A normal wiggly hesitant fuzzy set (NWHFS) is viewed as a powerful and useful tool to dig the potential uncertainty of decision makers (DMs) in the process of expressing their preferences, which can be regarded as an extended form of the traditional hesitant fuzzy set (HFS). The NWHFSs have the ability of both reserving the original hesitant fuzzy information completely and exploring potential fuzziness of DMs, which assist the DMs in advancing the decision-making efficiency and derive the reasonable ranking orders finally. To fully exert the strengths of the combined power average and Muirhead mean operators, based on the proposed distance measure of normal wiggly hesitant fuzzy elements (NWHFEs), we extend the power Muirhead mean (PMM) to the normal wiggly hesitant fuzzy environment and develop the normal wiggly hesitant fuzzy PMM (NWHFPMM) and its weighted form included. After that, several representative cases and attractive properties of the proposed normal wiggly hesitant fuzzy operators are investigated in depth. Finally, a novel MADM method for solving normal wiggly hesitant fuzzy decision-making problems is developed, then a numerical example is performed to analyze the strengths of our proposed method, which in the way of comparing with other existing studies.
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