Pith. sign in

REVIEW 5 major objections 6 minor 49 references

Explainable Evidential Clustering

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Evidential clustering can be explained by shallow decision trees, and for one-centroid-per-leaf trees minimizing evidential mistakeness is provably equivalent to maximizing explanation quality.

desk verdict Sound theoretical core for a new evidential-clustering explanation cost, but the greedy algorithm that bears the practical claims is unproven and the experiments validate it against its own objective. read the letter →

arxiv 2507.12192 v2 pith:KTDXZSO2 submitted 2025-07-16 cs.LG

Victor F. Lopes de Souza , Karima Bakhti , Sofiane Ramdani , Denis Mottet , Abdelhak Imoussaten This is my paper · ORCID
classification cs.LG
keywords explainabilitycautiousnessunsupervisedclassificationevidentialclusteringdecisiontreesbelieffunctionsutilityabductiveexplanation
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

This paper asks a question that existing explainability work skips: when a clustering algorithm returns not crisp labels but a credal partition — a mass function over subsets of clusters, expressing uncertainty and imprecision — what should an explanation even be? The authors show that, for decision trees, being representative (matching the clustering on every point) is both necessary and sufficient to give abductive explanations. They then carry this criterion into the evidential setting by defining utility functions $U(A,B)$ that score how tolerable it is to say $A$ when the truth is $B$, which turns explanation cost into an evidential mistakeness. The paper's main theoretical result is that, for the class of one-centroid-per-leaf trees used in the IMM algorithm, minimizing either form of evidential mistakeness orders trees exactly like maximizing evidential representativeness. On that foundation, the Iterative Evidential Mistake Minimization (IEMM) algorithm builds shallow, cautious decision trees, and the authors report explanations satisfactory up to 93% of the time when the decision-maker's preferences are taken into account.

What carries the argument

The load-bearing object is the pair of evidential mistakeness measures from Equations (6) and (7), together with the utility function $U$ that defines what counts as a tolerable mistake. Theorem 2 shows that, for IMM-like trees (one centroid per leaf), the total of either mistakeness and the evidential representativeness $R_{M,U}(\Delta)$ are affinely related by a tree-independent constant, which is all that is needed for the equivalence of orderings. This affine identity is what carries the argument: it licenses replacing maximize explanation quality with minimize evidential mistakeness in the algorithm, and it is what makes the greedy per-node split choice in IEMM (Algorithm 1) a sound heuristic inside the restricted family.

What would settle it

Construct a two-feature evidential clustering in which two metaclusters have centroids that lie on the same side of every allowed axis-aligned threshold, yet their member points are interleaved so that a deeper or oblique tree separates them cleanly. If on such data IEMM's best shallow tree has evidential representativeness far below 1 while a non-IMM tree is near-perfect, then minimizing evidential mistakeness within the IMM-like class fails to deliver faithful explanations.

Watch

Extended reading notes

Core claim

The central claim is that evidential clustering results can be faithfully explained by shallow decision trees once the notion of an explanation error is made utility-aware. Concretely, the paper proves two things. First, Theorem 1: for decision-tree explainers, representativity (the explainer's leaves match the clustering on every point) is equivalent to abductivity (every leaf gives a sufficient reason for its label), so a tree explains a clustering exactly when it reproduces it. Second, Theorem 2: for any two IMM-like trees — trees in which every leaf contains exactly one metacluster centroid — the ordering by evidential representativeness $R_{M,U}$, the ordering by the cost-of-not-assigning mistakeness, and the ordering by the expected-assignment-cost mistakeness are all identical, because the three quantities differ only by a constant that depends on the clustering and utility but not on the tree. Hence minimizing evidential mistakeness is provably equivalent to maximizing utility-weighted explanation quality inside the IMM-like family, and the choice of $U$ — equivalently the parameter $\lambda$ — encodes how cautious the explanation should be. This is what the IEMM algorithm exploits greedily, and it is why the resulting trees are interpretably shallow while still being optimal within their class.

Load-bearing premise

The framework assumes that a decision tree with at most $|F|-1$ axis-aligned splits, one leaf per metacluster centroid, can faithfully represent the evidential clustering; if the true credal boundaries need deeper, oblique, or centroid-independent splits, the explanation can be systematically wrong while still being optimal within that restricted class.

