Value and Ambiguity Index-based Ranking Approach for Solving Neutrosophic Data Envelopment Analysis

Abstract

The Neutrosophic set (NS), is a generalization of the fuzzy set and its extension sets, is a revolutionary type of fuzzy set that enables decision-makers (DMs) to express their level of uncertainty independently
by assigned the truth, indeterminacy and falsity degrees of each element of NS. This article purposes a novel
type of ranking function based on value and ambiguity index of a single value triangular neutrosophic number
(SVTNN), which associated with DM’s preference level and risk factor that show the attitude of the DM towards taking risk. Also, this article purposes a novel technique for solving the Neutrosophic DEA (Neu-DEA)
model having multiple input-outputs are the SVTNNs. The proposed ranking function is used to converts
the Neu-DEA model into a corresponding crisp DEA model which is solved to measure the efficiency of the
decision making units (DMUs) in Neutrosophic environment. The efficiency scores of the DMUs are calculated
based on the DM’s preference level by taking a specific risk (λ ∈ [0, 1]). A numerical example is provided to
demonstrate the proposed model’s validity and existence, and to compare efficiency scores with Yang et al.’s
ranking approach. Finally, How the DM’s preference level and risk factor affect the efficiency score of DMUs
are discussed in details.