{"id":"c42e3836-653b-44e7-987e-3c8814d4efe6","arxiv_id":"2501.18413","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"Granular-ball fuzzy rough sets replace sample points with coarse-grained balls to make feature selection more noise-robust.","lead":"This paper combines granular-ball computing with fuzzy rough sets, replacing individual sample points with clusters called granular-balls to define a new feature selection method. The authors claim this makes fuzzy rough set feature selection more robust to label and attribute noise, with experiments on UCI datasets showing accuracy gains at high noise levels.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fuzzy-similarity normalization C is used as a fixed constant in Def. 4 but as |B| in Theorem 3; Property 1's proof needs the former, Theorem 3 needs the latter, so the monotonicity and forward-search guarantee are unsupported.","rationale":"The paper's central claim is that granular-balls replace sample points and improve robustness. The experimental comparison is the main evidence, and the reader already identified several load-bearing problems, including invalid error statistics, a broken pseudocode, and the unjustified C=|B| assumption. I focus on the C parameter because it is the deepest theoretical fault: it simultaneously invalidates the monotonicity property that justifies the forward search and the convergence theorem that the paper advertises. The reader's stated weakest assumption is the center-only representation of granular-balls; that is a legitimate concern, but the C inconsistency is more decisive because it breaks the dependency function itself, not just the representational fidelity. If C is fixed, Theorem 3 is an unjustified redefinition; if C=|B|, Property 1's proof and the derived monotonicity fail on a simple two-ball example. Either way, the forward-search algorithm's theoretical foundation collapses, and the reported robustness results are not supported by the formal framework. The availability of source code on GitHub is a positive sign, but it does not repair the inconsistency between Definition 4, Property 1, and Theorem 3. I therefore keep the reader's REJECT verdict unchanged.","tokens_in":21329,"tokens_out":9909,"duration_ms":86151,"concrete_test":"Analytical check: instantiate Def. 4 with C=|B| on two balls with centers c_i=(0,0), c_j=(1,0) and B={a1}, A={a1,a2} (with a2 identical in both balls). Compute r_B and r_A. If r_A > r_B, Property 1 and Property 3 fail exactly as described. Then re-run the forward search on the zoo dataset twice: once with C chosen as a fixed constant independent of |B|, and once with C=|B| as Theorem 3 specifies, and compare the selected attribute subsets and Table II accuracies. If the outputs match, the paper should state and justify C's dependence explicitly; if they differ, the published algorithm is not reproducibly specified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Definition 4 and Eq. (3) define fuzzy similarity using a distance parameter C, while Theorem 3 (Sec. III-C) sets C = i = |B| and Eq. (19) uses sqrt(|B|/|B U {a}|). These two roles are incompatible. If C is fixed, the substitution C=|B| is an unjustified redefinition and Theorems 2-4 do not follow from the model. If C=|B|, Property 1's proof (Sec. III-B) fails because it compares r_B and r_A with the same C; with different normalizations, Delta_B <= Delta_A no longer implies r_B >= r_A. Example: two balls whose centers differ only in a1 by distance 1 and are equal in a2; for B={a1}, C=|B|=1 gives r_B=0, while for A={a1,a2}, C=|A|=2 gives r_A=1-1/sqrt(2) ~ 0.293. This violates Property 1 and hence Property 3 (monotonicity of W*d_B(D)). Since Algorithm 1's forward search (lines 15-27) and its stopping criterion rest on W*d increasing with B, the feature-selection procedure lacks the claimed theoretical guarantee, directly weakening the central claim of a robust fuzzy-rough feature-selection model.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes GBFRS, a fuzzy rough set model in which sample points are replaced by granular-balls. It defines fuzzy similarity between balls from their centers, introduces upper/lower approximations and a weighted dependency function, and presents a forward-search feature-selection algorithm. The authors claim that the coarse-grained representation improves robustness to label and attribute noise, and they report experiments on UCI datasets comparing GBFRS with five fuzzy-rough/neighborhood feature-selection methods. The main theoretical result is a reduction to the classical dependency when each ball contains one point, and the main empirical claim is that GBFRS achieves the highest accuracy under increasing noise levels.","tokens_in":21677,"tokens_out":6084,"duration_ms":56285,"significance":"The