Fuzzy Relation Equation

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Presentation transcript:

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 Example

Solution Method Solution Lattice Maximum Solution

Solution Method Maximum Solution

Solution Method Minimal Solution Reduced Problems Solution Method

Solution Method

SUP-I Fuzzy Relation Equation Solution Set Example

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

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

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.