Interval type-2 fuzzy DEA: An application

Kailash Mund; Meenakshi Kaushal; Q.M.Danish Lohani; Sunil Kumar

Kailash Mund Department of Mathematics, South Asian University, New Delhi.
Meenakshi Kaushal Department of Mathematics, South Asian University, New Delhi
Q.M.Danish Lohani Department of Mathematics, South Asian University, New Delhi.
Sunil Kumar Department of Economics, South Asian University, New Delhi.

Abstract

A data envelopment analysis (DEA) model evolved on the basis of intuitionistic fuzzy set (IFS) reduces to a fuzzy set based model, whenever hesitancy is not present in the environment. The IFS based DEA model measures efficiency of decision making units (DMUs) more accurately with incorporation of the ability to state their hesitancy, hence real world DMUs are suitably ranked by them. In the paper, the optimistic and pessimistic intuitionistic fuzzy data envelopment analysis (IFDEA) models proposed by Puri, Shiv Prasad Yadav,[Expert Systems with Applications, 11(2015), 4982-4998] along with their rankings are being analyzed using interval type-2 fuzzy sets. The interval type-2 fuzzy data envelopment analysis (IT2FDEA) model is proposed to study the ranking of IFDEA. In addition, a relationship between triangular intuitionistic fuzzy number (TIFN) and triangular interval type-2 fuzzy number (Tr IT2FN) has also been established here to interlink IFDEA model with IT2FDEA model.