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Fuzzy graph and relation

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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