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A crisp set of input data is collected and transformed into a fuzzy set using fuzzy language variables, fuzzy language terms, and membership functions (Hong et al., 1996). This step is called fuzzification. The measured (sharp) input is first converted from a fuzzy set to a fuzzy set, taking into account that it is a fuzzy set and not a number that activates the rule described as a non-numeric fuzzy set. Three types of purge fire are available for the interval type 2 FLS. If the measurements are

  • • perfect, then the noise is modeled as a crisp set.
  • • noisy, then the noise is fixed and modeled as a type 1 purge set, and
  • • noisy, then the noise is abnormal and modeled as a gap type 2 purge set (the latter type of purge cannot be cleaned in a type 1 FLS)

Exercise

  • 1. What is the Footprint of Uncertainty?
  • 2. Distinguish between type 1 and type 2 fuzzy sets.
  • 3. How can a type 2 membership function be considered as an improved version of a type 1 membership function?
  • 4. Write a short note on membership functions.

References

Azar, Ahmad Taher. "Adaptive neuro-fuzzy systems." Fuzzy Systems 42, no. 11 (2010): 85-110.

Chatzis, Vassilios, and Ioannis Pitas. "A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation." IEEE Transactions on Image Processing 9, no. 10 (2000): 1798-1810.

Colliot, Olivier, Oscar Camara, and Isabelle Bloch. "Integration of fuzzy spatial relations in deformable models: Application to brain MRI segmentation." Pattern Recognition 39, no. 8 (2006): 1401-1414.

Douglas, Andrew R, Arthur M. Breipohl, Fred N. Lee, and Rambabu Adapa. "Risk due to load forecast uncertainty in short term power system planning." IEEE Transactions on Power Systems 13, no. 4 (1998): 1493-1499.

Duch, Wlodzislaw. "Uncertainty of data, fuzzy membership functions, and multilayer perceptrons." IEEE Transactions on Neural Networks 16, no. 1 (2005): 10-23.

Fulcher, John, and Lakhmi C. Jain (Eds). Computational Intelligence: A Compendium, Vol. 21. Springer, Warsaw, Poland (2008).

Gray, Alexander Westley. "Enhancement of set-based design practices via introduction of uncertainty through use of interval type-2 modeling and general type-2 fuzzy logic agent based methods." PhD dissertation, University of Michigan (2011).

Hong, Tzung-Pei, and Chai-Ying Lee. "Induction of fuzzy rules and membership functions from training examples." Fuzzy Sets and Systems 84, no. 1 (1996): 33-47.

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