On The Study Of Lattice-valued Intuitionistic Fuzzy Rough Set Model

Lattice-valued intuitionistic fuzzy rough set is the extension of intuitionistic fuzzy rough set model. Lattice-valued intuitionistic fuzzy rough set can describe not only the intuitionistic fuzziness but also the uncomparability. The existing research works of intuitionistic fuzzy rough set focused on the construction of intuitionistic fuzzy rough approximation operators based on specific implication operators and the study of the structures of intuitionistic fuzzy rough set model. The purpose of this paper is to study the models and properties of lattice-valued intuitionistic fuzzy rough set. Based on the results of previous literatures, in this paper, we construct the lattice-valued approximation operators of intuitionistic fuzzy rough set, and discuss the axiomatic characterization of intuitionistic fuzzy rough approximation operators. By employing the intuitionistic fuzzy implication operator on the lattice, the structure and properties of approximation operator are discussed。The concrete results in this paper shows as follows.In part one,we discuss the properties of lattice-valued triangular norms, and construct the lattice-valued intuitionistic fuzzy rough set model by using lattice-valued triangular norms, and give some properties of rough approximation operators, and provide the axiomatic characterization of approximation operators.In part two, by using product operator and strong implication operator in residuated lattice, we construct the lattice-valued intuitionistic fuzzy rough set model based on residuated lattice, and discuss the properties of approximation operators.The research work of this paper belongs to foundamental theory of rough set. The results obtained in this paper are extensions of the existing research results. It is of certain theoretical significance for the study of rough set theory and its application.