Editorial extensions

If this is right

  • Because representativity and abductivity coincide for decision-tree explainers, any tree that reproduces a hard clustering gives provably sufficient reasons for its assignments, and this property extends pointwise to the evidential case through utility-weighted representativeness.
  • The parameter $\lambda$ is a single dial that turns explanation policy: negative $\lambda$ penalizes assigning points to metaclusters that cover too much (over-cautious errors), positive $\lambda$ penalizes assigning metaclusters that cover too little (under-cautious errors), and the extremes $\lambda \to \pm\infty$ recover pure inclusion rules based on subset relations.
  • Minimizing evidential mistakeness is guaranteed to order IMM-like trees identically to maximizing evidential representativeness, so the greedy split choice in IEMM is aligned with its stated objective rather than being a loose approximation.
  • When the clustering is hard and $\lambda = 0$, IEMM's mistakeness reduces to the IMM mistake count, so the new algorithm contains the classical explanatory decision-tree method as a special case.
  • IEMM trees are shallow by construction — at most $|F|-1$ internal nodes, one leaf per focal set — so interpretability is built into the algorithm, at the price of possible rigidity for complex patterns.

Reading between the lines

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

  • The theorem's equivalence is proven only within the IMM-like family; a natural extension would be to test whether representativeness and mistakeness also order trees identically when leaves may hold several centroids or splits may be oblique, which would justify applying the same greedy principle in a richer hypothesis space.
  • Because the proposed utilities depend only on set cardinalities, they treat every cluster symmetrically; plugging in an asymmetric utility that weights confusion between particular clusters more heavily would change the explanation without altering the algorithm.
  • The reported 93% satisfactory-explanation rate suggests that alignment between the decision-maker's tolerance and the tree's cautiousness drives perceived quality; a testable follow-up is whether this alignment matters more than tree size for real users.
  • The algorithm presupposes a centroid for every focal set; evidential clustering methods producing focal elements without a natural centroid would need an extended input representation before IEMM applies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. This paper proposes a framework and an algorithm for explaining evidential clustering results with decision trees. It introduces a utility-based representativeness score R_{M,U} for cautious explainers and two forms of evidential mistakeness (Eqs. 6 and 7). Theorem 2 claims that, for IMM-like decision trees with one centroid per leaf, maximizing evidential representativeness is equivalent to minimizing either mistakeness measure. The IEMM algorithm greedily grows a decision tree by splitting on coordinate thresholds to minimize a local mistakeness. Experiments on synthetic and real datasets report representativeness values up to 93%.

Significance. The paper addresses a genuine gap—explainability for evidential clustering—and the parameterized utility family for 'tolerable mistakes' is a useful idea. If the theoretical and algorithmic claims are made precise, the work would be a solid extension of the IMM approach to cautious, imprecise settings. The release of the code is a strength. However, the practical claim currently rests on a greedy algorithm with no optimality analysis, and the experiments are largely a self-consistency check rather than a comparative validation. With those gaps addressed, the paper could be a meaningful contribution to explainable clustering.

