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>. 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>C₁</i>/<i>C₄</i> = 1.76, δ<i>C₂</i> = 1.66, δ<i>C₃</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>C₁</i>-<i>C₄</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.