In this paper, we provide a systematic characterization of finite BZMVdM-algebra by using semi-tensor product of matrices. The abstract operation law about logic of the finite algebra is transformed into the simple operation of concrete logical matrices. In addition, we study some properties of BZMVdM-algebra, such as homomorphism, isomorphism, and the product of the BZMVdM-algebra. Through logical matrix operation, the direct verifiable conditions for detecting the above properties are given.
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