idea of using granular-balls as the atomic units in a fuzzy rough set model is coherent and could be valuable: if the framework is sound, it may offer a principled way to improve the efficiency and noise robustness of fuzzy-rough feature selection while retaining a well-defined dependency measure. Theorem 1 is correct, and the authors provide a public code/data link, which is a strength for reproducibility. However, the significance is currently undercut by load-bearing problems: the central monotonicity argument relies on an inconsistent treatment of the distance parameter C, the convergence theorem has an invalid proof, the pseudocode for the feature-selection algorithm is not executable as stated, and the reported standard deviations in the experiments are impossible for accuracy values from a 5-fold cross-validation. These issues affect both the theoretical guarantee and the empirical support for the paper's central claim.","major_comments":[{"comment":"The distance parameter C is used inconsistently. Definition 4 and Eq. (3) call C a fixed distance parameter, but the paragraph immediately after Definition 4 says 'C is a fixed distance parameter: the number of attribute sets B,' and Theorem 3 sets C = i = |B|. Property 1's proof compares r_B and r_A with the same C, which is valid only if C does not change with the attribute subset. Theorem 3 changes C when going from B to B ∪ {a}, so the monotonicity of Property 3 no longer follows. A concrete failure is: take two balls whose centers differ only in attribute a1 by distance 1 and are equal in a2; for B = {a1}, C = 1 gives similarity 0, while for A = {a1,a2}, C = 2 gives similarity 1 - 1/sqrt(2), violating Property 1. Since the forward-search algorithm in Algorithm 1 and the significance formula in Eq. (19) rest on Property 3, the theoretical guarantee for the feature-selection procedure is unsupported.","section":"Definition 4, Eq. (3), Property 1, and Theorem 3 (Section III-B/C)"},{"comment":"The proof of Theorem 4 is invalid. The step asserting W∂Ci_B(D) ≤ W∂Ci_{B∪{ajk}}(D) ≤ W∂Ci_{B∪{ajk}∪{ajk+1}}(D) and the diminishing-returns inequality W∂Ci_{B∪{ajk}}(D) - W∂Ci_B(D) ≥ W∂Ci_{B∪{ajk}∪{ajk+1}}(D) - W∂Ci_{B∪{ajk}}(D) is introduced as 'classical fuzzy rough set theory' without proof, and it is not a consequence of any property established earlier in the paper. Additionally, the conclusion 'bounded monotonic, therefore converges to 0' is false: a decreasing sequence bounded below converges to some limit, but not necessarily to 0. The proof also compares significances of different attributes relative to different current sets (a_jk relative to B versus a_jk+1 relative to B∪{a_jk}), which does not establish convergence of SIG(a,B,D) for a fixed attribute a. Therefore Theorem 4, which is used to justify the stopping criterion of the feature-selection algorithm, is not proven.","section":"Theorem 4 (Section III-C)"},{"comment":"The pseudocode for feature selection contains logical errors. Line 15 gives the loop condition as 'while B' = ∅ or max_W∂ ≤ W∂ do'; with the initial values max_W∂ = 0 and W∂ = 0 this condition is true, and if no attribute improves the dependency, max_W∂ remains 0, W∂ remains 0, and the loop never terminates. Inside the loop, line 19 tests 'if W∂ > W∂''B' and then overwrites W∂ at line 20, so W∂ no longer holds the dependency of the current best subset; the comparison at line 24 between max_W∂ and W∂ is therefore comparing against a value that has already been reassigned. Line 17 already adds every candidate attribute to B'' during the inner loop, and line 25 adds Ni again, so the output set B'' can contain all attributes regardless of whether they improve the dependency. These issues make the algorithm non-reproducible and prevent verification of the claimed forward-search behavior.","section":"Algorithm 1, lines 15-27"},{"comment":"The reported standard deviations in Tables II and III are impossible for accuracy values. Accuracy is a proportion in [0,1], and for a 5-fold cross-validation the sample standard deviation across the five fold accuracies cannot exceed about 0.55; yet the tables report values such as 0.7871 ± 0.7888 (lymphography, FAR_FIE, 0% noise), 0.5116 ± 1.9454 (lymphography, FAR_FIE, 20% noise), and multiple entries in Table III exceeding 1.0. These entries cannot arise from the described experimental procedure. Since the central empirical claim of improved robustness rests on these tables, the experimental support is not credible as reported.","section":"Tables II and III (Section IV)"}],"minor_comments":[{"comment":"There is a typo in the abstract: 'Muiti-garanularty' should be 'Multi-granularity'.","section":"Abstract"},{"comment":"The proof of Property 2 says 