Linguistic multi-attribute decision making with multiple priorities

•This paper deals with linguistic MADM with multiple priorities.•It proposes computational operators for both strict and weak priority hierarchies.•It can deal with interval-valued linguistic information.•It satisfies the idempotent property and overcomes the drawback of less sensitive operators.

Linguistic multi-attribute decision making (MADM) problems have received many attentions in theoretical and practical aspects. It is well known that center of the linguistic MADM is the aggregation of fuzzy linguistic information. As one widely used type of aggregation operators, the importance weighted aggregation assumes that all the attributes are at the same priority level. This paper deals with linguistic MADM with multiple priorities in terms of strict priority hierarchy or weak priority hierarchy. To do so, based on the 2-tuple linguistic model and the revised product t-norm, a prioritized linguistic idempotent scoring (PLIS) operator is first proposed for linguistic MADM with a strict priority hierarchy to guarantee the idempotent property of prioritized aggregation. Moreover, as an extension of the PLIS operator, a PLIS ordered weighted averaging (PLIS-OWA) operator is proposed to solve linguistic MADM with a weak priority hierarchy. In addition, in practice decision-makers (DMs) are often unsure of their evaluations due to time pressure, lack of experience and data, and therefore may provide uncertain linguistic assessments. The PLIS and PLIS-OWA operators are also extended to the cases of prioritized MADM with interval-valued linguistic 2-tuples. Finally, three illustrative examples and comparative analysis are provided to show the effectiveness and efficiency of the proposed aggregation operators. The proposed operators outperform existing studies in terms of the idempotent property, no information loss, and heterogeneous information.