The exact definition of fuzzy randomness: An application of the mathematics of partial presence

Abstract

Fuzzy randomness leads to fuzzy conclusions. Such fuzzy conclusions can indeed be made in terms of probability. In this article, the concept of fuzzy randomness has been discussed using the mathematics of partial presence. Two important points have been suggested in this article. First, fuzzy randomness should be explained with reference to the Randomness -Fuzziness Consistency Principle, and only then the mathematical explanations of fuzzy randomness would actually be complete. Secondly, in every case of fuzzy statistical hypothesis testing, the alternative hypotheses must necessarily be properly defined. The authors in this article have described fuzzy randomness with reference to a numerical example of using the Student's t-test statistic.