Note on fuzzifying probability density function and its properties

Dojin Kim; Lee Chae Jang; Seongook Heo; Patcharee Wongsason

doi:10.3934/math.2023790

Note on fuzzifying probability density function and its properties

Dojin Kim, Lee Chae Jang, Seongook Heo, Patcharee Wongsason

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

This paper applies the concepts of fuzzifying functions to the probability density function of a random variable and introduce a fuzzifying probability to better understand the probability arising from the uncertainties of the probability density function. Using the fuzzifying probability, we derive the fuzzifying expected value and the fuzzifying variance of a random variable with the fuzzifying probability density function. Additionally, we provide examples of a fuzzifying probability density function to validate that the proposed fuzzy concepts generalize crisp expected value and variance in probability theory.

Original language	English
Pages (from-to)	15486-15498
Number of pages	13
Journal	AIMS Mathematics
Volume	8
Issue number	7
DOIs	https://doi.org/10.3934/math.2023790
State	Published - 2023

Keywords

fuzzifying expected value
fuzzifying function
fuzzifying probability
fuzzifying probability density function

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10.3934/math.2023790

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Note on fuzzifying probability density function and its properties

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Keywords

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