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REVIEW 3 major objections 5 minor 80 references

Conventional and Fuzzy Data Envelopment Analysis with deaR

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper describes deaR, an R package for data envelopment analysis that implements a broad menu of conventional and fuzzy models and is claimed to be the only package offering the Kao-Liu, Guo-Tanaka, and possibilistic fuzzy DEA models.

desk verdict A thorough, honest software description that mostly delivers on its replication claims; one unresolved FDH discrepancy and an overstrong exclusivity claim need fixing, but the package is a real contribution. read the letter →

arxiv 2506.03766 v1 pith:NTMVDQI2 submitted 2025-06-04 econ.EM cs.MS

Vicente J. Bolos , Rafael Benitez , Vicente Coll-Serrano This is my paper
classification econ.EMcs.MS
keywords dataenvelopmentanalysisDEAsoftwareRpackagefuzzyKao-LiumodelGuo-TanakapossibilisticMalmquistproductivityindex
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Data envelopment analysis (DEA) measures how efficiently each decision-making unit converts inputs into outputs relative to a best-practice frontier. This paper describes deaR, an R package that turns DEA into a three-step workflow — read data, run a model function, and extract scores and targets — and claims to cover most of the standard model menu, including radial and non-radial models, super-efficiency, cross-efficiency, Malmquist productivity indices, bootstrapping, and metafrontier analysis. Its distinctive claim is fuzzy coverage: deaR is the only package to date implementing the Kao-Liu, Guo-Tanaka, and possibilistic fuzzy models, which handle inputs and outputs known only imprecisely. The paper supports the implementations by reproducing published numerical results from more than 20 bundled datasets drawn from books and research papers. If the claims hold, a single package gives researchers and practitioners access to the full conventional-and-fuzzy DEA toolbox without switching software.

What carries the argument

The machinery is the S3 class pair deadata and deadata_fuzzy, which hold crisp or trapezoidal-fuzzy input and output matrices, together with the model functions that convert each DEA formulation into a linear program solved by an external LP solver. The result object of class dea stores all extracted quantities. Kao-Liu models work as metamodels: at each $\alpha$-cut they run a chosen crisp model under worst-case and best-case scenarios for each DMU, producing fuzzy efficiency scores. Guo-Tanaka and possibilistic models work at $h$-levels, respectively yielding triangular fuzzy scores and crisp scores per level, and each fuzzy family has its own visualization.

What would settle it

Run the input-oriented free disposal hull model on the bundled Supply_Chain dataset: deaR reports 0.98156 for DMU sc16 while the cited source reports 1, and a direct re-solve of that linear program would show which side is wrong; extending the same independent re-solve to all bundled datasets would test the paper's reproduction claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that deaR provides a unified implementation of the DEA model landscape, covering both conventional and fuzzy models with a consistent interface and with special support for non-controllable, non-discretionary, and undesirable variables. It further claims that the fuzzy models Kao-Liu, Guo-Tanaka, and possibilistic are unique to deaR among current packages. The package is designed so that each model is a function that takes a data object, builds the corresponding linear program, solves it, and returns a result object from which efficiencies, lambdas, slacks, targets, and multipliers can be extracted. The paper presents numerical examples from classical datasets and treats agreement with published results as evidence that the implementations are correct, while also introducing graphical representations of efficiency frontiers, cross-efficiency matrices, and fuzzy efficiency scores.

Load-bearing premise

The package's correctness is judged by agreement with published results, so the central claim stands only if the source datasets are faithful and the published numbers they are benchmarked against are themselves correct.

