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Fuzzy Relation Equation

Fuzzy Relation Equation. Problem Definition. Notations Problem. Meaning of Relation Equation. Suppose we know the overall relation between X and Z, and a part of the relation between Y and Z, what should be between X and Y. Problem Partition. Partitioned solution set. Solution. Condition

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Fuzzy Relation Equation

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  1. Fuzzy Relation Equation

  2. Problem Definition • Notations • Problem

  3. Meaning of Relation Equation • Suppose we know the overall relation between X and Z, and a part of the relation between Y and Z, what should be between X and Y.

  4. Problem Partition • Partitioned solution set

  5. Solution • Condition • Example

  6. Solution Method • Solution Lattice • Maximum Solution

  7. Solution Method • Maximum Solution

  8. Solution Method • Minimal Solution • Reduced Problems • Solution Method

  9. Solution Method

  10. SUP-I Fuzzy Relation Equation • Solution Set • Example

  11. INF-Omega I Fuzzy Relation Equation • Solution Set • Example • Other Type of Problem

  12. Some Measures of Set Equality • Equality Index • The equality index can be used as a goodness measure of approximate solution of relation equations.

  13. Application • Example: • A system can be represented as a fuzzy relation, which can be decomposed into two subsystem, the one is reachable, but the other is unreachable. Suppose the overall system and the reachable subsystem can be known and modeled by fuzzy relations. Find the relation of the other subsystem.

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