Some models for generating and ranking multiplicative weights

• The ranking of multiplicative weights is consistent with the multiplicative constraint.
• The AAM method avoids information distortion in multiplicative AHP.
• The defuzzification formula represents the centroid of multiplicative triangular fuzzy weight.

The ranking of multiplicative interval and fuzzy weights is often necessary in multiplicative analytic hierarchy process. The existing ranking method is found flawed and needs to be revised. Firstly, this paper presents a correct formula for ranking multiplicative interval weights, and offers the relevant properties and lemmas to support them. Secondly, since different rank orders of interval weights are derived by the two-stage logarithmic goal programming (TLGP) method under different α-cuts, an approximation and adjustment (AAM) method is developed to generate multiplicative triangular fuzzy weights. In order to compare two multiplicative triangular fuzzy weights, the geometric mean centroid of multiplicative triangular fuzzy weight is proposed. Thus, a practical algorithm for decision making is introduced based on the above model and formulas. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed method.