The matrix of dominant support parameters plays an important role in solving the normal and pseudo parameter reduction problems for soft sets. This paper aims to make a fundamental investigation on the properties of matrix of dominant support parameters. Firstly, we obtain some basic structural and quantitative properties. Then we give some retrieving algorithms and filling algorithms for computing the initial soft sets and the matrix itself by using only part of the matrix. Next we propose

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... characterization theorems to check which kind of set-valued matrices can be induced by a soft set as its matrix of dominant support parameters. Finally, we make a comparison between the matrix of dominant support parameters and the soft discernibility matrix. It's shown that the matrix of dominant support parameters has its own characteristic and can represent the soft discernibility matrix in a simple way. An alternative and simple procedure for computing the order relations with the matrix of dominant support parameters is brought in. INDEX TERMS soft set; matrix of dominant support parameters; normal parameter reduction; soft discernibility matrix