The Rough Approximation of Distributive BZ Lattice

In this paper, interval structure of distributive BZ lattices and properties of rough approximation operators are discussed. For any element a in distributive BZ lattices, the rough approximation ( ν(a),μ(a ))of a is obtained by using two modal like unary operators ν and μ ( ν for necessity and μ for possibility). It is proved that a rough algebra can be induced from a distributive BZ lattice by means of rough operator pair denoted by ( ν,μ ). Finally, necessary optimal solutions and possibly optimal solutions of uncertain programming are characterized by modal like unary operators which is called necessity and possibility measures, respectively, an illustrative example is given.