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A multiple attribute decision-making three-way model at four-branch fuzzy environment

Three-way decisions (TWDs) theory is one of the core ideas of decision-theoretic rough sets (DTRSs). Reviewing the existing research results, we find that TWDs provides us with more flexible decision choices. And the traditional fuzzy number does not take into account the absence of information (indifference) in the evaluation process. In order to construct a new model which can get flexible decision results in complex decision environment, we introduce four-branch fuzzy numbers (FBFNs) to describe the evaluation information, so that the decision-makers can express the evaluation information more comprehensively. In this paper, a novel TWDs model in four-branch fuzzy environment is proposed to solve multiple-attribute decision-making (MADM) problem. The first challenge is to construct a TWDs model based on FBFNs and to develop a new linguistic interpretation of the loss functions. Then, we extend a method for aggregating the loss functions obtained from the attribute evaluation values. Finally, we use the nonlinear solution to solve the threshold, and apply TOPSIS method to solve the conditional probability of FBFNs. The effectiveness of this method is illustrated by an example, and the decision results are compared with a MADM method based on OWGA operator.