major comments (5)
  1. [3.2, Algorithm 1 (line 11)] The split-selection function M(x, m, v, F, i, θ) is never defined in the text. This function is the core of IEMM: it is called in every non-terminal node to choose the best threshold, and the values labeled 'mistakeness of cut' in Figure 5 must be its output. Without a precise definition, the algorithm is not reproducible and the claimed connection to Eqs. (6) and (7) cannot be checked.
  2. [3.2 and Theorem 2] The paper states that IEMM 'fits a decision tree based on an evidential clustering by minimizing the evidential mistakeness function', but no result links the greedy split selection to global minimization of the total mistakeness. Theorem 2 is a statement about global optimizers over the class of IMM-like trees; it does not imply that the recursively chosen locally optimal cuts produce such a global optimizer. An exchange argument, an approximation guarantee, or an explicit acknowledgment that IEMM is a heuristic (with a gap evaluation against exact search on small instances) is needed. Without this, the 93% representativeness result cannot be attributed to the theoretical equivalence.
  3. [Appendix C, proof of Theorem 2] The proof of Theorem 2 contains several notational and algebraic errors. In the first displayed equation, the inner sum is written as Σ_{Δ(x)≠C} U(C,B), whereas Eq. (6) sums over metaclusters whose centroids lie outside S. In the second displayed equation, the denominator from Eq. (7) is omitted; it equals 1 for a singleton leaf, but this should be stated. The sums in the theorem range over A⊂Ω, although leaves are indexed by focal sets A∈F_M. Finally, κ_{M,U} is used as a scalar, but the preceding expression defines a sum over x with varying masses m_x; the definition of κ_{M,U} should be made explicit.
  4. [3.2, 'The Tests' and Tables 3–4] The experiments report only the representativeness R_{M,U} of the trained trees, which is the same objective that the algorithm optimizes during training. There are no confidence intervals, no repeated runs, and no baselines such as random thresholds, CART trained on the hard partition, or hard-label IMM. The '93% satisfactory' statement is therefore a self-consistency check: it shows that the greedy tree can achieve high values of the optimized score, not that the explanations are satisfactory relative to alternative explainers. Baselines and variability estimates should be added.
  5. [3.2, Algorithm 1 input] Algorithm 1 takes as input the focal sets F and their centroids v, assuming every focal set has a centroid. This is not guaranteed for arbitrary evidential partitions produced by common algorithms, which typically return prototypes for individual clusters rather than for every metacluster. The paper should state this assumption explicitly, discuss how such centroids are obtained, or restrict the algorithm's scope accordingly.
minor comments (6)
  1. [3.1, Theorem 2] The term 'IMM-like decision tree' is used in Theorem 2 but never formally defined; please define it (e.g., a decision tree with axis-aligned splits and exactly one centroid per leaf) before the theorem.
  2. [3.1, Eqs. (6)–(7)] The two mistakeness functions are both denoted with similar symbols 'M_{M,U}' and '\mathcal{M}_{M,U}' in the text; please use clearly distinct notation to avoid confusion.
  3. [Appendix A and Section 1] There are small typos and grammatical issues, such as 'attributtes' in Appendix A and 'this have drawn criticism' in Section 1; these should be corrected.
  4. [Figure 5] Leaf labels such as 'label: 3' are ambiguous; they should indicate the metacluster, e.g., '{ω3}', and the 'mistakeness of cut' values should explicitly reference Eq. (6) or Eq. (7).
  5. [Section 2.2] The expression 'FM = S x∈X Fmx' should be written as the union ⋃_{x∈X} F_{m_x}.
  6. [Table 4] For the real-world datasets, please state the number of samples, the number of attributes, and how the evidential partitions were generated, since this information is needed to interpret the reported representativeness values.

Circularity Check

1 steps flagged · score 5.0 of 10

Partial circularity: the validation metric is the same objective IEMM minimizes by construction, so the 93% claim is a self-consistency result rather than an independent prediction.

  1. self definitional [Section 3.2 (Algorithm 1); Appendix D (Tables 3/4); Theorem 2 in Appendix C]
    "Inspired by IMM, we propose the Iterative Evidential Mistake Minimization (IEMM). The IEMM fits a decision tree based on an evidential clustering by minimizing the evidential mistakeness function (see Algorithm 1). We can see that decision trees trained with λ-evidential mistakeness function tend to be the best in terms of U λ-evidential representativeness."

    Theorem 2 proves that for any IMM-like tree the total evidential mistakeness and the U-evidential representativeness are affinely equivalent (T6 = κ − |X|R and T7 = |X| − |X|R). Thus the quantity IEMM minimizes, M^λ, and the quantity reported as the evaluation score, R_{M,U^λ}, are the same objective up to constants. The diagonal 'best' entries in Tables 3 and 4 therefore follow by construction from the definitions: a tree trained to minimize the λ-mistakeness is, up to the greedy heuristic, the tree that maximizes the λ-representativeness in the same column. The abstract's 'satisfactory up to 93%' is the largest cell of this self-consistency grid, so it is not independent evidence about explanation quality or utility.

