Neighborhood Rough Sets And Multi-Granulation Fuzzy Rough Sets Based On Overlap Functions

Neighborhood rough set is an important research direction of rough set theo-ry.Compared with traditional rough set,neighborhood rough set plays an im-portant role in the analysis and mining of continuous data and complex data.Overlap function is closely related to triangular norm(t-norm),which can be regarded as a new extension of logical conjunction "and".Multi-granulation rough set is the fusion product of granular computing and rough set theory.The traditional multi-granulation rough set takes "maximum" and "minimum" operators as the fusion operators of multiple granularities,which are often used in the decision-making field.As a new aggregation operator,overlap function can better express information fusion.Therefore,this paper aims to apply overlap function to im-prove neighborhood rough sets based on t-norm and multigranulation fuzzy rough sets.In this paper,by using the idea of combining triangular norm with rough set theory for reference,the overlap function is applied to construct neighborhood fuzzy rough sets,and the neighborhood fuzzy rough sets model based on overlap function(O-NRS)is established.In addition,taking overlap function as aggregation operator,the rough set model is described from the perspective of granularity aggregation,and a multi-granulation fuzzy rough set model based on overlap function(OMGFRS)is established for the first time.The properties of two kinds of new models are deeply studied,and the advantages of the new models are illustrated by application.The results obtained in this paper are as follows:1.The O-NRS model is established for the first time,and the basic properties of the upper and lower approximation operators of the new model are explored and proved.On this basis,a new multi-attribute decision-making algorithm is proposed by combining the new neighborhood rough set model with TOPSIS method,and the effectiveness of the new model is illustrated by comparing the experimental results of "medical diagnosis" with the existing other methods.2.The optimistic OMGFRS and the pessimistic OMGFRS models are established for the first time.Overlap function is used as the aggregation operator of multiple granularity fusion,and multiple fuzzy relations are fused to construct two types of rough set models.Firstly,the basic properties of the upper and lower approximation operators of the two models are proved,such as squeezing,polarity,monotonicity and duality,which solves the problem that the lower approximation of the existing fuzzy rough set model based on overlap function is not included in the upper approximation.Secondly,the two models are compared with the traditional multi-granulation fuzzy rough set model(based on "maximum" and "minimum" opera-tors),and the inclusion relationship between its upper and lower approximation operators is proved.3.A multi-attribute group decision-making algorithm based on the OMGFRS model is proposed.A new multi-attribute group decision-making algorithm is proposed by combining the optimistic OMGFRS with TOPSIS method,and it is applied to a concrete example of "Evaluation System Analysis Engineer".Experiments are carried out by grouping three class of overlap functions and compared with other existing models.Secondly,three class of overlap functions are convexly combined and the step size is changed.After many experiments,the decision-making results have not changed,which shows the feasibility and stability of the new model in many ways.