Editorial extensions

If this is right

  • A non-expert R user can apply CCR, BCC, directional, SBM, additive, FDH, multiplier, cost/revenue/profit, super-efficiency, cross-efficiency, Malmquist, bootstrap, and metafrontier analyses from one package without switching software.
  • The Kao-Liu, Guo-Tanaka, and possibilistic fuzzy DEA models become available in a single reference implementation, filling a gap that the paper says no other package covers.
  • Bundled datasets allow users to reproduce published numerical results, making the package a practical check on the correctness of its implementations.
  • Special features such as non-controllable, non-discretionary, and undesirable inputs and outputs are handled within the same workflow, so studies with irregular data do not require separate software.
  • The package's graphical outputs, including reference graphs and cross-efficiency heat maps, give users a direct visual route to interpreting efficiency scores and frontier relationships.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the reproduction claims hold, the bundled datasets effectively become a public test suite: any future DEA implementation, in any language, could use the same inputs and published outputs to check numerical correctness.
  • The paper itself shows a discrepancy for DMU sc16 in the Supply_Chain dataset, where deaR returns 0.98156 and the cited source reports 1, so users should not assume every bundled dataset is error-free; a maintainer-added list of known discrepancies would make the package more transparent.
  • Because Kao-Liu is a metamodel that wraps any chosen conventional model, the package implicitly offers a general way to fuzzify all its crisp models, even though the paper demonstrates only a subset of possible combinations.
  • The uniform three-step workflow across crisp and fuzzy models suggests that deaR could serve as a teaching platform for fuzzy DEA, letting students compare fuzzy results against the corresponding crisp baseline with minimal code changes.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper describes deaR, an R package on CRAN for conventional and fuzzy data envelopment analysis. It documents the data-reading workflow, radial and non-radial models, special variable types, super-efficiency, cross-efficiency, fuzzy models (Kao-Liu, Guo-Tanaka, and possibilistic), Malmquist indices, bootstrap procedures, and metafrontier analysis. The authors validate the implementation by reproducing published numerical results on roughly twenty bundled datasets and provide worked R examples with concrete output and plots.

Significance. If the implementation is correct, deaR is a practically valuable one-stop package for DEA in R, and its coverage of fuzzy models is a genuine differentiator. The paper's strengths are the breadth of models, the bundled datasets, and the many worked examples with concrete numerical output that match published sources. However, the central validation-by-replication strategy is weakened by an unresolved, explicitly reported discrepancy in the FDH example, and two further points in the SBM and Malmquist sections need attention before the paper's claims are fully supported.

major comments (3)
  1. [3.2] The FDH example on the Supply_Chain dataset reports an efficiency score of 0.98156 for DMU sc16, while Mamizadeh-Chatghayeh and Sanei (2013) report 1, and the text says only that this is 'contrary to the results shown' without saying which side is wrong. This is a concrete counterexample to the replication-based validation promised in Section 2.2, and the comparison is not fully specified because the paper does not state whether Supply_Chain is exactly the dataset used in the source or how the source computed its score. The authors should resolve the discrepancy by checking the source data and definition or by correcting the implementation, and they should either revise the reproduction claim or document the mismatch explicitly as a known limitation.
  2. [3.6] For SBM models with zero output data, the paper states that Tone's Case 2 is applied 'but taking 1/100 instead of 1/10.' This is an unexplained deviation from the cited Tone (2001) algorithm, and it changes the numerical scores whenever a zero output is present. The authors should justify the constant or re-run the benchmark against Tone's exact formulation and report the impact of the change.
  3. [8] The text around Eq. (41) attributes the index M^t_o = D^t(x^{t+1}, y^{t+1}) / D^t(x^t, y^t) to Ray and Desli (1997); that paper's VRS Malmquist index is usually written as a geometric mean of distance-function ratios, not as a single-period ratio. The subsequent 'rd' decomposition should be checked against the source. Either the formula needs correction or the description should clarify that the package implements the generalized Grifell-Tatjé and Lovell (1999) index under the label 'rd'.
minor comments (5)
  1. [2.2] The function name appears as 'make deadata' in the prose in several places; it should be 'make_deadata' for consistency with the code and with the rest of the paper.
  2. [2.3] The text refers to 'Table 2.3' for the list of model functions, while the printed caption is 'Table 1'; similarly, Section 8 refers to 'Table 8' when the caption says 'Table 4'. These cross-references should be corrected.
  3. [3.7] The profit-efficiency score is written as 'pyo - cxo / py* - cx*' without parentheses; the intended ratio should be typeset as (py_o - c x_o)/(p y^* - c x^*) so that the reader is not left to guess the order of operations.
  4. [3.1] The statement that epsilon = 1e-6 is 'too high' could be misleading; the issue is that a finite epsilon imposes additional constraints that may be infeasible for a particular dataset. The sentence should state that the threshold depends on the data scale.
  5. [Abstract] The claim that deaR is 'the only package to date' incorporating Kao-Liu, Guo-Tanaka, and possibilistic fuzzy models is an absolute statement that is not substantiated by a systematic comparison; a date-stamped survey or a softer formulation would make it verifiable.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation; the paper documents an R package and validates it against external benchmarks.

