modelfuzzy_guotanaka function

Fuzzy DEA model

Solve the Fuzzy input-oriented and output-oriented DEA model proposed by Guo and Tanaka (2001) under constant returns to scale. In deaR is implemented the LP poblem given by the model (16) in Guo and Tanaka (2001, p.155). The fuzzy efficiencies are calculated according to equations in (17) (Guo and Tanaka, 2001, p.155). The (crisp) relative efficiencies and multipliers for the case h = 1 are obtained from the CCR model (model_multiplier).

modelfuzzy_guotanaka(datadea,
                     dmu_eval = NULL,
                     dmu_ref = NULL,
                     orientation = c("io", "oo"),
                     h = 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.
• dmu_ref: A numeric vector containing which DMUs are the evaluation reference set. If NULL (default), all DMUs are considered.
• orientation: A string, equal to "io" (input oriented) or "oo" (output oriented).
• h: A numeric vector with the h-levels (in [0,1]).

Returns

An object of class deadata_fuzzy.

Note

The optimal solution of model (16) is not unique.

Examples

# Example 1.
# Replication results in Guo and Tanaka (2001, p. 159). 
# In deaR is implemented the LP poblem given by the model 16 in Guo and Tanaka (2001, p. 155).
# The fuzzy efficiencies are calculated according to equations in (17) (Guo and Tanaka, 2001,p.155).
data("Guo_Tanaka_2001")
data_example <- make_deadata_fuzzy(Guo_Tanaka_2001, 
                                   inputs.mL = 2:3, 
                                   inputs.dL = 4:5, 
                                   outputs.mL = 6:7,
                                   outputs.dL = 8:9)
result <- modelfuzzy_guotanaka(data_example, 
                               h = c(0, 0.5, 0.75, 1), 
                               orientation = "io")
efficiencies(result)
 
# Example 2. 
data("Guo_Tanaka_2001")
data_example <- make_deadata_fuzzy(Guo_Tanaka_2001, 
                                   inputs.mL = 2:3, 
                                   inputs.dL = 4:5, 
                                   outputs.mL = 6:7, 
                                   outputs.dL = 8:9)
result2 <- modelfuzzy_guotanaka(data_example, 
                                h = seq(0, 1, by = 0.1), 
                                orientation = "io")
efficiencies(result2)

References

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. tools:::Rd_expr_doi("10.1007/978-3-642-41372-8_1")

Guo, P.; Tanaka, H. (2001). "Fuzzy DEA: A Perceptual Evaluation Method", Fuzzy Sets and Systems, 119, 149–160. tools:::Rd_expr_doi("10.1016/S0165-0114(99)00106-2")

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. tools:::Rd_expr_doi("10.1016/j.ejor.2011.02.001")

See Also

model_basic, model_multiplier, modelfuzzy_kaoliu, modelfuzzy_possibilistic, cross_efficiency_fuzzy

Author(s)

Vicente Coll-Serrano (vicente.coll@uv.es ). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós (vicente.bolos@uv.es ). Department of Business Mathematics

Rafael Benítez (rafael.suarez@uv.es ). Department of Business Mathematics

University of Valencia (Spain)