On Data Envelopment Analysis Framework for Optimizing Two-Stage  Systems Under Neutrosophic Environment

Basma E. El- Demerdash; A. Almutairi; Sultan S. Alodhaibi; Hamiden Abd El- Wahed Khalifa; Heba Ghareb Goma

Authors

Basma E. El- Demerdash Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
A. Almutairi Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia,
Sultan S. Alodhaibi Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
Hamiden Abd El- Wahed Khalifa Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Heba Ghareb Goma Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt

Keywords:

Data Envelopment Analysis, Mathematical model; Neutrosophic Sets, Two-Stage Model, Efficiency Assessment, Competitive Business Environment, Uncertainty

Abstract

Recently, DEA became one of the evaluation method and used widely by the researchers
for the analysis. It’s used to evaluate units under evaluation that produce multiple outputs by consuming
multiple inputs This paper presents a neutrosophic set-based, two-stage DEA framework to surmount the
weak linkages within the traditional DEA model when uncertainties and imprecise values exist. Neutrosophic
sets capture the uncertainty by considering membership degrees of truth, indeterminacy, and falsity. Overall,
this framework decomposes overall system efficiency into stage efficiencies and provides deep insights into
the system performance. We developed a two-stage DEA optimization model with neutrosophic variables and
constraints. This framework can apply to any organization in order to support decision-makers to make
rational decisions and allocate resources optimally, especially in the modern competitive business
environment. A case study introduced to show how the model could handle neutrosophic uncertainty, and the
mathematical formulation presents succinctly for practical implementation.

DOI: 10.5281/zenodo.15265632