| Rough sets(RSs)are powerful tool to deal with incomplete decision information systems,mainly relying on relevant uncertain measures.Now the uncertainty measures of incomplete decision information systems are becoming more and more perfect,but still have the disadvantages of information singleness,lack of hierarchy,perspective simpleness and so on.Hence,the dual viewpoint fusion and hierarchy construction of measures are implemented on RSs,perspective synthesis and hierarchy construction of measures are implemented on multi-granulation rough sets(NMRSs),and all the measures are applied.Therefore,expand existing uncertainty measures,and enhance the robustness and applicability of measures.The research content includes the following two aspects.(1)The dual viewpoint fusion and hierarchical construction of measures are implemented,and further applied to the multi-attribute decision making based on the single-granulation RSs.At first,the conditional entropy is hierarchically decomposed,while the dependency degree is introduced;two new types of conditional entropy with direct and hierarchical fusion are constructed,and their properties of granulation monotonicity and measurement sizes are acquired.Then,two multi-attribute decision sorting algorithms are designed by two types of hybrid conditional entropy,and they exhibit effectiveness and improvements in contrast to five sorting ways.Finally,the actual datasets is selected to carry out the decision sorting experiment,and the new sorting strategies are verified to achieve consistent effects for the existing algorithm based on conditional entropy.The hybrid conditional entropy hierarchically combines the information and algebra representations,and it improves the current conditional entropy to comprehensively characterize the system uncertainty,so its rational sorting profits multi-attribute decision making applications in incomplete decision information systems.(2)Three-way and three-level uncertainty measures and attribute reduction on NMRSs are established by combining optimistic and pessimistic perspectives from the perspective of multi-granulation.At first,the measures multi-granulation monotonicity and non-monotonicity based on NMRSs are explored,and then an optimistic NMRSs is introduced based on the pessimistic perspective symmetry to construct the underlying measures,that is pessimistic neighborhood multi-granulation dependency joint entropy PDJE and optimistic neighborhood multigranulation dependency joint entropy ODJE;then the pessimism-trend neighborhood multigranulation dependency joint entropy Pt DJE and the optimistic-trend neighborhood multigranulation dependency joint entropy Ot DJE are proposed through the preference tolerance on attitude-epitaxy level;the compromise-system neighborhood multi-granulation dependency joint entropy Cs DJE is proposed by the compromise criterion at the balanced-synthesis level.Three-way and three-level uncertainty measures(i.e.PDJE,ODJE,Pt DJE,Ot DJE,Cs DJE)imply pessimistic,optimistic and compromise three-way measures,and the dependency degree factor,calculation algorithm,size relation,coefficient expansion and multi-granulation non-monotonicity properties are obtained.In addition,the three-way and three-level measures induce attribute significance,so the correlation heuristic attribute reduction algorithms(i.e.PDJE-AR,ODJE-AR,Pt DJE-AR,Ot DJE-AR,Cs DJE-AR)are constructed.Finally,the measures properties and attribute reductions are verified by data experiments.By experimental comparison,four new algorithms(especially Cs DJE-AR)hesitate the existing PDJE-AR in the overall classification performance.In this paper,the uncertainty measures based on incomplete systems are improved by fusion and hierarchical analysis,then relevant applications are implemented.Specifically,the direct hybrid conditional entropy,hierarchical hybrid conditional entropy and correlation decision algorithm are constructed on single granulation RSs,and the three-level and three-way uncertainty measures and attribute reduction algorithms are constructed on NMRSs,further,the granulation monotonicity/non-monotonicity and other properties are studied.Decision making and attribute reduction are implemented by using correlation measures and algorithms,and the corresponding results provide a new perspective,optimize the structure,have advantages and extensibility of RSs measures. |