full rationale

The paper contains no claimed derivation from first principles. It presents standard DEA models with equations taken from the literature (Charnes-Cooper-Rhodes, Banker-Charnes-Cooper, Tone, Kao-Liu, Guo-Tanaka, León et al., etc.) and describes how deaR wraps lpSolve. Every reported numerical example is computed from a fixed linear program and checked against results published by other authors, such as Tone (2001), Tone (2002), Wu et al. (2011), Guo and Tanaka (2001), León et al. (2003), and Wang and Lan (2011). No parameter is fitted to the benchmark datasets and then used to predict the same benchmark; the models are deterministic and are not defined in terms of their outputs. The only self-citation, Coll-Serrano et al. (2022), is the CRAN package reference and is descriptive rather than load-bearing for any numerical claim. The FDH discrepancy in Section 3.2 (sc16 = 0.98156 versus 1 in Mamizadeh-Chatghayeh and Sanei (2013)) is an unresolved correctness or validation issue, but not a circularity: the paper explicitly reports the mismatch without redefining the model or fitting the contested result. Because no specific reduction of a claimed result to its own inputs can be exhibited, the circularity score is minimal.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

This paper is a software manual, so the ledger records what the package's correctness depends on: standard DEA production-postulate assumptions, the reliability of the lpSolve library, the fidelity of bundled datasets to their cited sources, and the fuzzy-number semantics adopted from three cited papers. The free parameters are user-facing defaults and translation choices that demonstrably change scores.

free parameters (4)
  • non-Archimedean epsilon in multiplier models = default 0; example uses 1e-6 and yields NA for 2 of 15 DMUs
    Section 3.1: epsilon forces positive weights in multiplier forms; the paper warns that a too-high value alters results and causes infeasibilities, so scores depend on this user choice.
  • bootstrap bandwidth h = 0.014 default; alternatives h1-h4 computed from data
    Section 9: the bias-corrected scores and confidence intervals depend on the smoothing bandwidth, an implementation default the user can override.
  • SBM zero-output scaling constant = 1/100 (Tone's Case 2 uses 1/10)
    Section 3.6: for zero output data, the package substitutes 1/100 for Tone's 1/10 with no derivation, changing efficiency scores for such datasets.
  • translation vectors for undesirable variables = max + 1 per variable by default; user can override (e.g., 1500 in the Hua-Bian example)
    Section 4.3: the Seiford-Zhu transformation (22) requires translation constants; the paper notes translation invariance only holds under VRS, so orientation and translation choice jointly affect results.
assumptions (4)
  • domain assumption The production possibility sets and LP formulations from the cited literature correctly characterize efficiency in all models implemented.
    Sections 2-10 restate published models (CCR, BCC, FDH, SBM, Kao-Liu, Guo-Tanaka, possibilistic) without re-deriving them; the paper's correctness claim inherits the correctness of those sources.
  • domain assumption lpSolve returns optimal solutions for every generated linear or mixed-integer problem.
    Section 2.1 states deaR is a wrapper of lpSolve; the paper itself warns about ill-posed problems from disparate magnitudes (Hotels example) and infeasibilities from epsilon settings (Section 3.1).
  • domain assumption The bundled datasets faithfully reproduce the data used in the cited studies.
    Section 2.2 says datasets come from books and papers so users can reproduce published results; Section 3.2's sc16 contradiction with Mamizadeh-Chatghayeh and Sanei (2013) shows this premise can fail silently.
  • domain assumption Fuzzy efficiency is what the three cited models define it to be.
    Section 7 adopts Kao-Liu alpha-cut worst/best decomposition, Guo-Tanaka h-level fuzzy multipliers, and Leon et al. possibilistic radial models as the package's fuzzy semantics; the paper offers no independent justification that these represent data uncertainty correctly.

