Approach for three-parameter interval grey linguistic variable decision-making based on fuzzy integral and Mobius transformation

This paper presents the concept of three-parameter interval grey linguistic variable, which combines three-parameter interval grey numbers with grey linguistic variables. Firstly, basic definitions and new laws are given. Secondly, considering the attributes interdependency, this paper utilises the fuzzy integral theory to construct a grey fuzzy integral correlation degree decision-making model under three-parameter interval grey linguistic variable environment. To solve this model, the Mobius transformation coefficients based on weights and interaction degrees are defined to calculate two-order additive fuzzy measures. Then the maximum projection models are used to calculate the weights, and the interaction relations and interaction degrees are determined by decision makers. Subsequently, the grey fuzzy integral correlation degrees of alternatives are calculated by precise function transformation, grey correlation degree and fuzzy measures. At last, an illustrative example has been taken to demonstrate the validity and feasibility of the proposed method.