Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 705-721.

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability–possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018075
Classification : 90Cxx, 90C15, 90C70
Mots-clés : Data envelopment analysis, fuzzy random variable, possibility—probability, ranking
Ebrahimnejad, Ali 1 ; Nasseri, Seyed Hadi 1 ; Gholami, Omid 1

1 
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     title = {Fuzzy stochastic {Data} {Envelopment} {Analysis} with application to {NATO} enlargement problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Ebrahimnejad, Ali; Nasseri, Seyed Hadi; Gholami, Omid. Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 705-721. doi : 10.1051/ro/2018075. http://archive.numdam.org/articles/10.1051/ro/2018075/

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