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Cite this review

Pith. "Pith review of Conventional and Fuzzy Data Envelopment Analysis with deaR." pith.science (2026). https://pith.science/paper/NTMVDQI2

@misc{pith2026250603766,
  author       = {Pith},
  title        = {Pith review of: Conventional and Fuzzy Data Envelopment Analysis with deaR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NTMVDQI2}},
  note         = {Machine review of arXiv:2506.03766}
}
read the original abstract

deaR is a recently developed R package for data envelopment analysis (DEA) that implements a large number of conventional and fuzzy models, along with super-efficiency models, cross-efficiency analysis, Malmquist index, bootstrapping, and metafrontier analysis. It should be noted that deaR is the only package to date that incorporates Kao-Liu, Guo-Tanaka and possibilistic fuzzy models. The versatility of the package allows the user to work with different returns to scale and orientations, as well as to consider special features, namely non-controllable, non-discretionary or undesirable variables. Moreover, it includes novel graphical representations that can help the user to display the results. This paper is a comprehensive description of deaR, reviewing all implemented models and giving examples of use.

Figures

Figures reproduced from arXiv: 2506.03766 by the authors.

Figure 1
Figure 1. deaR workflow. From raw data, we construct the corresponding linear program￾ming models which are solved with lpSolve. Finally, parameters of interest are extracted from the solution. 3 Itochu 65708.9 4271.1 7182 169164.6 121.2 4 General Motors 217123.4 23345.5 709000 168828.6 6880.7 5 Sumitomo 50268.9 6681.0 6193 167530.7 210.5 6 Marubeni 71439.3 5239.1 6702 161057.4 156.6 In this standard DEA dataset, the first co… view at source ↗
Figure 2
Figure 2. Plots returned by plot(ccrFortune). In the last plot, efficient DMUs are repre￾sented by green circles and inefficient DMUs by red circles. In each inefficient DMU, there are arrows pointing to the DMUs of its corresponding reference set. Moreover, the size of the circle of an efficient DMU depends on the relevance of this DMU in the reference sets. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Plots of the cross-efficiency matrices E from aggressive and benevolent formulations of method II, returned by plot(crossGolany). R> dataLim <- make_deadata(Lim_Zhu_2015, ni = 1, no = 5) R> crossLim <- cross_efficiency(dataLim, rts = "vrs", correction = TRUE) R> head(crossLim$Arbitrary$e) Project_1 Project_2 Project_3 Project_4 Project_5 Project_6 0.7073056 0.6138268 0.1847451 0.4605659 0.4957667 0.5759273 R> head(c… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Types of fuzzy numbers considered in package [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]
Figure 5
Figure 5. Figure 5: Structure of the field alphacut. Inside of each field DMU1, DMU2, . . . are stored efficiency scores, lambdas, slacks, targets, multipliers and other results of the submodel. One of the difficulties about fuzzy efficiency models is the representation of the efficiency …
Figure 6
Figure 6. Figure 6: Fuzzy efficiency scores obtained with Kao-Liu model. For each DMU, the fuzzy [PITH_FULL_IMAGE:figures/full_fig_p028_6.png]
Figure 7
Figure 7. Figure 7: Fuzzy efficiency scores obtained with Guo-Tanaka model. For each DMU and [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: Efficiency scores obtained with possibilistic model. For each DMU and each [PITH_FULL_IMAGE:figures/full_fig_p030_8.png]
Figure 9
Figure 9. Figure 9: Non-parametric metafrontier analysis. The efficient frontiers of each group [PITH_FULL_IMAGE:figures/full_fig_p035_9.png]

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