'according to Property 2, we have ΔB1 ≤ ΔB2,' which is circular; the reference should be to Property 1 or to the definition of the distance.","section":"Property 2 proof (Section III-B)"},{"comment":"The text after Eq. (3) says C places GBRa in the interval '[0.1]'; this should be '[0,1]'.","section":"Definition 4, Eq. (3)"},{"comment":"The text says 'we randomly select 9 UCI data sets,' but Table I lists 10 datasets; the count should be corrected.","section":"Section IV, Table I"},{"comment":"The sentence 'Since fuzzy rough sets are very sensitive to noise in uncertainty data, the evaluation of uncertainty is not accurate' appears twice in the introduction; one occurrence should be removed.","section":"Section I"}],"recommendation":"reject","confidential_remarks":"The paper's central idea is plausible and the Theorem 1 reduction is correct, but the impossibility of the error bars in Tables II and III is a serious data-integrity concern: standard deviations above 1.0 for accuracies from a 5-fold cross-validation cannot result from the described procedure. The editor may wish to ask the authors for the raw per-fold results and the exact experimental code before any resubmission is considered. The theoretical issues with the distance parameter C and the invalid proof of Theorem 4 are also load-bearing, since the feature-selection algorithm is explicitly justified by the resulting monotonicity. These problems are too extensive for a minor revision; a rejection is appropriate unless the authors can rework the model, the proofs, the algorithm, and the experiments as a fundamentally revised submission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper has a genuinely appealing idea—replace sample points with granular-balls inside fuzzy rough set feature selection—and the authors get the reduction-to-classic right (Theorem 1). But the theoretical engine of the forward search is broken: the distance parameter C is treated as a fixed constant in Property 1 and as C=|B| in Theorem 3, and those two uses are incompatible. On top of that, the experimental tables contain impossible error bars. I wouldn't trust the current claims.\n\nWhat's new: first granular-ball fuzzy rough set framework for feature selection, with ball-based upper/lower approximations and a weighted dependency function. The motivation (coarse balls absorb label noise) is coherent, and Theorem 1—single-sample balls recover the classic dependency—is correct. The authors provide code and data.\n\nSoft spots: The C inconsistency is load-bearing. If C is fixed, Property 1 goes through but Theorem 3's redefinition is unjustified. If C=|B|, then Property 1 fails; the stress-test example is valid: with features a1,a2, balls separated by distance 1 in a1 only, B={a1} gives r_B=0 while A={a1,a2} gives r_A≈0.293, so monotonicity fails. No monotonicity, no forward-search guarantee, and Algorithm 1's stopping criterion is unsupported. Theorem 4's proof is also not valid as written—it mixes normalizations and the convergence step doesn't follow. Algorithm 1 has clear pseudocode errors: line 15's while condition should be \"B' not empty\" but reads \"B' = ∅\", and line 19's update condition appears inverted.\n\nExperiments: Tables II and III include standard deviations larger than the accuracy range (e.g., FNRS at 0.5940 ± 7.9441 on primary-tumor, and several ±2–3 entries). Those are impossible for bounded accuracies, so the empirical comparison can't be taken at face value. The GBFRS rows look plausible (small SDs), but the baseline numbers are the yardstick and they're corrupted.\n\nThe center-only ball representation is a limitation worth naming but not a fatal one; you could argue it as a modeling choice. The real problems are the C inconsistency and the experimental tables.\n\nWho this is for: people working on rough-set feature selection might find the idea worth a read, but the current form doesn't support the claims. My recommendation: this deserves a serious referee only if the authors can fix the normalization definition and provide clean experimental numbers. As it stands, I'd decline it and invite a major revision with those specifics.","headline":"A promising granular-ball fuzzy rough set idea with a broken monotonicity guarantee and impossible error bars—revision needed before it can be trusted.","tokens_in":22125,"tokens_out":4777,"would_cite":false,"duration_ms":39895,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Replacing sample points with granular-balls makes fuzzy rough set feature selection more robust under label and attribute noise.","keywords":["granular-ball computing","fuzzy rough sets","feature selection","attribute reduction","noise robustness","granular computing","fuzzy dependency"],"falsifier":"A synthetic