Normal wiggly hesitant fuzzy linguistic power Hamy mean aggregation operators and their application to multi-attribute decision-making

•Give a new concept of normal wiggly hesitant fuzzy linguistic term set (NWHFLTS).•Define basic operational rules and the score function of NWHFLTSs.•Propose three distance measures between two NWHFLTSs.•Propose some power Hamy mean aggregation operators for NWHFLTSs.•Give a multi-attribute decision-making method with the information of NWHFLTSs. As a useful tool for information representation, hesitant fuzzy linguistic term sets (HFLTSs) have received extensive attention and in-depth discussion in recent years. However, in real decision making, it is impossible for decision makers to express all preference information only through a few continuous linguistic terms. Much valuable information is hidden in the original evaluation information. Thus, this paper mainly studies how to mine deeper uncertain information from the original hesitant fuzzy linguistic evaluation information. To achieve this goal, we present a new representation tool called the normal wiggly hesitant fuzzy linguistic term set (NWHFLTS). The NWHFLTS not only retains the original evaluation information, but it also delivers and quantifies potential uncertain information. First, we propose some basic theories of NWHFLTS, such as some basic operational rules, score function and distance measures between two NWHFLTSs. Then, based on the distinctive features of the power average (PA) operator and Hamy mean (HAM) operator, we propose two new information aggregation operators, i.e., the normal wiggly hesitant fuzzy linguistic power Hamy mean (NWHFLPHAM) operator and its weighted form (NWHFLPWHAM). Furthermore, based on the NWHFLPWHAM operator, a new method is proposed to address multi-attribute decision-making (MADM) problems. Finally, we use a numerical example to show the specific calculation steps and provide a comparison with other methods to validate the effectiveness and advancement of our proposed method.