Methods for generating multiplicatively normalized interval and fuzzy weights

In the interval and fuzzy multiple attribute decision making it is very important to estimate the corresponding set of normalized weights from the interval and fuzzy pairwise comparison matrix. Most existing works computing normalized weights which are under the condition of the conventional additive weights (sum is one). This paper, from another perspective, introduces the concept of multiplicative interval and fuzzy weights and proposes the corresponding normalization methods for multiplicative interval and fuzzy weights. Based on these definitions and theorems, a new eigenvalue method, where weights satisfy multiplicative preference relations rather than additive, is developed for obtaining multiplicatively normalized interval weights and subsequently the global weights from interval pairwise comparison matrices. Finally, numerical examples are examined to demonstrate proposed methods.