full rationale

The theoretical core survives scrutiny: Theorem 2 is internally valid and the equivalence between evidential mistakeness and representativeness is a genuine algebraic result proven in Appendix C, not an unsupported self-citation. There is no load-bearing self-citation or imported uniqueness theorem; the inspirations (IMM), implementation base, and datasets are external. The circularity is confined to the empirical framing: IEMM's loss M^λ and the reported evaluation R_{M,U^λ} are the same objective up to affine constants, so Tables 3 and 4 mostly confirm that the algorithm optimizes what it was designed to optimize. The paper's own conclusion acknowledges the shallow-tree expressiveness limitation, which is a correctness risk for the practical claim, not a circularity; the lack of an optimality guarantee for the greedy split search is likewise a correctness risk, not a circularity. Score 5 reflects one partially definitional validation loop while the central theorem retains independent mathematical content.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The framework rests on standard belief-function theory plus several modeling restrictions: metacluster centroids, closed-world assumption, finite attributes, and a user-supplied utility parameter. No new physical entities or forces are introduced. The main non-standard construct is the family of utility functions, whose suitability is not empirically validated against human preferences.

free parameters (1)
  • lambda (utility parameter) = user-specified in {-inf, ..., 0, ..., +inf}; not fitted
    Controls tolerance to insufficient or excessive coverage in the utility family. Experiments sweep over lambda values but no value is estimated from data; the framework depends on the decision-maker supplying this preference.
assumptions (5)
  • domain assumption Every focal set has a well-defined centroid in the feature space.
    Algorithm 1 requires v_A for every A in F as input. Not every evidential clustering method provides metacluster centroids, so this limits applicability.
  • domain assumption The closed-world hypothesis holds and the empty set is not a focal set (outliers are rejected).
    Section 2.2 states: 'For the remainder of this work, we assume empty set not in F_M'. This excludes outlier mass, which is a substantial modeling restriction for imperfect real-world data.
  • domain assumption All attributes are finite; continuous attributes are discretized using binary threshold literals.
    Footnote 5 introduces finite attributes and threshold-based discretization as crucial for decision tree operations. This shapes the hypothesis space.
  • domain assumption A shallow decision tree with one leaf per metacluster is an adequate explanation structure.
    Section 3.2 says IEMM follows the IMM design principle. The paper does not validate this architectural restriction on evidential partitions.
  • domain assumption Decision-makers can specify a utility function reflecting their risk tolerance and understand the feature space.
    The conclusion states the target audience is informed stakeholders such as medical professionals. The usefulness of the utility parameter depends on this premise.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Explainable Evidential Clustering." pith.science (2026). https://pith.science/paper/KTDXZSO2

@misc{pith2026250712192,
  author       = {Pith},
  title        = {Pith review of: Explainable Evidential Clustering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KTDXZSO2}},
  note         = {Machine review of arXiv:2507.12192}
}
read the original abstract

Unsupervised classification is a fundamental machine learning problem. Real-world data often contain imperfections, characterized by uncertainty and imprecision, which are not well handled by traditional methods. Evidential clustering, based on Dempster-Shafer theory, addresses these challenges. This paper explores the underexplored problem of explaining evidential clustering results, which is crucial for high-stakes domains such as healthcare. Our analysis shows that, in the general case, representativity is a necessary and sufficient condition for decision trees to serve as abductive explainers. Building on the concept of representativity, we generalize this idea to accommodate partial labeling through utility functions. These functions enable the representation of "tolerable" mistakes, leading to the definition of evidential mistakeness as explanation cost and the construction of explainers tailored to evidential classifiers. Finally, we propose the Iterative Evidential Mistake Minimization (IEMM) algorithm, which provides interpretable and cautious decision tree explanations for evidential clustering functions. We validate the proposed algorithm on synthetic and real-world data. Taking into account the decision-maker's preferences, we were able to provide an explanation that was satisfactory up to 93% of the time.

Figures

Figures reproduced from arXiv: 2507.12192 by the authors.

Figure 1
Figure 1. A representation of different clustering functions over a synthetic [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Scheme of explainable clustering. It is then natural to use AccuracyC (∆) as the quality measure for how well the decision tree ∆ explains the original clustering C. A notable algorithm developed for this purpose is the Iterative Mistake Minimization (IMM) [29]. IMM is a decision tree fitting algorithm that leverages the original hard cluster centroid structure to construct an explainer where each leaf contains exac… view at source ↗
Figure 3
Figure 3. Scheme of Explainable Evidential Clustering. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Illustration of a categorical evidential classifier and space partition in X = R 2 . The partition ∆ separates x1 and x2 from their respective meta￾clusters, while correctly assigning all other observations. x x0 x1 x2 ∆(x) {ω1} {ω1, ω2} {ω2} CostMc,∆(x) 0 1 − U({ω1, ω…
Figure 5
Figure 5. Figure 5: Decision tree obtained with IEMM for the evidential clustering function Mfull and λ = 0. The decision trees generated by IEMM are shallow by construction, having at most |F| − 1 levels. Each non-terminal node indicates the mistakeness of the corresponding split. Then, …
Figure 6
Figure 6. Figure 6: The results of the IEMM on the synthetic dataset for the evidential [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 32 canonical work pages

