In order to extend and unify the definitions of $W$-weighted DMP, $W$-weighted MPD, $W$-weighted CMP and composite outer inverses, we present the weighted composite outer inverses. Precisely, the notions of MNOMP, MPMNO and MPMNOMP inverses are introduced as appropriate expressions involving the $(M,N)$-weighted $(B,C)$-inverse and Moore–Penrose inverse. Basic properties and a number of characterizations for the MNOMP, MPMNO or MPMNOMP inverse are discovered. Various representations and characterizations of weighted composite outer inverses are studied. General solutions for certain systems of linear equations are given in terms of weighted composite outer inverses. Numerical examples are presented on randomly generated matrices of various orders.

为了扩展和统一定义 $宽$-加权DMP， $宽$-加权MPD， $宽$-加权 CMP 和复合外逆，我们呈现加权复合外逆。准确地说，引入了 MNOMP、MPMNO 和 MPMNOMP 逆的概念作为适当的表达式，包括$(米,N)$-加权 $(乙,C)$-inverse 和 Moore-Penrose 逆。发现了 MNOMP、MPMNO 或 MPMNOMP 逆的基本属性和许多特征。研究了加权复合外逆的各种表示和表征。某些线性方程组的一般解是根据加权复合外逆给出的。数值例子是在随机生成的各种阶数的矩阵上呈现的。