Geometric least square models for deriving \([0,1]\)-valued interval weights from interval fuzzy preference relations based on multiplicative transitivity (Q1664876)

Summary: This paper presents a geometric least square framework for deriving \([0,1]\)-valued interval weights from interval fuzzy preference relations. By analyzing the relationship among \([0,1]\)-valued interval weights, multiplicatively consistent interval judgments, and planes, a geometric least square model is developed to derive a normalized \([0,1]\)-valued interval weight vector from an interval fuzzy preference relation. Based on the difference ratio between two interval fuzzy preference relations, a geometric average difference ratio between one interval fuzzy preference relation and the others is defined and employed to determine the relative importance weights for individual interval fuzzy preference relations. A geometric least square based approach is further put forward for solving group decision making problems. An individual decision numerical example and a group decision making problem with the selection of enterprise resource planning software products are furnished to illustrate the effectiveness and applicability of the proposed models.