Inventory classification is a fundamental issue in the development of inventory policy that assigns each inventory item to several classes with different levels of importance. This classification is the main determinant of a suitable inventory control policy of inventory classes. Therefore, a great deal of research is done on solving this problem. Usually, the problem of inventory classification is considered in a multi-criteria and uncertain environment. The proposed method in this paper inspired by the notion of heterogeneous decision-making problems in which decision-makers deal with different types of data. To this aim, a mathematical modeling-based approach is proposed considering different types of uncertainty in classification information. Demand information is considered to be stochastic due to its time-varying nature and cost information is considered to be fuzzy due to its cognitive ambiguity. A hybrid algorithm based on chance-constrained and possibilistic programming is proposed to solve the problems. Considering the stochastic nature of demand information, solving the proposed model using the hybrid algorithm, the classification of items to three classes of extremely important, class A, moderately important, class B, and relatively unimportant, class C, items are determined along with a minimum inventory level required to deal with the stochasticity of demands information. The proposed approach is applied to a case study of classifying 51 inventory items. The obtained results assigned 22%, 39%, and 39% of the items to A, B, and C classes, respectively. © Springer-Verlag GmbH Germany, part of Springer Nature 2020.