Research On Attribute Reduction Of Intuitionistic Fuzzy Concept Lattice

The theories of concept lattice, fuzzy set, intuitionistic fuzzy set proposed by theGerman mathematician Wille R, American expert on computer and control Zadeh, Bulgariaacademic Atanassov respectively, are mathmatic tools to deal with knowledge discoveryand the uncertain and vague problems, which are being the hot topic in the field ofinformation science. Intuitionistic fuzzy attribute reduction and cognitive process based onthe formal concept analysis, studied in the paper, are the main purpose for data analysisand knowledge discovery. In order to make most use of various theoretical advantages indealing with knowledge discovery and uncertain problems effectively, it is necessary tocombine them organically. The paper studies the fuzzy concept lattice, intuitionistic fuzzyconcept lattice and a novel cognitive system model and approach to transformation ofinformation granules. The original results of the thesis are summarized in the following:1. One novel cognitive system model is established based on formal concept analysis toexactly describe human cognitive processes. Two new operators, extent–intent andintent–extent, are introduced between objects and attributes. By analyzing the necessityand sufficient relations between objects and portion of the corresponding attributes,attributes and portion of the corresponding objects, the information granule concept isinvestigated in human cognitive processes. Furthermore, theories of transforming arbitraryinformation granule into necessary, sufficient, sufficient and necessary informationgranules are addressed carefully. Algorithm of the transformation is constructed, by whichwe can provide an efficient approach to the conversion among information granules. Thelarge-scale case is calculated by the experimental computing program and validates theproposed algorithm.2. We introduce the intuitionistic fuzzy theory into the concept lattice theory, establish adata analysis model of intuitionistic fuzzy concept lattice based on a pair of T implicationoperators, and analyze the hierarchical structure characterize of the intuitionistic fuzzyconcept lattice. Then an approach to attribute reduction based on the discernibility matrixis proposed and investigated in the case of maintain the hierarchical structure. Furthermore,an attribute reduction algorithm for computing concept lattice and attribute reduction isdeveloped, which realizing the goal to deal with the mass data in the intuitionistic fuzzyformal context. Then the effectiveness of the algorithm is assessed by the experimentaldata. 3. One kind of concept lattice in the intuitionistic fuzzy consistent decision formalcontext is proposed. Then we establish a data analysis model of intuitionistic fuzzy conceptlattice based on a pair of T implication operators and analyze the hierarchical structurecharacterize of the conditional attribute concept lattice and decision attribute conceptlattice. Furthermore, an approach to attribute reduction based on the discernibility matrix isproposed and investigated in the case of maintaining the hierarchical structure.4. We propose a data analysis model of intuitionistic fuzzy concept lattice based on apair of T implication operators in the intuitionistic fuzzy generalized consistent decisionformal context and analyze the hierarchical structure characterize of the conditionalattribute concept lattice and decision attribute concept lattice and their relation. Then anapproach to attribute reduction based on the discernibility matrix is proposed andinvestigated in the case of maintaining the hierarchical structure and given relationbetween them. Furthermore, we develop an attribute reduction algorithm for computingconditional concept lattice, decision attribute concept, attribute reduction and theirimplication, which realizing the goal to deal with the mass data in the intuitionistic fuzzygeneralized consistent decision formal context. Finally, the effectiveness of the algorithm isassessed by the experimental data.