PART 10Pattern Recognition

1. Fuzzy clustering2. Fuzzy pattern recognition3. Fuzzy image processing

FUZZY SETS AND

FUZZY LOGICTheory and Applications

Fuzzy clustering

Fuzzy c-means clustering method

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

• Fuzzy c-means algorithm

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

• Clustering by Equivalence The fuzzy clustering problem can be viewed as the

problem of identifying an appropriate fuzzy equivalence relation on given data.

It usually cannot be done directly, we can readily determine a fuzzy compatibility relation (reflexive and symmetric) in terms of an appropriate distance function applied to given data.

Then, a meaningful fuzzy equivalence relation is defined as the transitive closure of this fuzzy compatibility relation.

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Fuzzy clustering

Distance function

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Fuzzy clustering

Theorem 10.1

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Fuzzy clustering

Example 10.2

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

Example 10.3

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

Membership-Roster method

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Fuzzy clustering

Example 10.4

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

• Fuzzy syntactic method

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Fuzzy clustering

Grammar

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Fuzzy clustering

Fuzzy Grammar

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Fuzzy clustering

Example 10.5

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy clustering

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Fuzzy image processing

• Fuzzy matrix

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Fuzzy image processingExample 10.6

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Fuzzy image processing

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Fuzzy image processing

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Fuzzy image processing

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Fuzzy image processing

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Fuzzy image processing

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Exercises

• 10.2

• 10.5