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1 year ago in Applied Mathematics , Computational Intelligence By Testing

How can a gray number be converted to a fuzzy number?

In my systems modeling work, I encounter gray numbers representing uncertain intervals. To use fuzzy logic controllers, I need to convert these into proper fuzzy numbers with membership functions. I’m unsure about the principled approach whether it’s a direct mapping or if it requires additional assumptions about the data distribution within the gray interval.

FuzzyLogic GraySystems

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By Adi Answered 11 months ago

In my applied work with uncertain engineering parameters, this conversion is about interpreting the gray interval’s "potential." A gray number gives you a range, but no distribution. To convert it, you must impose an assumption. I typically recommend a triangular fuzzy number: the gray interval’s bounds become the support (membership = 0), and you choose a most plausible point, often the midpoint, for the peak (membership = 1). This is pragmatic. For more nuance, if you have historical data hinting at a distribution within the interval, you can shape a trapezoidal or Gaussian-like fuzzy set to reflect it.

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