scholarly journals Algebra of Fuzzy Random Variable and its Application to Science and Engineering Problem- Radon Transport from Soil into Building

2019 ◽  
Vol 8 (10S) ◽  
pp. 308-314
Keyword(s):  
Transport Model ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mathematical Structure ◽  
Engineering Problem ◽  
Temporal Behaviour ◽  
Diffusion Parameters ◽  
Uncertainty Index ◽  
Fuzzy Random

The theme of this paper is to bring out the mathematical details of fuzzy random variable and its application to model radon transport from soil into buildings. The physical processes that influence radon transport are advection and diffusion. Parameters associated with the governing partial differential equation describing radon transport from soil into buildings are radon diffusion coefficient and advective velocity of radon in air. Both the parameters are imprecise. Imprecision of these parameters is addressed as fuzzy random variable due to presence of inherent randomness within their fuzziness. Handling fuzziness within randomness is an innovative concept of computation to quantify the uncertainty of any physical system. Paper presents the mathematical structure (algebra) of fuzzy random variables. The concept of fuzzy randomness is implemented in developing radon transport model. Numerical solution of radon transport model with fuzzy random parameters is obtained by explicit forward time central space finite difference method. Support, uncertainty index, possibility, necessity and credibility of the spatial and temporal behaviour of the random behaviour of radon concentration are also computed to explore the concept and role of the fuzzy randomness in decision making issue

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

The Compatibility Assessment between Voltage Sags and Equipment Tolerance Based on Fuzzy-Random Method

2012 ◽  
Vol 588-589 ◽  
pp. 458-462
Author(s):  
Zhi Jian Yuan ◽  
Yan Li
Keyword(s):  
Engineering Application ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Assessment Model ◽  
Voltage Sags ◽  
Equipment Failure ◽  
Failure Event ◽  
Cut Set ◽  
The Impact ◽  
Fuzzy Random

The impact of voltage sags on equipment is usually described by equipment failure probability.It is generally difficult to assess and predict the probability because of the uncertainty of both the nature of voltage sags and the VTL (VTL) of equipment. By defining the equipment failure event caused by voltage sags as a fuzzy-random event, a fuzzy-random assessment model incorporating those uncertainty is developed. The model is able to convert the probability problem of a fuzzy-random variable to that of a common random variable by using λ-cut set. It is thus valuable in theoretical analysis and engineering application. The validity of the developed model is verified by Monte Carlo stochastic simulation using personal computers (PCs)as test equipment.

scholarly journals On the Generalization Performance of a Regression Model with Imprecise Elements

2017 ◽  
Vol 25 (05) ◽  
pp. 723-740 ◽  
Author(s):  
Maria Brigida Ferraro
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Prediction Error ◽  
Random Element ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Generalization Performance ◽  
Bootstrap Procedure ◽  
Link Functions ◽  
Fuzzy Random

A linear regression model for imprecise random variables is considered. The imprecision of a random element has been formalized by means of the LR fuzzy random variable, characterized by a center, a left and a right spread. In order to avoid the non-negativity conditions the spreads are transformed by means of two invertible functions. To analyze the generalization performance of that model an appropriate prediction error is introduced, and it is estimated by means of a bootstrap procedure. Furthermore, since the choice of response transformations could affect the inferential procedures, a computational proposal is introduced for choosing from a family of parametric link functions, the Box-Cox family, the transformation parameters that minimize the prediction error of the model.

A FUZZY RELIABILITY ANALYSIS BASED ON THE TRANSFORMATION BETWEEN DISCRETE FUZZY VARIABLES AND DISCRETE RANDOM VARIABLES

2006 ◽  
Vol 13 (01) ◽  
pp. 25-35 ◽  
Author(s):  
YUGE DONG ◽  
AINAN WANG
Keyword(s):  
Reliability Analysis ◽  
Fuzzy Variable ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Information ◽  
Discrete Random Variable ◽  
Fuzzy Reliability ◽  
Fuzzy Variables ◽  
Discrete Random Variables ◽  
Fuzzy Random

When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended to continuous case, and can also be used in the fuzzy reliability analysis of repairable system.

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