ANP Method on Generalized Set-Valued Neutrosophic Quintuple Numbers

In this study, a new method was developed by using the Analytic Network Process method (ANP) for the first time in decision making applications on neutrosophic quintuple numbers. Information about the application steps of this method and how to apply it to problems encountered in current life is given. Thus, a new method has been developed in which neutrosophic quintuple sets, one of the new structures of neutrosophic set theory, and ANP method, one of the applications of multi-criteria decision making, are used together. This new method includes consistency calculation, step 3 and step 6 of the classical ANP method. Also, an example application from current life was made. In the case study, the impact of environmental, social and economic criteria on each other in the selection of renewable energy sources was analyzed using fictitious data. As a result of this application, it was concluded that the environmental criterion was more effective, followed by the social criterion and the economic criterion, respectively. Moreover, the interdependencies between the criteria changed the weights of the criteria. It is concluded that the interdependencies of the criteria that cause changes in the weights of the criteria may lead to a certain ranking change in the decision-making process. It is also concluded that the consistency ratios of the comparison matrices obtained with different operators may vary and the importance rankings obtained with an inconsistent matrix and a consistent matrix may be different.