In the past, approaches often generalized classical multi-criteria decision-making (MCDM) methods under fuzzy environment to solve fuzzy multi-criteria decision-making (FMCDM) problems and encompass decision-making messages uncertainty and vagueness. These MCDM methods included analytic hierarchy process (AHP), simple additive weighting method (SAW), technique for order preference by similarity to ideal solution (TOPSIS), etc. In the MCDM methods, SAW is a famous method that is applied in fuzzy environment, but fuzzy multiplication is a drawback to generalize SAW under fuzzy environment. To resolve the multiplication drawback, we utilize a relative preference relation that is from fuzzy preference relation in fuzzy generalized SAW. Generally, fuzzy preference relation is an option to reserve lots of messages. However, pair-wise comparison for fuzzy preference relation is complex on operation. Through the description above, the relative preference relation is improved form fuzzy preference relation to avoid comparing fuzzy numbers on pair-wise and reserving fuzzy messages. Through the relative preference relation, we can generalize SAW under fuzzy environment. It is said that we propose a FMCDM model based on SAW and the relative preference relation to easily and quickly solve FMCDM problems. 
A fuzzy multi-criteria decision-making model based on simple additive weighting method and relative preference relation