en روش های تحلیل و تصمیم گیری Decision Analysis and Methods پژوهشي Research Preventive maintenance (PM) of machines has the critical role in a factory or enterprise. It decreases number of failures, increases reliability, as well as minimizes costs of production systems.  The managers’ duty of maintenance section is to prioritize machines and then, implement PM programs for them. Since machines have the different measures with respect to the maintenance costs, reliability, mean time between failures (MTBF), availability of spare parts, etc., the machines evaluation problem can be considered as a multiple criteria decision-making (MCDM) problem. Accordingly, the MCDM techniques can be applied to solve them. The aim of this paper is to extend the ELECTRE III (eLimination et choix traduisant la realite´– elimination and choice translation reality) method to interval type-2 fuzzy sets (IT2FSs) using curved (such as Gaussian) membership functions (MFs). The extended ELECTRE III methodology is then utilized to a maintenance group MCDM (GMCDM) matrix including the quantitative and qualitative criteria. In the proposed approach, the criteria weights, the assessment of alternatives with respect to criteria, and the thresholds are stated with Gaussian interval type-2 fuzzy sets (GIT2FSs). In order to show the effectiveness and applicability of the proposed approach, a case study and an illustrative example are exhibited using real decision-making problems. Due to the high correlation coefficients between our method and the others, as well as the results obtained by the proposed method, it can be taken into account as a valid and reliable approach to prioritize machines for PM. ,ELECTRE III,Gaussian interval type-2 fuzzy sets,Alpha cuts,Preventive maintenance 1 19 http://ijiepr.iust.ac.ir/browse.php?a_code=A-10-1982-3&slc_lang=en&sid=1 Amir Mohamadghasemi a.mghasemi@yahoo.com 180031947532846007337 180031947532846007337 Yes Department of Management, Zabol Branch, Islamic Azad University, Zabol, Iran Abdollah Hadi-vencheh abdh12345@yahoo.com 180031947532846007338 180031947532846007338 No Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Farhad hosseinzadeh lotfi farhad@hosseinzadeh.ir 180031947532846007339 180031947532846007339 No Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran