N-Soft Rough Sets And Its Applications In Decision Making

In the information age,the growth rate of the data involved in human production and life is closer to exponential growth,and the relationship between the data is becoming more and more complex.Although amounts of data provides the necessary basis for human to extract knowledge,more information is hidden in the information ocean and can not be truly used by people.Therefore,it is particularly important to use mathematical models to explore the internal rules and knowledge from a large number of data and make decisions.This paper introduces the two new hybrid models—N-soft rough sets and Dominance-based N-soft rough sets based on the theories of rough sets,N-soft sets and dominance relation.The two models are the extensions of the classical rough sets model,and provide new analysis methods for dealing with uncertainty and fuzziness information.The two models can effectively analyze the problems that the objects have grades and dominance relation in ordered decision information system,they can also provide more possibilities for solving the inconsistent multi-criteria decision-making problems.Firstly,N-soft sets,Pawlak rough sets,dominance relation,attribute reduction and related theories are introduced respectively in this paper.Based on these theories,the approximate spaces and approximate operators of N-soft rough sets and dominancebased N-soft rough sets are proposed.Secondly,the new decision algorithms are proposed in this paper by combining with the distribution discernibility matrix attribute reduction under the dominance relation.Finally,the examples prove that the two models can solve the multi-criteria decision-making(MCDM)problem well,and provide more convenient,more effective and more objective evaluation methods for decision maker.