Combining quality function deployment with simple additive weighting for interval-valued fuzzy multi-criteria decision-making with dependent evaluation criteria

In the past, lots of multi-criteria decision-making (MCDM) methods included simple additive weighting (SAW) extended under fuzzy environment into multi-criteria decision-making (FMCDM) methods to encompass uncertainty and vagueness of data. The extensions were first used in FMCDM with independent evaluation criteria, and then, FMCDM could be associated with quality function deployment (QFD) to break the tie of dependent evaluation criteria. Commonly, alternative ratings and criteria weights in FMCDM were expressed by general fuzzy numbers (i.e., triangular or trapezoidal fuzzy numbers). Recently, some approaches proposed FMCDM with independent evaluation criteria under interval-valued fuzzy environment. For interval-valued fuzzy numbers, FMCDM with dependent evaluation criteria was scarcely elaborated due to computation complexity. Besides, QFD was also generalized under some fuzzy environments consisting of triangular fuzzy numbers or trapezoidal fuzzy numbers, but not interval-valued fuzzy environment. Practically, interval-valued fuzzy numbers are deemed as a kind of fuzzy number that can grasp more information than other fuzzy numbers, but the kind of fuzzy number is more complex on computation than others. Based on above, we desire to extend QFD and SAW under interval-valued fuzzy environment for FMCDM with dependent evaluation criteria. By a rational technique of combining QFD with SAW under fuzzy environment, the computation tie of interval-valued fuzzy numbers corresponding to dependent evaluation criteria is resolved, and more messages are grasped than using other fuzzy numbers in FMCDM.