HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems
Uncertainty quantification in cloud models requires simultaneous characterization of fuzziness (via Entropy, <i>En</i>) and randomness (via Hyper-entropy, <i>He</i>), yet existing similarity measures often neglect the stochastic dispersion governed by <i>He</i>. T...
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| author | Jiaozi Pu Zongxin Liu |
| author_facet | Jiaozi Pu Zongxin Liu |
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| description | Uncertainty quantification in cloud models requires simultaneous characterization of fuzziness (via Entropy, <i>En</i>) and randomness (via Hyper-entropy, <i>He</i>), yet existing similarity measures often neglect the stochastic dispersion governed by <i>He</i>. To address this gap, we propose HECM-Plus, an algorithm integrating Expectation (<i>Ex</i>), <i>En</i>, and <i>He</i> to holistically model geometric and probabilistic uncertainties in cloud models. By deriving <i>He</i>-adjusted standard deviations through reverse cloud transformations, HECM-Plus reformulates the Hellinger distance to resolve conflicts in multi-expert evaluations where subjective ambiguity and stochastic randomness coexist. Experimental validation demonstrates three key advances: (1) Fuzziness–Randomness discrimination: HECM-Plus achieves balanced conceptual differentiation (δ<i>C<sub>1</sub></i>/<i>C<sub>4</sub></i> = 1.76, δ<i>C<sub>2</sub></i> = 1.66, δ<i>C<sub>3</sub></i> = 1.58) with linear complexity outperforming PDCM and HCCM by 10.3% and 17.2% in differentiation scores while resolving <i>He</i>-induced biases in HECM/ECM (<i>C<sub>1</sub></i>–<i>C<sub>4</sub></i> similarity: 0.94 vs. 0.99) critical for stochastic dispersion modeling; (2) Robustness in time-series classification: It reduces the mean error by 6.8% (0.190 vs. 0.204, *<i>p</i>* < 0.05) with lower standard deviation (0.035 vs. 0.047) on UCI datasets, validating noise immunity; (3) Design evaluation application: By reclassifying controversial cases (e.g., reclassified from a “good” design (80.3/100 average) to “moderate” via cloud model using HECM-Plus), it resolves multi-expert disagreements in scoring systems. The main contribution of this work is the proposal of HECM-Plus, which resolves the limitation of HECM in neglecting <i>He</i>, thereby further enhancing the precision of normal cloud similarity measurements. The algorithm provides a practical tool for uncertainty-aware decision-making in multi-expert systems, particularly in multi-criteria design evaluation under conflicting standards. Future work will extend to dynamic expert weight adaptation and higher-order cloud interactions. |
| format | Article |
| id | doaj-art-d52930cb15a34de1becb9f7d25aa5328 |
| institution | OA Journals |
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| language | English |
| publishDate | 2025-04-01 |
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| spelling | doaj-art-d52930cb15a34de1becb9f7d25aa53282025-08-20T02:33:54ZengMDPI AGEntropy1099-43002025-04-0127547510.3390/e27050475HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision SystemsJiaozi Pu0Zongxin Liu1School of Culture and Art, Chengdu University of Information Technology, Chengdu 610103, ChinaWest China School of Medicine, Sichuan University, Chengdu 610041, ChinaUncertainty quantification in cloud models requires simultaneous characterization of fuzziness (via Entropy, <i>En</i>) and randomness (via Hyper-entropy, <i>He</i>), yet existing similarity measures often neglect the stochastic dispersion governed by <i>He</i>. To address this gap, we propose HECM-Plus, an algorithm integrating Expectation (<i>Ex</i>), <i>En</i>, and <i>He</i> to holistically model geometric and probabilistic uncertainties in cloud models. By deriving <i>He</i>-adjusted standard deviations through reverse cloud transformations, HECM-Plus reformulates the Hellinger distance to resolve conflicts in multi-expert evaluations where subjective ambiguity and stochastic randomness coexist. Experimental validation demonstrates three key advances: (1) Fuzziness–Randomness discrimination: HECM-Plus achieves balanced conceptual differentiation (δ<i>C<sub>1</sub></i>/<i>C<sub>4</sub></i> = 1.76, δ<i>C<sub>2</sub></i> = 1.66, δ<i>C<sub>3</sub></i> = 1.58) with linear complexity outperforming PDCM and HCCM by 10.3% and 17.2% in differentiation scores while resolving <i>He</i>-induced biases in HECM/ECM (<i>C<sub>1</sub></i>–<i>C<sub>4</sub></i> similarity: 0.94 vs. 0.99) critical for stochastic dispersion modeling; (2) Robustness in time-series classification: It reduces the mean error by 6.8% (0.190 vs. 0.204, *<i>p</i>* < 0.05) with lower standard deviation (0.035 vs. 0.047) on UCI datasets, validating noise immunity; (3) Design evaluation application: By reclassifying controversial cases (e.g., reclassified from a “good” design (80.3/100 average) to “moderate” via cloud model using HECM-Plus), it resolves multi-expert disagreements in scoring systems. The main contribution of this work is the proposal of HECM-Plus, which resolves the limitation of HECM in neglecting <i>He</i>, thereby further enhancing the precision of normal cloud similarity measurements. The algorithm provides a practical tool for uncertainty-aware decision-making in multi-expert systems, particularly in multi-criteria design evaluation under conflicting standards. Future work will extend to dynamic expert weight adaptation and higher-order cloud interactions.https://www.mdpi.com/1099-4300/27/5/475entropy (<i>En</i>)hyper-entropy (<i>He</i>)cloud modelHellinger distanceuncertainty quantificationmulti-expert conflict resolution |
| spellingShingle | Jiaozi Pu Zongxin Liu HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems Entropy entropy (<i>En</i>) hyper-entropy (<i>He</i>) cloud model Hellinger distance uncertainty quantification multi-expert conflict resolution |
| title | HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems |
| title_full | HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems |
| title_fullStr | HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems |
| title_full_unstemmed | HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems |
| title_short | HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems |
| title_sort | hecm plus hyper entropy enhanced cloud models for uncertainty aware design evaluation in multi expert decision systems |
| topic | entropy (<i>En</i>) hyper-entropy (<i>He</i>) cloud model Hellinger distance uncertainty quantification multi-expert conflict resolution |
| url | https://www.mdpi.com/1099-4300/27/5/475 |
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