Research On Parameter Reduction In Soft Sets Based On Soft Discernibility Matrix

Soft sets theory as a new mathematical tool to dealing with uncertainties problem is widely used in various field. Especially in the application of decision making in soft sets, and it is important to research parameter reduction for deal with the problem of decision making. In this paper, we deal with the problem of parameter reduction in complete soft sets and incomplete soft sets based on soft discernibility matrix. More details are as follows:In complete soft sets, we propose a method of parameter reduction of soft set based on soft discernibility matrix. Firstly, the notions of the change of choice value q and the cardinality of reduced set p are given, and their values range are researched. Thus the number of elements in the candidate parameter reduction set is further shrunk. Secondly, we design an efficient algorithm which involves less computation compared with the other existing approaches based on soft discernibility matrix. Finally, an illustrative example is provided to show the feasibility of our approach.In incomplete soft sets, the concept of incomplete soft discernibility matrix is constructed firstly, and the notions of similarity degree and dissimilarity degree between one object with unknown data and other objects are introduced. Secondly, a novel efficient algorithm of data filling based on incomplete soft discernibility matrix is designed. Thus, the incomplete soft sets can be converted into complete soft set, and an example is provided to show that the validity of the proposed approach. Finally, we use the algorithm of parameter reduction in complete soft sets to solve the problem of parameter reduction in incomplete soft sets.