  1. [1]

    https://doi.org/10.1016/j.ins.2024.120282

    Alvarez-Garcia, M., Ibar-Alonso, R., Arenas-Parra, M.: A comprehensive frame- workforexplainableclusteranalysis.InformationSciences 663,120282(Mar2024). https://doi.org/10.1016/j.ins.2024.120282

    work page arXiv 2024

  2. [2]

    In: Proceed- ings of the Thirty-First International Joint Conference on Artificial Intelligence

    Amgoud, L., Ben-Naim, J.: Axiomatic Foundations of Explainability. In: Proceed- ings of the Thirty-First International Joint Conference on Artificial Intelligence. pp. 636–642. International Joint Conferences on Artificial Intelligence Organiza- tion, Vienna, Austria (Jul 2022).https://doi.org/10.24963/ijcai.2022/90

    doi:10.24963/ijcai.2022/90 2022

  3. [3]

    https://doi.org/10.48550/ arXiv.2009.14193

    Angelopoulos, A., Bates, S., Malik, J., Jordan, M.I.: Uncertainty Sets for Image Classifiers using Conformal Prediction (Sep 2022). https://doi.org/10.48550/ arXiv.2009.14193

    arXiv doi:10.48550/arxiv.2009.14193 2022

  4. [4]

    Data & Knowledge Engineering 142, 102088 (Nov 2022).https://doi.org/10.1016/j.datak.2022.102088

    Audemard, G., Bellart, S., Bounia, L., Koriche, F., Lagniez, J.M., Marquis, P.: On the explanatory power of Boolean decision trees. Data & Knowledge Engineering 142, 102088 (Nov 2022).https://doi.org/10.1016/j.datak.2022.102088

    arXiv 2022

  5. [5]

    Baehrens, D., Schroeter, T., Harmeling, S., Kawanabe, M., Hansen, K., Müller, K.R.: How to Explain Individual Classification Decisions. J. Mach. Learn. Res.11, 1803–1831 (Aug 2010)

    work page 2010

  6. [6]

    Bandyapadhyay, S., Fomin, F.V., Golovach, P.A., Lochet, W., Purohit, N., Si- monov, K.: How to find a good explanation for clustering? Artificial Intelligence 322, 103948 (Sep 2023).https://doi.org/10.1016/j.artint.2023.103948

    arXiv 2023

  7. [7]

    Information Fusion58, 82–115 (Jun 2020)

    Barredo Arrieta, A., Díaz-Rodríguez, N., Del Ser, J., Bennetot, A., Tabik, S., Bar- bado, A., Garcia, S., Gil-Lopez, S., Molina, D., Benjamins, R., Chatila, R., Herrera, F.: Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion58, 82–115 (Jun 2020). https://doi.org/10.1016/j...

    doi:10.1016/j.inffus.2019.12.012 2020

  8. [8]

    Journal of Machine Learning Research (2001)

    Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support Vector Clustering. Journal of Machine Learning Research (2001)

    work page 2001

Show all 49 references
  1. [9]

    Advances in Neural Information Processing Systems 35, 29205–29216 (Dec 2022)

    Bengs,V.,Hüllermeier,E.,Waegeman,W.:PitfallsofEpistemicUncertaintyQuan- tification through Loss Minimisation. Advances in Neural Information Processing Systems 35, 29205–29216 (Dec 2022)

    2022

  2. [10]

    Electronics 8(8), 832 (Aug 2019)

    Carvalho, D.V., Pereira, E.M., Cardoso, J.S.: Machine Learning Interpretability: A Survey on Methods and Metrics. Electronics 8(8), 832 (Aug 2019). https: //doi.org/10.3390/electronics8080832

    2019 doi

  3. [11]

    In: Bouyssou, D., Dubois, D., Pirlot, M., Prade, H

    Dubois, D., Prade, H.: Représentations formelles de l’incertain et de l’imprécis. In: Bouyssou, D., Dubois, D., Pirlot, M., Prade, H. (eds.) Concepts et Méthodes Pour l’aide à La Décision : Outils de Modélisation, pp. 111–171. No. Chapitre 3 in Traité IC2, Série Informatique e...

