International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/646 2020 2020 Department of Mathematics, Arul Anandar College (Autonomous), Karumathur admin admin Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA Florentin Smarandache Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco Said Broumi   The production sectors are optimizing its profit with the employment of smart materials at recent times and one of the challenges faced is the selection of smart materials. This article proposes a new decision-making method based on the approach of PROMTHEE plithogenic Pythagorean hypergraph. The efficiency of the proposed method is determined in the selection of smart materials that are significantly utilized in the production processes by the production sectors. In this research work, the decision making on smart material selection environment is characterized by four major influencing factors such as production processes, operational necessities, fiscal constraints and external effects with eighteen sub-factors. The main objective of this research work is to determine the core sub-factors persuading the selection of smart materials based on the five-point scale of expert’s opinion represented as Pythagorean neutrosophic number. Out of eighteen sub-factors four significant factors belonging to each of the major factors were identified by this method.  The plithogenic hypergraphs with Pythagorean representation are the extension of plithogenic hypergraphs and the novel decision - making method with the integration of PROMTHEE developed in this article will certainly benefit the decision makers on smart material selection. Comparative analysis on the criteria is also made based on Pythagorean neutrosophic sets & neutrosophic sets.   2021 2021 52 60 10.54216/IJNS.130105 https://www.americaspg.com/articleinfo/21/show/646