modelfuzzy_kaoliu: Fuzzy DEA model.

In deaR: Conventional and Fuzzy Data Envelopment Analysis

Fuzzy DEA model.

Description

Solve the fuzzy DEA model by Kao and Liu (2000)

Usage

modelfuzzy_kaoliu(datadea,
                  dmu_eval = NULL,
                  kaoliu_modelname = c("basic", "additive", "addmin",
                                       "addsupereff", "deaps", "dir", "fdh",
                                       "lgo", "multiplier", "nonradial",
                                       "profit", "qgo", "rdm", "sbmeff",
                                       "sbmsupereff", "supereff"),
                  alpha = 1,
                  ...)

Arguments

datadea	A deadata_fuzzy object, including DMUs, inputs and outputs.
dmu_eval	A numeric vector containing which DMUs have to be evaluated. If NULL (default), all DMUs are considered.
kaoliu_modelname	a string containing the name of the model.
alpha	A numeric vector with the alpha-cuts (in [0,1]). If alpha>1, it determines the number of alpha-cuts, equispatially distributed in [0,1].
...	dmu_ref, orientation, rts and other model parameters.

Value

A list of class dea_fuzzy with the results for the evaluated DMUs (DMU component, we note that we call "targets" to the "efficient projections" in the strongly efficient frontier), along with any other necessary information to replicate the results, such as the name of the model and parameters orientation, rts, alpha, dmu_eval and dmu_ref.

Author(s)

Vicente Coll-Serrano ([e-mail]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([e-mail]). Department of Business Mathematics

Rafael Benítez ([e-mail]). Department of Business Mathematics

University of Valencia (Spain)

References

Boscá, J.E.; Liern, V.; Sala, R.; Martínez, A. (2011). "Ranking Decision Making Units by Means of Soft Computing DEA Models". International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(1), p.115-134.

Emrouznejad, A.; Tavana, M.; Hatami-Marbini, A. (2014). “The State of the Art in Fuzzy Data Envelopment Analysis”, in A. Emrouznejad and M. Tavana (eds.), Performance Measurement with Fuzzy Data Envelopment Analysis. Studies in Fuzziness and Soft Computing 309. Springer, Berlin.

Hatami-Marbini, A.; Emrouznejad, A.; Tavana, M. (2011). "A Taxonomy and Review of the Fuzzy Data Envelopment Analysis Literature: Two Decades in the Making", European Journal of Operational Research, 214, 457–472.

Kao, C.; Liu, S.T. (2000). “Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems”, 119, 149–160.

Kao, C., Liu, S.T., (2000). “Data envelopment analysis with missing data: An application to university libraries in Taiwan”, Journal of the Operational Research Society, 51, 897–905.

Kao, C., Liu, S.T. (2003). “A mathematical programming approach to fuzzy efficiency ranking”, International Journal of Production Economics, 85.

See Also

model_basic, model_multiplier, modelfuzzy_possibilistic, modelfuzzy_guotanaka

Examples

# Example 1. 
# Replication of results in Boscá, Liern, Sala and Martínez (2011, p.125)
data("Leon2003")
data_example <- make_deadata_fuzzy(datadea = Leon2003,
                                   inputs.mL = 2, 
                                   inputs.dL = 3, 
                                   outputs.mL = 4, 
                                   outputs.dL = 5)
result <- modelfuzzy_kaoliu(data_example,
                            kaoliu_modelname = "basic", 
                            alpha = seq(0, 1, by = 0.1), 
                            orientation = "io", 
                            rts = "vrs")
efficiencies(result)

# Example 2.
# Replication of results in Kao and Liu (2003, p.152)
data("Kao_Liu_2003")
data_example <- make_deadata_fuzzy(Kao_Liu_2003, 
                                   inputs.mL = 2, 
                                   outputs.mL = 3:7, 
                                   outputs.dL = c(NA, NA, 8, NA, 10),
                                   outputs.dR = c(NA, NA, 9, NA, 11))
result <- modelfuzzy_kaoliu(data_example, 
                            kaoliu_modelname = "basic", 
                            orientation = "oo", 
                            rts = "vrs", 
                            alpha = 0)
sol <- efficiencies(result)
eff <- data.frame(1 / sol$Worst, 1 / sol$Best)
names(eff) <- c("eff_lower", "eff_upper")
eff

deaR documentation built on Nov. 5, 2025, 6:35 p.m.