Note on fuzzifying probability density function and its properties

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

doi:10.3934/math.2023790

AIMS Mathematics

2023, Volume 8, Issue 7: 15486-15498. doi: 10.3934/math.2023790

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Note on fuzzifying probability density function and its properties

1.
Department of Mathematics, Dongguk University, Seoul 04620, Republic of Korea
2.
Graduate School of Education, Konkuk University, Seoul 05029, Republic of Korea
3.
Department of Mathematics, Statistics and Computers, Faculty of Sciences, Ubon Ratchathani University, Ubon Ratchathani, 34190, Thailand

Received: 29 October 2022 Revised: 29 March 2023 Accepted: 19 April 2023 Published: 26 April 2023
MSC : 28E10, 46S40

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.
- fuzzifying function,
- fuzzifying probability density function,
- fuzzifying probability,
- fuzzifying expected value
Citation: Dojin Kim, Lee-Chae Jang, Seongook Heo, Patcharee Wongsason. Note on fuzzifying probability density function and its properties[J]. AIMS Mathematics, 2023, 8(7): 15486-15498. doi: 10.3934/math.2023790

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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.

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