Many decision problems are under uncertain environments with vague and imprecise information using multi-granularity linguistic variables. In this paper, we describe the linguistic hierarchical structure in a different way. The suitable numerical scales are given with the purpose of making transformation between multi-granularity linguistic variables and numerical values. A novel distance measure between multi-granularity linguistic variables is proposed. Its advantage is to solve problems of linguistic variables with different semantics. Then we develop a maximizing deviation method to determine the optimal relative weights of attributes under linguistic environment where preferences are labels in different levels of linguistic hierarchy. Application of the method is illustrated in a case study on medical diagnosis.