Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model

Abstract The present paper studies the efficiency assessment of Decision-Making Units (DMUs) when their inputs and outputs are described under uncertainty of the type of integer interval data. An axiomatic derivation of the production possibility set (PPS) is presented. An additive, slacks-based data envelopment analysis (DEA) model is formulated, consisting of two phases. This has required the use of adequate arithmetic and LU-partial orders for integer intervals. This novel integer interval DEA approach is the first step towards DEA models under fuzzy integer intervals, with the extension of the corresponding arithmetic and LU-partial orders to fuzzy integer intervals. The proposed method is applied on a dataset, taken from the literature, that involves both continuous and integer interval variables.