    2006

  4. [12]

    Computational Intelligence4(3), 244–264 (1988)

    Dubois, D., Prade, H.: Representation and combination of uncertainty with be- lief functions and possibility measures. Computational Intelligence4(3), 244–264 (1988). https://doi.org/10.1111/j.1467-8640.1988.tb00279.x

    1988

  5. [13]

    Frontiers in Psychiatry15, 1165424 (Feb 2024).https://doi.org/10.3389/ fpsyt.2024.1165424

    Ellis, C.A., Miller, R.L., Calhoun, V.D.: Explainable fuzzy clustering framework reveals divergent default mode network connectivity dynamics in schizophre- nia. Frontiers in Psychiatry15, 1165424 (Feb 2024).https://doi.org/10.3389/ fpsyt.2024.1165424

    2024

  6. [14]

    https://doi.org/10.48550/arXiv.2105.08053

    Ellis, C.A., Sendi, M.S.E., Geenjaar, E.P.T., Plis, S.M., Miller, R.L., Calhoun, V.D.: Algorithm-Agnostic Explainability for Unsupervised Clustering (Aug 2021). https://doi.org/10.48550/arXiv.2105.08053

    2021 doi arXiv

  7. [15]

    Math- ematical Programming 79(1), 191–215 (Oct 1997)

    Hansen, P., Jaumard, B.: Cluster analysis and mathematical programming. Math- ematical Programming 79(1), 191–215 (Oct 1997). https://doi.org/10.1007/ BF02614317 16 Lopes de Souza et al

    1997

  8. [16]

    Applied Statistics 28(1), 100 (1979)

    Hartigan, J.A., Wong, M.A.: Algorithm AS 136: A K-Means Clustering Algorithm. Applied Statistics 28(1), 100 (1979). https://doi.org/10.2307/2346830

    1979 doi

  9. [17]

    Expert Systems with Applications230, 120652 (Nov 2023).https://doi.org/10

    Hoarau, A., Martin, A., Dubois, J.C., Le Gall, Y.: Evidential Random Forests. Expert Systems with Applications230, 120652 (Nov 2023).https://doi.org/10. 1016/j.eswa.2023.120652

    2023

  10. [18]

    In: FUZZ (Jan 2023)

    Hoarau, A., Thierry, C., Martin, A., Dubois, J.C., Gall, Y.L.: Datasets with Rich Labels for Machine Learning. In: FUZZ (Jan 2023)

    2023

  11. [19]

    In: Proceed- ings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence

    Hüllermeier, E., Destercke, S., Shaker, M.H.: Quantification of Credal Uncertainty in Machine Learning: A Critical Analysis and Empirical Comparison. In: Proceed- ings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence. pp. 548–557. PMLR (Aug 2022)

    2022

  12. [20]

    Proceedings of the AAAI Conference on Artificial In- telligence 33(01),1511–1519(Jul2019)

    Ignatiev, A., Narodytska, N., Marques-Silva, J.: Abduction-Based Explanations for Machine Learning Models. Proceedings of the AAAI Conference on Artificial In- telligence 33(01),1511–1519(Jul2019). https://doi.org/10.1609/aaai.v33i01. 33011511

    doi

  13. [21]

    International Journal of Approximate Reasoning142, 130–146 (Mar 2022).https://doi.org/10.1016/j.ijar.2021.11.009

    Imoussaten,A.,Jacquin,L.:Cautiousclassificationbasedonbelieffunctionstheory and imprecise relabelling. International Journal of Approximate Reasoning142, 130–146 (Mar 2022).https://doi.org/10.1016/j.ijar.2021.11.009

    2022 doi

  14. [22]

    Journal of Artificial Intelligence Research75, 261–321 (Sep 2022)

