Answers.Body: <p>After re-reading Jang's original (1993?) paper on ANFIS, I learned he recommended simply squaring the b-parameter to deal with the notion that b could be changed to a negative value when using back-propagation. While this solves the negative domain issue, the issue still remains that if b is a non-integer, then the bell function loses its intended shape. I suppose after squaring one could round to the nearest integer, but I suspect that doing so might hinder convergence. Perhaps a consideration is only tuning the a and c parameters using something like a genetic algorithm.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2018-03-01T18:12:53.193Z
Answers.LastActivityDate: 2018-03-01T18:12:53.193Z
Answers.UserDisplayName: Matt Cremeens
Body: <p>In order for the generalized bell membership function to retain its defined shape and domain, two restrictions must be placed on the b parameter: 1) b must be positive and 2) b must be an integer. Using backpropagation to tune the membership parameters (a,b and c in the bell), it appears to be possible that the correction to b will break one or both of these restrictions on b. Can someone please explain to me how we can use backpropagation to tune the b parameter (as well as a and c) without violating 1) and 2)?</p>
  
Tags: <neural-networks><machine-learning><fuzzy-logic>
Title: Tuning the b parameter, ANFIS
UserDisplayName: Matt Cremeens
ThreadText: # Tuning the b parameter, ANFIS
  
  (Asked by: username_0 on 2018-02-12)
  
  In order for the generalized bell membership function to retain its defined shape and domain, two restrictions must be placed on the b parameter: 1) b must be positive and 2) b must be an integer. Using backpropagation to tune the membership parameters (a,b and c in the bell), it appears to be possible that the correction to b will break one or both of these restrictions on b. Can someone please explain to me how we can use backpropagation to tune the b parameter (as well as a and c) without violating 1) and 2)?
  
  **Tags:** neural-networks, machine-learning, fuzzy-logic
  
  
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  ## 1 answers
  
  ### Answer by username_0 on 2018-03-01. Score: 1 | Accepted answer
  
  After re-reading Jang's original (1993?) paper on ANFIS, I learned he recommended simply squaring the b-parameter to deal with the notion that b could be changed to a negative value when using back-propagation. While this solves the negative domain issue, the issue still remains that if b is a non-integer, then the bell function loses its intended shape. I suppose after squaring one could round to the nearest integer, but I suspect that doing so might hinder convergence. Perhaps a consideration is only tuning the a and c parameters using something like a genetic algorithm.
  
  
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