The hesitant fuzzy set is a mathematical tool to express multiple values in decision making. If they could not give a resolution, it is important to give priority and importance to a number of different values. Here, we propose normal wiggly dual hesitant fuzzy set (NWDHFS), as an extension of normal wiggly hesitant fuzzy set. We define a new score function of normal wiggly dual hesitant fuzzy information. The NWDHFS can express deep ideas of membership and non-membership information. In this work, we use hesitant fuzzy set to expose the deepest ideas hidden in the thought-level of the decision makers. We show that the NWDHFS can handle the hesitant fuzzy information. It expresses the deeper ideas of hesitant fuzzy set. An illustration is provided to demonstrate the practicality and effectiveness to the application of site selection of the underground storage of hydrogen. We are compelled to look for alternating fuels to suits changing weather conditions and increasing number of vehicles. This alternative fuel is necessary to control global warming and to be economically viable. Based on this, hydrogen gas is selected as a good alternative fuel. The most important statement is the saving of the selected hydrogen gas. Thus, when saving hydrogen fuel, a safe storage space must be selected. Here, we use the MCDM ideas by use of proposed NWDHFV method is to select the appropriate hydrogen underground storage location. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.