A soft matrix multiplication of matrices in different types was not possible so far. In this study, we generalize the soft matrix products And, And-Not, Or, Or-Not defined in Cagman and Enginoglu (Comput Math Appl 59:3308-3314, 2010) so as to multiply soft matrices in different types. Furthermore, these generalizations allow us to multiply soft matrices more than two soft matrices. Therefore, we can solve decision making problems with multiple decision makers using a single product. These new operations make the process of solving decision making problems faster, easier and more convenient. Then we construct some effective decision making methods called soft distributive max-min (max-max, min-min, min-max) decision making methods. We also provided Scilab codes to demonstrate our methods.