A novel interval-valued three-way decision theory under multiple criteria environment

Three-way decision (TWD) theory provides us with a new perspective and methodology to improve the flexibility of traditional multiple criteria decision-making (MCDM) methods. However, the construction of TWD theory under uncertain environment is still a serious challenge. In light of this, this paper proposes a novel interval-valued TWD theory for solving MCDM problems under uncertain environment. First, several rules are defined to calculate the interval-valued thresholds under multiple criteria environment. Afterwards, on the basis of interval-valued Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, a new approach is developed to calculate the interval-valued conditional probability of each alternative. Then, a new information transformation and fusion mechanism in the framework of evidential reasoning algorithm is established to conduct the interval-valued thresholds under multiple criteria into overall interval-valued thresholds. Finally, according to the overall interval-valued thresholds and interval-valued conditional probabilities, several new decision rules for objects under different decision situations are provided to generate the classifications and rankings of alternatives. To illustrate the feasibility of the proposed method, an application about purchasing green vehicles is performed. Further detailed discussions and comparisons with other methods are also conducted to show the effectiveness and superiority of the current proposal.