MAGDM in hesitant interval-valued Pythagorean linguistic Z-number based on combined score function and entropy

In this paper, a new linguistic fuzzy model is proposed by combining a linguistic fuzzy set and a linguistic Z-number and is named hesitant interval-valued Pythagorean linguistic Z-number (HIVPLZN). It can be used as an effective tool for actual uncertain decision-making, which can effectively enhance the reliability of decision-making information, reflect the fuzziness, flexibility and practicability of decision-making information, and offer wide application prospects in economics, risk assessment, decision-making and other fields. This paper mainly studies a method to solve the problem of multi-attribute group decision-making. First, three new linguistic scale functions are presented, and HIVPLZN is then proposed. Next, some related operators and the aggregation operator of HIVPLZN are proposed, three kinds of score functions of HIVPLZN are presented to measure the strengths and weaknesses of HIVPLZNs, and a combined score function method is proposed based on the optimal model. Furthermore, the distance formula of HIVPLZN is proposed based on the risk attitude of the decision-maker, and entropy is suggested to measure the uncertainty of HIVPLZN. Finally, a multi-attribute group decision-making (MAGDM) model is constructed, and an example is provided to verify the feasibility and validity of this method by sensitivity analysis and comparison with some existing methods.