Algebra of Fuzzy Random Variable and its Application to Science and Engineering Problem- Radon Transport from Soil into Building
Debabrata Datta1, Shakeela Sathish2

1Debabrata Datta, Radiological Physics & Advisory Division Bhabha Atomic Research Centre ,Mumbai – 400085

2Shakeela Sathish, Department of Mathematics SRM IST (Ramapuram Campus),Chennai – 600089 

Manuscript received on 02 October 2019 | Revised Manuscript received on 13 October 2019 | Manuscript Published on 29 June 2020 | PP: 308-314 | Volume-8 Issue-10S2 August 2019 | Retrieval Number: J100558810S19/2019©BEIESP | DOI: 10.35940/ijitee.J1055.08810S19

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Abstract: 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.

Keywords: Fuzziness, Randomness, Advection, Contaminant Migration, Dispersion, Retardation
Scope of the Article: Computer Science and Its Applications