dataset with two classes separated only by feature variance, not by feature mean, would settle it: if GBFRS never selects the variance-only feature while a point-based fuzzy rough set does, the center-only ball representation is discarding discriminative information.","tokens_in":21175,"feed_emoji":"🟠","tokens_out":10344,"duration_ms":82010,"temperature":0.7,"pith_summary":"This paper sets out to cure the noise sensitivity of fuzzy rough set feature selection. Instead of computing fuzzy similarities between individual samples, it first covers the dataset with granular-balls—groups of nearby points summarized by a center and radius and labeled by the majority class—and then runs the fuzzy rough set machinery on those balls. The resulting granular-ball fuzzy rough set (GBFRS) defines lower and upper approximations, a weighted fuzzy dependency function, and a forward attribute-selection algorithm built on it. Across ten UCI datasets, GBFRS holds up better than point-based fuzzy rough set baselines as label noise rises to 30%, and it is best or second-best on most datasets under attribute perturbation. If the claim holds, practitioners get a feature-selection method that trades a modest approximation for a large gain in robustness.","feed_headline":"Granular balls replace points to make fuzzy rough sets noise-robust","feed_subtitle":"Ball-based fuzzy rough sets keep feature selection accurate even when 30% of labels are corrupted.","key_machinery":"The load-bearing object is the granular-ball, a cluster of samples represented only by its center $c$ and mean radius $r$, with quality controlled by a purity threshold on the majority class. Fuzzy similarity between balls uses only the Euclidean distance between centers, $GBR_a(GB_i, GB_j) = 1 - \\Delta^a_2(c_i,c_j)/\\sqrt{C}$, and the weighted granular-ball fuzzy dependency $W\\partial_B(D) = \\sum_i |GB_i| \\cdot GBPOS_B(D)(GB_i) / |U|$ is what the forward search maximizes. Theorem 2's identity $W\\partial^{i+1}_B = \\sqrt{C_i/C_{i+1}} \\, W\\partial^i_B$ is the computational hinge: it turns a change in the distance parameter $C$ into a scalar rescaling, so attribute significance can be updated incrementally rather than recomputed from scratch.","core_discovery":"The paper's central discovery is that fuzzy rough set reasoning can be carried out on granular-balls rather than points without losing the formal structure that makes dependence-based attribute reduction work. It defines fuzzy similarity between balls using only the Euclidean distance between their centers (Eq. 3), reproduces the upper and lower approximations in that setting (Definition 5), and introduces a weighted granular-ball fuzzy dependency $W\\partial_B(D)$ (Definition 6) that weights each ball's positive-domain membership by the number of original samples it contains. This weighted dependency reduces exactly to the classical fuzzy dependency when every ball is a singleton (Theorem 1), is monotone with attribute-set inclusion (Property 3), and satisfies $W\\partial^{i+1}_B = \\sqrt{C_i/C_{i+1}} \\, W\\partial^i_B$ (Theorem 2), letting the forward search reuse prior computations. The empirical claim is that majority-label balls absorb minority noise, so the lower approximation—the part of the model that decides which features matter—stays accurate under heavy label noise and attribute perturbation.","pith_inferences":["The same ball-substitution principle should transfer to other instance-based and prototype-based learners, because the robustness mechanism—majority labels inside a ball absorbing minority noise—is not specific to fuzzy sets.","A stress test the paper does not run: if a feature's signal lives in within-ball variance rather than the center, GBFRS should fail to select it, which would expose the exact boundary of the center-only approximation.","The paper's closing limitation—that granular-ball computing is not fully adaptive because of the purity threshold—implies the threshold $T$ must be tuned per dataset, and an automatic rule for $T$ is a natural next step.","The experiments validate selected features only with kNN, so whether the robustness carries over to other classifiers remains an open check."],"forward_implications":["Under label noise up to 30%, GBFRS degrades more gracefully than the point-based fuzzy rough set baselines in the reported experiments, often keeping the highest kNN accuracy.","With 10% attribute perturbation, GBFRS is either the best or the second-best feature selector on most of the ten UCI datasets tested.","Because the weighted dependency collapses to the classical fuzzy dependency when each ball holds one sample, GBFRS is a strict generalization of point-based fuzzy rough set attribute reduction.","The scaling identity in Theorem 