Title: Construction of a fuzzy probability space with Gumbel function, Gaussian function, derivative of Gaussian function and Weibull function
Authors: Rituparna Chutia; D. Datta
Addresses: Department of Mathematics, Cotton College, Guwahati, Assam, India ' Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Mumbai, India
Abstract: Random variable basically addresses a probability space and fuzzy random variable (FRV) will address the fuzzy probability space. Concepts of FRV valued functions such as exponential function, logarithmic function and power function have been already researched. But applications in the field of failure analysis of structures very often are dealt with extreme value probability distribution functions such as Gumbel, Frechet (Type-I and Type II) and Weibull function. However such functions are well defined in presence of a large number of data. But the failure analysis of structures with insufficient information in the similar footing needs corresponding FRV valued functions. Therefore the basic thrust of this paper is to propose a concept of formulating FRV valued such type of extreme value distribution functions viz., Gumbel, Frechet and the Weibull. In this paper we have proposed the FRV valued Gumbel and Weibull function. In addition to this we have also proposed the similar concept for FRV valued Gaussian and its derivative function. Fundamental properties of these functions in the fuzzy probability space are also discussed in this paper.
Keywords: failure analysis; fuzzy probability space; Gumbel function; Gaussian function; Weibull function; fuzzy random variables; FRVs; structural failure.
International Journal of Fuzzy Computation and Modelling, 2016 Vol.2 No.1, pp.1 - 13
Accepted: 29 Aug 2015
Published online: 20 Jul 2016 *