A novel hybrid fuzzy PROMETHEE-IDEA approach to efficiency evaluation

Abstract

Efficiency evaluation is a desirable kind of a decision making analysis for experts in various fields because if something can be measured, it can also be improved more easily. Measuring efficiency has been a topic of many research studies, and many quantitative methods to deal with this problem under various assumptions have already been established. However, most methods struggle with barriers limiting their use in practice. The aim of this paper is to establish a method for efficiency evaluation which is as traceable as possible, provides a graphical representation of the results, and yields results that are easily interpretable for problems with uncertain input data expressed by fuzzy evaluations. In particular, a new hybrid method for efficiency evaluation is presented. This method is based on a combination of the PROMETHEE (i.e. outranking multi-criteria decision making method) and data envelopment analysis (DEA) under uncertainty, similar to the study published by Ishizaka et al. (Soft Comput 22(22):7325-7338, 2018) who, however, worked only with deterministic data. The PROMETHEE method allows a computationally easy and traceable evaluation of alternatives. The DEA method is currently the most popular method for efficiency evaluation. However, its original version provides a graphical representation only for very simple models. In addition, the results are usually not easy to interpret because it mixes scale-dependent and scale-independent data together. Fuzziness in the DEA model is handled using measures of possibility and necessity, which provide easily interpretable results for a decision maker. In particular, the results reveal to what extent each unit under evaluation can possibly be, or certainly is, efficient. The proposed algorithm is applied to one artificial and one real-life numerical example, and the results are compared with the pure DEA model.