Uncertainty in inverse data envelopment analysis: A novel approach for $CO_2$ emission efficiency

Articles in Press

Document Type : Original paper

Authors

Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract

Industries are increasingly relying on analytical approaches for performance evaluation and decision-making. Consequently,  they must invest suitable resources at the right time for the appropriate engagements. Inverse  Data Envelopment Analysis is a post-DEA sensitivity analysis method designed to tackle resource allocation. The primary objective of Inverse DEA is to determine the optimal input and/or output levels for each decision-making unit under varying conditions to achieve a specified efficiency target. Traditional inverse DEA models require precise data on the inputs and outputs of Decision-Making Units. However,  in many scenarios,  such as system flexibility,  social and cultural contexts information may be indeterminate. In these cases,  experts' opinions are used to model uncertainty. Uncertainty theory,  a branch of mathematics,  logically deals with degrees of belief. This paper aims to develop an InvDEA model incorporating uncertainty theory. We assume that inputs and outputs of decision-making units are based on experts' belief degrees. An input-oriented model is developed,  and several properties are proven. To demonstrate the model is performance,  we employ a case study involving  CO$_2$ emission data from OPEC countries.

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References

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Communications in Combinatorics and Optimization

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Available Online from 02 October 2025

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