    Izza, Y., Ignatiev, A., Marques-Silva, J.: On Tackling Explanation Redundancy in Decision Trees. Journal of Artificial Intelligence Research75, 261–321 (Sep 2022). https://doi.org/10.1613/jair.1.13575

    2022 doi

  15. [23]

    Izza, Y., Ignatiev, A., Narodytska, N., Cooper, M.C., Marques-Silva, J.: Provably Precise, Succinct and Efficient Explanations for Decision Trees (May 2022).https: //doi.org/10.48550/arXiv.2205.09569

    2022 doi arXiv

  16. [24]

    IEEE Trans- actions on Fuzzy Systems1(2), 98–110 (May 1993).https://doi.org/10.1109/ 91.227387

    Krishnapuram, R., Keller, J.: A possibilistic approach to clustering. IEEE Trans- actions on Fuzzy Systems1(2), 98–110 (May 1993).https://doi.org/10.1109/ 91.227387

    1993

  17. [25]

    Journal of Intelligent Information Systems23(1), 5–16 (Jul 2004).https://doi

    Lingras, P., West, C.: Interval Set Clustering of Web Users with Rough K-Means. Journal of Intelligent Information Systems23(1), 5–16 (Jul 2004).https://doi. org/10.1023/B:JIIS.0000029668.88665.1a

    2004

  18. [26]

    Lundberg, S.M., Erion, G.G., Lee, S.I.: Consistent Individualized Feature Attri- bution for Tree Ensembles (Mar 2019).https://doi.org/10.48550/arXiv.1802. 03888

    2019 doi

  19. [27]

    In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, vol

    MacQueen, J.: Some methods for classification and analysis of multivariate ob- servations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, vol. 5.1, pp. 281–298. University of California Press (Jan 1967)

    1967

  20. [28]

    Pattern Recognition41(4), 1384–1397 (Apr 2008).https://doi.org/ 10.1016/j.patcog.2007.08.014

    Masson, M.H., Denœux, T.: ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition41(4), 1384–1397 (Apr 2008).https://doi.org/ 10.1016/j.patcog.2007.08.014

    2008 doi

  21. [29]

    In: Proceedings of the 37th International Conference on Machine Learning

    Moshkovitz, M., Dasgupta, S., Rashtchian, C., Frost, N.: Explainable k-Means and k-Medians Clustering. In: Proceedings of the 37th International Conference on Machine Learning. pp. 7055–7065. PMLR (Nov 2020)

    2020

  22. [30]

    In: Janota, M., Lynce, I

    Narodytska, N., Shrotri, A., Meel, K.S., Ignatiev, A., Marques-Silva, J.: Assessing Heuristic Machine Learning Explanations with Model Counting. In: Janota, M., Lynce, I. (eds.) Theory and Applications of Satisfiability Testing – SAT 2019. pp. 267–278. Springer International P...

    2019

  23. [31]

    In: Proceed- Explainable Evidential Clustering 17 ingsoftheTwenty-SeventhInternationalJointConferenceonArtificialIntelligence

    Nguyen, V.L., Destercke, S., Masson, M.H., Hüllermeier, E.: Reliable Multi-class Classification based on Pairwise Epistemic and Aleatoric Uncertainty. In: Proceed- Explainable Evidential Clustering 17 ingsoftheTwenty-SeventhInternationalJointConferenceonArtificialIntelligence....

    2018

  24. [32]

    IEEE Transactions on Fuzzy Systems 4(3), 238–250 (Aug 1996)

    Nozaki, K., Ishibuchi, H., Tanaka, H.: Adaptive fuzzy rule-based classification sys- tems. IEEE Transactions on Fuzzy Systems 4(3), 238–250 (Aug 1996). https: //doi.org/10.1109/91.531768

    1996 doi

  25. [33]

    Fuzzy Sets and Systems 138(2), 221–254 (Sep 2003).https://doi.org/10.1016/S0165-0114(03) 00089-7

    Olaru, C., Wehenkel, L.: A complete fuzzy decision tree technique. Fuzzy Sets and Systems 138(2), 221–254 (Sep 2003).https://doi.org/10.1016/S0165-0114(03) 00089-7

    2003 doi

  26. [34]

    International Journal of Computer & Information Sciences 11(5), 341–356 (Oct 1982).https://doi.org/10.1007/BF01001956

    Pawlak, Z.: Rough sets. International Journal of Computer & Information Sciences 11(5), 341–356 (Oct 1982).https://doi.org/10.1007/BF01001956

    1982 doi

  27. [35]

    International Journal of Man-Machine Studies 27(3), 221–234 (Sep 1987)

    Quinlan, J.R.: Simplifying decision trees. International Journal of Man-Machine Studies 27(3), 221–234 (Sep 1987). https://doi.org/10.1016/S0020-7373(87) 80053-6

    1987 doi

  28. [36]

    Why Should I Trust You?

