THE MATHEMATICS OF FUZZINESS: REALITIES AND BEYOND

THE MATHEMATICS OF FUZZINESS: REALITIES AND BEYOND

Randomness - Fuzziness Consistency Principle

LAP Lambert Academic Publishing ( 2010-09-01 )

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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.

Book Details:

ISBN-13:

978-3-8383-9941-6

ISBN-10:

3838399412

EAN:

9783838399416

Book language:

English

By (author) :

HEMANTA BARUAH

Number of pages:

84

Published on:

2010-09-01

Category:

Theory of probability, stochastics, mathematical statistics