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This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of $$DMU_o$$ D M U o increases from $$Y_o$$ Y o to $$\beta _o$$ β o , such the new DMU is given by $$(\alpha _o^*,\beta )$$ ( α o ∗ , β ) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.

This paper studies the efficiency assessment of Decision Making Units (DMUs) when their inputs and outputs are fuzzy sets. An axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders, and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The proposed approach has been compared with other fuzzy DEA approaches on different datasets from the literature, and the results show that it has more discriminant power and more flexibility in modelling the input and output data.