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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)


  • 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.


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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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