Abstract :
In this paper, a class of 1D fuzzy numbers is studied. The definitions of arithmetic operations such as addition, subtraction, scalar multiplication and multiplication between fuzzy number and fuzzy number are given without the aid of alpha-level set. And also we study the expectation, variance, covariance of fuzzy random variables and differential, Stieltjes integral of fuzzy number-valued functions without the aid of set-valued theory which is very different from the present research approach. Fuzzy number-valued Brownian motion and its properties are studied, which are very similar to real-valued Brownian motion.
Keywords :
Brownian motion; fuzzy set theory; integral equations; stochastic processes; 1D fuzzy numbers; Stieltjes integral; addition operation; arithmetic operations; differential; fuzzy Brownian motion; fuzzy random variables covariance; scalar multiplication; subtraction operation; Cybernetics; Machine learning; Stieltjes integral; arithmetic operations; differential; fuzzy Brownian motion; fuzzy number; stochastic integral;
