A novel hybrid fuzzy PROMETHEE-IDEA approach to efficiency evaluation
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METHODOLOGIES AND APPLICATION
A novel hybrid fuzzy PROMETHEE-IDEA approach to efficiency evaluation František Zapletal1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Additive DEA · PROMETHEE · Level sets · Fuzzy · Possibility · Necessity · Efficiency frontier
1 Introduction Efficiency is a natural desired state of each human, company, and economic subject in general. An efficient subject consumes less inputs than all other alternatives, and ideally produces more outputs at the same time. However, it is not easy to choose how to measure the efficiency from the number of all available mathematical methods. Moreover, in the case of more complex problems, it is usually not possible to visualise the results of the efficiency evaluation, which makes the methods less applicable in practice.
Communicated by V. Loia.
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František Zapletal [email protected] VŠB- Technical University of Ostrava, Faculty of Economics, Department of Systems Engineering, Ostrava, Czech Republic
The most used method for efficiency evaluation is data envelopment analysis (DEA), established by Charnes et al. (1978). The number of modifica
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