Note on fuzzifying probability density function and its properties-Reference-Cited by-同舟云学术

Note on fuzzifying probability density function and its properties

Published:2023 Issue:7 Volume:8 Page:15486-15498
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Kim Dojin¹,Jang Lee-Chae²,Heo Seongook¹,Wongsason Patcharee³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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