TY - JOUR

T1 - Chance-constrained DEA models with random fuzzy inputs and outputs

AU - Tavana, Madjid

AU - Shiraz, Rashed Khanjani

AU - Hatami-Marbini, Adel

AU - Agrell, Per J.

AU - Paryab, Khalil

PY - 2013/11/1

Y1 - 2013/11/1

N2 - Data Envelopment Analysis (DEA) is a widely used mathematical programming technique for comparing the inputs and outputs of a set of homogenous Decision Making Units (DMUs) by evaluating their relative efficiency. The conventional DEA methods assume deterministic and precise values for the input and output observations. However, the observed values of the input and output data in real-world problems can potentially be both random and fuzzy in nature. We introduce Random Fuzzy (Ra-Fu) variables in DEA where randomness and vagueness coexist in the same problem. In this paper, we propose three DEA models for measuring the radial efficiency of DMUs when the input and output data are Ra-Fu variables with Poisson, uniform and normal distributions. We then extend the formulation of the possibility-probability and the necessity-probability DEA models with Ra-Fu parameters for a production possibility set where the Ra-Fu inputs and outputs have normal distributions with fuzzy means and variances. We finally propose the general possibility-probability and necessity-probability DEA models with fuzzy thresholds. A set of numerical examples and a case study are presented to demonstrate the efficacy of the procedures and algorithms.

AB - Data Envelopment Analysis (DEA) is a widely used mathematical programming technique for comparing the inputs and outputs of a set of homogenous Decision Making Units (DMUs) by evaluating their relative efficiency. The conventional DEA methods assume deterministic and precise values for the input and output observations. However, the observed values of the input and output data in real-world problems can potentially be both random and fuzzy in nature. We introduce Random Fuzzy (Ra-Fu) variables in DEA where randomness and vagueness coexist in the same problem. In this paper, we propose three DEA models for measuring the radial efficiency of DMUs when the input and output data are Ra-Fu variables with Poisson, uniform and normal distributions. We then extend the formulation of the possibility-probability and the necessity-probability DEA models with Ra-Fu parameters for a production possibility set where the Ra-Fu inputs and outputs have normal distributions with fuzzy means and variances. We finally propose the general possibility-probability and necessity-probability DEA models with fuzzy thresholds. A set of numerical examples and a case study are presented to demonstrate the efficacy of the procedures and algorithms.

KW - Data envelopment analysis

KW - Necessity-probability

KW - Possibility-probability

KW - Random fuzzy variable

UR - http://www.scopus.com/inward/record.url?scp=84883878925&partnerID=8YFLogxK

U2 - 10.1016/j.knosys.2013.05.014

DO - 10.1016/j.knosys.2013.05.014

M3 - Article

AN - SCOPUS:84883878925

VL - 52

SP - 32

EP - 52

JO - Knowledge-Based Systems

JF - Knowledge-Based Systems

SN - 0950-7051

ER -