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Understanding Logic Frameworks: Fuzzy vs. Crisp in Data Classification

Explore the concepts of fuzzy and crisp logic in determining and classifying data sets, including examples, definitions, and limitations. Understand set operators and their relevance to geography.

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Understanding Logic Frameworks: Fuzzy vs. Crisp in Data Classification

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  1. Lecture 02: Logic Frameworks Topics: Logic frameworks (fuzzy vs. crisp) References: Chapter 11 in Burrough and McDonnell, 1998, pp. 265-291 Chapter 1 in Zimmermann, H.J. 1985

  2. Lecture 02: Logic Frameworks Outlines Logic frameworks (fuzzy vs. crisp) 1. Set Definition: Example: Definition of Pine Forests Determination: - classification Example: Determine if a patch is Pine Forests

  3. 2. Crisp logic vs. fuzzy logic 1) Crisp logic Definition: Example: tall people (height > 6 ft) Determination: Example: Limitations:

  4. 2) Fuzzy logic Definition: Example: tall people if x< 9’: [x, A(x)=(x-6)/3] otherwise: [x, A(x)=1] (diagram) Membership function (three basic forms) Determination: Example: [(6, 0.0); (7, 0.33); (7.5, 0.5); (8.0, 0.67)]

  5. 3) Crisp sets vs. fuzzy sets 3. Simple set operators The AND and OR operators for sets 1) under crisp logic 2) under fuzzy logic 4. The relevance to geography

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