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The Mathematics of Fuzziness

The Mathematics of Fuzziness


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About the Book

Imposing a probability law on an interval in which a normal fuzzy number has been defined, and then trying to find consistency between randomness and fuzziness is not logical. If we need to establish a probability law followed by a random variable defined in a given interval, there are mathematical formalisms in the theory of statistical inferences to do so. Instead, defining a normal fuzzy number around a point, and then using a conversion factor to deduce a probability density function from the fuzzy membership function is against statistical norms. Probability densities are not found in this way. In fact, the left reference function of a normal fuzzy number is a probability distribution function, and the right reference function is a complementary probability distribution function. Hence, we need two probability laws to define the membership function of a normal fuzzy number. That the membership function is expressible as a distribution function and a complementary distribution function on the left and on the right respectively of the value with unit membership should be the real randomness- fuzziness consistency principle.


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Product Details
  • ISBN-13: 9783838399416
  • Publisher: Lap Lambert Academic Publishing
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 5 mm
  • Weight: 186 gr
  • ISBN-10: 3838399412
  • Publisher Date: 01 Sep 2010
  • Height: 229 mm
  • No of Pages: 84
  • Series Title: English
  • Sub Title: Realities and Beyond
  • Width: 152 mm


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