type-2 fuzzy system. alpha-plane fuzzy inference
Post on 13-Dec-2015
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Type-2 Fuzzy System
Type-2 Fuzzy System
Alpha-plane
Alpha-plane
Fuzzy inference
Rule: IF is AND is then is
The t-norm of PRODUCT operations:
Type Reduce
For a type-1 fuzzy set
For a interval type-2 fuzzy set
Type Reduce
Let [ ] are the type-1 fuzzy set, and each is different.
[ ] [ ]
Karnik-Mendel algorithm is a way to find and .
Defuzzifier
Result
Example 1:T1m=2T1v=0.3T2v=0.1X={0,0.1,0.2,0.3,…,4.0}alpha=[0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0];
Result
Example 2:T1m=2T1v=0.3T2v=0.1T2b=0.1X={0,0.1,0.2,0.3,…,4.0}alpha=[0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0];
Result
Example 3:T1m=2T1v=0.3T2v=0.1T2b=0.15X={0,0.1,0.2,0.3,…,4.0}alpha=[0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0];
Result
Example 4:T1m=2T1v=0.3T2v=0.1T2b=0.2X={0,0.1,0.2,0.3,…,4.0}alpha=[0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0];
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