Interval-valued fuzzy multi-criteria decision-making based on simple additive weighting and relative preference relation

Abstract

To encompass imprecise messages, traditional multi-criteria decision-making (MCDM) was generalized into fuzzy multi-criteria decision-making(FMCDM) in solving decision-making problems. In numerous MCDM methods, simple additive weighting(SAW) is the simplest one, but fuzzy multiplication for generalizing SAW under fuzzy environment is still complicated, especially interval-valued fuzzy numbers. In the past, Wang proposed a model based on SAW and relative preference relation to resolve fuzzy multiplication tie. Practically, Wang's model is useful to fuzzy generalization of SAW. However, the model is only used in triangular fuzzy numbers. Recently, more and varied messages are obtained and processed for decision-making problems. Triangular fuzzy numbers are insufficient to express the variance, whereas interval-valued fuzzy numbers are suitable. Therefore, SAW had to be generalized under interval-valued fuzzy environment. In this paper, we combine SAW with a relative preference relation into interval-valued FMCDM to avoid fuzzy multiplication and grasp more messages. Our proposed relative preference relation improved from Lee's fuzzy preference relation is similar to Wang's relative preference relation. The main difference is that the proposed relation is utilized in interval-valued fuzzy numbers, whereas Wang's is used in triangular fuzzy numbers. To sum up, we provide the FMCDM to solve decision-making problems with interval-valued fuzzy numbers easily and quickly.