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Let $X$ and $Y$ be compact K\"ahler manifolds of dimension $3$. Abimeromorphic map $f:X\rightarrow Y$ is pseudo-isomorphic if$f:X-I(f)\rightarrow Y-I(f^{-1})$ is an isomorphism.  In this paper we investigate some properties of pseudo-isomorphisms. As anapplication, we associate to any pseudo-isomorphism in dimension $3$ and asmooth closed $(3,3)$ form $\delta$ on $X\times X$ representing the cohomologyclass of the diagonal $\Delta_X$, a Monge-Ampere operator$MA(f^*(\theta),\delta)=f^*(\theta)\wedge f^*(\theta)\wedge f^*(\theta)$, here$\theta$ is a smooth closed $(1,1)$ form on $Y$. We show that this Monge-Ampereoperator is independent of the choice of $\delta$, if the followingcohomologous condition is satisfied:  {\bf Condition.} For any curve $C\subset I(f^{-1})$, we have $\{\theta\}.\{C\}=0$ in cohomology.  We conclude the paper examining a simple pseudo-isomorphism in dimension $3$.

Pseudo-isomorphisms in dimension $3$ and applications to complex Monge-Ampere equation