Approximations And Reduction In Intuitionistic Fuzzy Decision Systems

Rough set theory is a mathematical tool for dealing with uncertain,imprecise and incom-plete information. One important research of rough set is the rough approximations and at-tritube reduction.Intuitionistic fuzzy set is an extension of fuzzy set theory,which is more pre-cise to describe the fuzzy phenomena. Based on the theory of rough set and intuitionistic fuzzy set,the five types of rough approximations are constructed, and the three types of attribute reduction algorithms are designed in intuitionistic fuzzy decision systems. The specific work is as follows:The rough approximations of intuitionistic fuzzy set have been closely concerned. Based on the α,β-similarity relation and intuitionistic fuzzy similarity relation, the five types of upper and lower approximations of intuitionistic fuzzy rough set are constructed in this paper.Firstly, based on the weighted Euclidean distance,the similarity degree and dissimilarity degree are introduced to construct α,β-similarity relation.Moreover,α,β-maximal consistent block is induced.On this basis, the four types of upper and lower approximations of intuitionistic fuzzy rough set are con-structed,and the relationship among rough approximations is reasearched.Specially, the fourth type of rough approximations considers the effect of all elements in the same α,β-maximal con-sistent block.By the intuitionistic fuzzy logical operators,the upper and lower approximations of intuitionistic fuzzy rough set are constructed based on the intuitionistic fuzzy similarity relation.Attribute reduction is one of the most important problems in intuitionistic fuzzy rough set. In the intuitionistic fuzzy decision systems,three attribute reduction algorithms are proposed in this paper. Firstly,A new method for ranking intuitionistic fuzzy values is used to design a heuristic attribute reduction algorithm based on dependency relationship.Secondly,the discerni-bility matrix is constructed based on α,β-maximal consistent block, and attribute reduction algorithm is designed based on the discernibility matrix.This algorithm have the capability of tol- erating certain error data.Thirdly,the heuristic attribute reduction algorithm is designed based on intuitionistic fuzzy conditional entropy.Finally,an illustrative example is employed to show the validity of the algorithms in this paper. Specially,the first attribute reduction algorithms keeps the lower approximation unchanged,and the other two of attribute reduction algorithms keep the classification ability unchanged.