Haar Measure on Fuzzy Lie Group

Abstract

Let $\mathfrak{G}$ be a locally compact Lie group and \(dμ\) a Haar measure defined on $\mathfrak{G}$. We consider the existence of a fuzzy analogue of $\mathfrak{G}$ denoted by $\mathfrak{G_f}$ called a fuzzy Lie group and develop a fuzzy Haar measure \(μ_f\) on $\mathfrak{G_f}$. Also we construct a fuzzy Haar integral with respect to the corresponding fuzzy Haar measure on $\mathfrak{G_f}$. And finally we show that there exists a fuzzy Haar integral that is unique up to a multiplicative constant.