A novel algorithm for all normal parameter reductions of a soft set based on object weighting and integer partition

This paper aims to propose a novel algorithm for computing all normal parameter reductions of the soft set (# NPRS for short). Firstly, a weight vector is assigned to objects of the soft set domain. Then, a necessary condition for a normal parameter direction can be derived. A parameter subset is a solution only if the total value of the weighted sum of corresponding parameter approximations is a multiple of a constant number, which is equal to the sum of weights. Based on this necessary condition, we can figure out all potential solutions by using integer partition technique. It needs only to screen out the right ones at last. Experimental results are listed and compared when weight vectors are UNA, BIN, TER, OCT, DEC, DUO and HEX. Comparison results show that our method has a better performance for solving # NPRS.