2 lets the forward search update dependencies after a change in the distance parameter $C$ by a scalar factor, avoiding full recomputation.","Replacing $n$ sample points with $k$ granular-balls shrinks the similarity matrix from $n \\times n$ to $k \\times k$, so the method's per-iteration cost depends on the number of balls rather than the number of samples."],"supporting_citations":[{"why":"Introduces the fuzzy rough set model whose upper and lower approximations GBFRS redefines on granular-balls.","marker":"[14]"},{"why":"Provides the classic fuzzy-rough attribute reduction framework whose point-based dependency function Theorem 1 recovers when balls are singletons.","marker":"[23]"},{"why":"Supplies the granular-ball computing model: covering samples with balls, purity-based splitting, and learning at the ball level.","marker":"[35]"},{"why":"Proposes the granular-ball neighborhood rough set, the predecessor that replaces points with balls in rough-set attribute reduction.","marker":"[39]"},{"why":"Gives the unified granular-ball rough set model that GBFRS extends into the fuzzy setting.","marker":"[36]"},{"why":"Defines the FNRS baseline feature-selection algorithm whose accuracy GBFRS is compared against under label noise.","marker":"[31]"},{"why":"Defines the HANDI baseline feature-selection algorithm used as a point-based comparison.","marker":"[29]"},{"why":"Defines the FAR_FIE baseline fuzzy-rough feature-selection method used in the experiments.","marker":"[19]"},{"why":"Defines the FS_NDEM baseline feature-selection method used in the experiments.","marker":"[18]"},{"why":"Defines the FRDMAR baseline local-reduction method used in the experiments.","marker":"[13]"}],"fun_headline_variants":["Ball-based fuzzy rough sets absorb label noise","Granular-ball fuzzy rough sets resist heavy noise","Coarse-grained balls keep fuzzy rough sets reliable","Ball centers alone drive robust fuzzy feature selection"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each granular-ball's center and majority label preserve the information needed for feature selection, so the ball's internal spread, shape, or label distribution can be ignored.","fun_headline_variants_meta":{"raw":{"variants":["Ball-based fuzzy rough sets absorb label noise","Granular-ball fuzzy rough sets resist heavy noise","Coarse-grained balls keep fuzzy rough sets reliable","Ball centers alone drive robust fuzzy feature selection"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000229,"raw_usage":{"total_tokens":1493,"prompt_tokens":972,"completion_tokens":521,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":588,"completion_tokens_details":{"reasoning_tokens":464}},"tokens_in":588,"tokens_out":521,"duration_ms":5205,"temperature":1.0,"reasoning_tokens":464,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T23:35:09.761795+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A synthetic dataset with two classes separated only by feature variance, not by feature mean, would settle it: if GBFRS never selects the variance-only feature while a point-based fuzzy rough set does, the center-only ball representation is discarding discriminative information.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the FAR_FIE baseline fuzzy-rough feature-selection method used in the experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the FS_NDEM baseline feature-selection method used in the experiments."},{"cited_title":"Degang and Z","cited_arxiv_id":null,"evidence_quote":"Defines the FRDMAR baseline local-reduction method used in the experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the HANDI baseline feature-selection algorithm used as a point-based comparison."},{"cited_title":"Dubois and H","cited_arxiv_id":null,"evidence_quote":"Introduces the fuzzy rough set model whose upper and lower approximations GBFRS redefines on granular-balls."},{"cited_title":"Jensen and Q","cited_arxiv_id":null,"evidence_quote":"Provides the classic fuzzy-rough attribute reduction framework whose point-based dependency function Theorem 1 recovers when balls are singletons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the granular-ball computing model: covering samples with balls, purity-based splitting, and learning at the ball level."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes the granular-ball neighborhood rough set, the predecessor that replaces points with balls in rough-set attribute reduction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the unified granular-ball rough set model that GBFRS extends into the fuzzy setting."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the FNRS baseline feature-selection algorithm whose accuracy GBFRS is compared against under label noise."}],"review_version":1}