| Granular computing is a model of thinking and a problem-solving method based on granular structure,it is also a discipline concerning information processing models,methods,technology and tools,as well as a new computing method in the area of intelligent information processing.It starts from the needs of practical problems,and replaces exact solutions with satisfactory ones by simulating structured solving model of people in face of large-scale complex problems,with the aim of simplifying problems and improving e ciency.Multigranularity feature selection and fusion are the inner requirement of complex problem solving.Multigranularity means that people analyze collected information granules from multiple perspectives,and make decisions based on the discovered useful knowledge.Such a method analyses a problem from diverse viewpoints and levels,and thus leads to a more satisfactory and plausible results.In all,multigranularity principle based modeling and realization has a guiding role in complex problem solving.The main models of multigranularity include multigranulation rough sets,multiscale rough sets,formal concept analysis based on property(object)granulation,etc.So far,although these topics have been studied extensively,some fundamental problems remain to be solved,logical principle of multigranulation rough set remains to be clarified;the optimal scale selection in multi-scale decision tables needs to be investigated in detail;a unified study of di?erent multigranulation methods has not been conducted;the existing three-way models need to be extended from crisp ones to fuzzy ones.Motivated by such a consideration,we firstly study the combination principle of multigranulation rough set and the problem property granulation and optimal scale selection.Then,we investigate interval-set concept analysis based on property granulation and examines their relationship.Lastly,we extend the three-way models from crisp cases to fuzzy ones.The main research work and innovation point include:(1)we analyze the combination principle of multigranulation rough sets from the viewpoint of aggregation functions,and provide the characteristic of the uninorm semantic representation.Moreover,we give a more general aggregation method by using uninorm and compromise operators from qualitative methods to quantitative ones.(2)We present an approach to transforming a multi-scale decision table into a multi-scale formal context,and vice versa.Then,a novel approach of optimal scale selection is provided by using mixed multigranularity method.Lastly,a comparative study between mixed granularity approach used for deriving all maximally general decision rules and the approach of cut in granularity trees is performed.(3)We mainly study the interval set concept lattice derived from a multi-scale formal context.The definition,properties and the construction methods of propertyoriented interval set concept lattice are firstly given,then,the relationship between property-oriented interval set concept lattice and object-oriented interval set concept lattice is investigated.(4)By using the inner operators in fuzzy logic,we extend the present three-way decision model from crisp cases to fuzzy ones and provide a type of L-fuzzy threeway decision theory based on residuated lattice.Similarly,we give the definition of object(property)-oriented L-fuzzy three-way decision and its properties.The proposed model can be treated as a combination of crisp concept analysis and L-fuzzy concept lattice.We also provide a novel viewpoint of L-fuzzy three-way analysis by using possibility theory,the obtained results show that L-fuzzy three-way decision can be understood in terms of set-functions in possibility theory,moreover,another three types of L-fuzzy three-way concepts can be derived by using possibility theory.Lastly,we give a type of fuzzy reasoning method based on L-fuzzy three-way concept analysis.The obtained results in this thesis provide an integrated study of fuzzy logic,three-way decision and formal concept analysis. |
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