Abstract
Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.
Highlights
Normal distribution occupied an important position on probability theory and mathematical statistics both theoretically and practically
Normal distribution is an index influenced by many independent random factors, but each of them only has a tiny effect
We provide a model to calculate the fuzzy concepts’ probability by the integral of normal distribution probability density function
Summary
Normal distribution occupied an important position on probability theory and mathematical statistics both theoretically and practically. It widely exists in various fields including natural phenomenon, industrial production and high-technology, etc. 1956, and a lot of combinations between fuzzy numbers and other mathematical theories were built rapidly. H. Guan 750 mathematical statistics, “may-occur”, “very-likely-occur” or “rarely-occur” are vague expressions, but we can use the fuzzy membership function to quantify, and fix them into the calculation of the normal distribution. CM Stein published in 1981 that using sum of squared errors as loss, estimation of the ways of normal in dependent random variables is advised, he suggested that mean vector centered at an arbitrary estimate could be an application of calculating approximate sets [1]. We provide a model to calculate the fuzzy concepts’ probability by the integral of normal distribution probability density function
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