    Ribeiro, M.T., Singh, S., Guestrin, C.: "Why Should I Trust You?": Explaining the Predictions of Any Classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 1135–

  29. [37]

    In: Maimon, O., Rokach, L

    Rokach, L., Maimon, O.: Decision Trees. In: Maimon, O., Rokach, L. (eds.) Data Mining and Knowledge Discovery Handbook, pp. 165–192. Springer-Verlag, New York (2005).https://doi.org/10.1007/0-387-25465-X_9

    2005 doi

  30. [38]

    Nature Machine Intelligence1(5), 206–215 (May 2019).https://doi.org/10.1038/s42256-019-0048-x

    Rudin, C.: Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence1(5), 206–215 (May 2019).https://doi.org/10.1038/s42256-019-0048-x

    2019 doi

  31. [39]

    Information and Control15(1), 22–32 (Jul 1969)

    Ruspini, E.H.: A new approach to clustering. Information and Control15(1), 22–32 (Jul 1969). https://doi.org/10.1016/S0019-9958(69)90591-9

    1969 doi

  32. [40]

    Princeton University Press (Apr 1976)

    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (Apr 1976)

    1976

  33. [41]

    (ed.): Non-Standard Logics for Automated Reasoning

    Smets, P. (ed.): Non-Standard Logics for Automated Reasoning. Academic Press, San Diego (1988)

    1988

  34. [42]

    https://doi.org/10.48550/arXiv.2502.06587

    Soubeiga, A., Antoine, V.: Evclust: Python library for evidential clustering (Feb 2025). https://doi.org/10.48550/arXiv.2502.06587

    2025 doi arXiv

  35. [43]

    1511.07361

    Su, G., Wei, D., Varshney, K.R., Malioutov, D.M.: Interpretable Two-level Boolean Rule Learning for Classification (Nov 2015).https://doi.org/10.48550/arXiv. 1511.07361

    2015 doi arXiv

  36. [44]

    In: Proceedings of the 32nd ACM International Conference on Information and Knowledge Management

    Tutay, S., Somech, A.: Cluster-Explorer: An interactive Framework for Explain- ing Black-Box Clustering Results. In: Proceedings of the 32nd ACM International Conference on Information and Knowledge Management. pp. 5106–5110. ACM, Birmingham United Kingdom (Oct 2023). https://...

    doi

  37. [45]

    Chapman & Hall (1991)

    Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman & Hall (1991)

    1991

  38. [46]

    IEEE Transactions on Neu- ral Networks 16(3), 645–678 (May 2005)

    Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Transactions on Neu- ral Networks 16(3), 645–678 (May 2005). https://doi.org/10.1109/TNN.2005. 845141

    2005 doi

  39. [47]

    Information and Control8(3), 338–353 (Jun 1965).https: //doi.org/10.1016/S0019-9958(65)90241-X

    Zadeh, L.A.: Fuzzy sets. Information and Control8(3), 338–353 (Jun 1965).https: //doi.org/10.1016/S0019-9958(65)90241-X

    1965 doi

  40. [48]

    Why is Γ (x) = ω?

    Zhang,Z.,Zhang,Y.,Tian,H.,Martin,A.,Liu,Z.,Ding,W.:Asurveyofevidential clustering: Definitions, methods, and applications. Information Fusion p. 102736 (Oct 2024). https://doi.org/10.1016/j.inffus.2024.102736 18 Lopes de Souza et al. A Appendix: On Simplification Explanation T...

    2024

  41. [1144]

    https://doi.org/10.1145/2939672.2939778

    KDD ’16, Association for Computing Machinery, New York, NY, USA (Aug 2016). https://doi.org/10.1145/2939672.2939778

    2016

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.