  2. Outline • Graph and fuzzy graph • Characteristics of fuzzy relations • Types of fuzzy relations

  3. Graph and fuzzy graph • Graph

  4. Graph and fuzzy graph • Fuzzy graph ~ ~ V : is fuzzy node

  5. Graph and fuzzy graph • Fuzzy graph and fuzzy relation

  6. Graph and fuzzy graph • α-cut of fuzzy graph

  7. Graph and fuzzy graph • α-cut of fuzzy graph

  8. Graph and fuzzy graph • Fuzzy network

  9. Characteristics of fuzzy relations • Reflexive relation

  10. Characteristics of fuzzy relations • Symmetric relation ) ( ) ( ) ( ) (

  11. Characteristics of fuzzy relations • An example of perfect antisymmetric

  12. Characteristics of fuzzy relations • Transitive relation

  13. Characteristics of fuzzy relations • An example of transitive relation

  14. Characteristics of fuzzy relations • Transitive closure

  15. Characteristics of fuzzy relations • An example of transitive closure

  16. Types of fuzzy relation • Fuzzy equivalence relation • Reflexive relation • Symmetric relation • Transitive relation

  17. Types of fuzzy relation (i) Reflexive relation √ (ii) Symmetric relation √ (iii) Transitive relation X

  18. Types of fuzzy relation • Fuzzy equivalence relation applications • Partition of sets

  19. Types of fuzzy relation • Fuzzy equivalence relation applications • Partition by α-cut

  20. Types of fuzzy relation • Fuzzy equivalence relation applications • Set similar to element x Set similar to d Set similar to e

  21. Types of fuzzy relation • Fuzzy compatibility relation • Reflexive relation • Symmetric relation

  22. Types of fuzzy relation • Fuzzy pre-order relation • Reflexive relation • Transitive relation

  23. Types of fuzzy relation • Fuzzy semi-pre-order or nonreflexive fuzzy pre-order relation • Reflexive relation • Transitive relation

  24. Types of fuzzy relation • Anti-reflexive fuzzy pre-order relation • Anti-reflexive relation • Transitive relation (x,x) = 0

  25. Types of fuzzy relation • Fuzzy order relation • Reflexive relation • Antisymmetric relation • Transitive relation • Perfect fuzzy order

  26. Types of fuzzy relation • Fuzzy order relation  crisp order

  27. Types of fuzzy relation • Fuzzy order relation • Dominating class • Dominated class

  28. Types of fuzzy relation

  29. Types of fuzzy relation • Dissimilitude relation • Antireflexive relation • Symmetric relation • Min-Max transitive relation

  30. Types of fuzzy relation • ex Min number = 0.2

  31. Types of fuzzy relation • ex (b,c); 0.4 v 0.1 = 0.4 0.0 v 0.2 = 0.2 0.2 v 0.0 = 0.2 1.0 v 0.3 = 1.0 (d,c) ; 0.0 v 0.1 = 0.1 1.0 v 0.2 = 1.0 0.3 v 0.0 = 0.3 0.0 v 0.3 = 0.3 Min number = 0.2 Min number = 0.1

  32. Types of fuzzy relation • Fuzzy morphism • Homomorphism • Fuzzy homomorphism

  33. Types of fuzzy relation • Fuzzy morphism • Strong homomorphism • Fuzzy strong homomorphism

  34. Types of fuzzy relation • Fuzzy homomorphism

  35. Types of fuzzy relation • Fuzzy strong homomorphism

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