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

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