Research On An Incremental Algorithm For Constructing Concept Trilattices

With the development of technology,there are a large amount of three-dimensional data.Formal concept analysis(FCA)is unable to excavate worthy information to analyze it.With the improvement of FCA,TCA gets more and more attentions.TCA is a kind of new theory to analyze three-dimensional data.And to study triadic concept analysis(TCA)can help us to acquire some valuable things.It is a practical research subject.An algorithm of constructing concept trilattices is foundational to realize application of TCA.Based on fundamental theories of TCA,The major work of this thesis are as follows:(1)We prove the related theorem of algorithm for constructing concept trilattices.In the part of the related theorem,the first is to exclude the triple that is not triadic concept.Meanwhile,the theorem prove that combination operation can create every triadic concept.Then,the following content is about the proof of the completeness and the key of constructing theorem.Finally,the relation between triadic concepts is built by theorem.(2)On the basisof the related theorem,the thesis introduces an incremental algorithm for constructing concept trilattices.Godin is a kind of important incremental algorithm for constructing concept lattice.In this paper,we develop an algorithm for constructing concept trilattices in triadic context.The algorithm decomposes a given triadic context into several triadic contexts just having one condition as formal contexts firstly.It gets a set of triadic concepts under each decomposed triadic context utilizing a construction algorithm of concept lattice.Concepts convert to triadic concept by adding the corresponding additon as modus.Secondly the set of triadic concepts under the given triadic context can be got through specific combination operation.Finally the algorithm builds the relation between all triadic concepts by utilizing the quasiorder relation between triadic concepts.If we increase a condition for a triadic context that it already have triadic concepts and keep objects and attributes invariable,we will get a new triadic context.We can get triadic concepts in the new triadic context utilizing already existent triadic concepts after the combination operation.(3)The experiment not only results that the algorithm can construe concept trilattices,but also shows the performance of the algorithm.The proposed algorithm is proved and tested by data from other papers.The result shows that the algorithm is correct.At the end of this paper,it shows what we should be improved in the future.Those contents will be explored in depth in our future work.