Abstract The concept of emergence has great importance in physical phenomena as it highlights how local rules can generate global behavior and reveal optimal choices hidden within isolated data sets. Emergent integration of heterogeneous information sources remains a fundamental challenge in computational systems, particularly when uncertainty, hierarchy, and partial ordering must be preserved simultaneously. Whereas fuzzy soft set theory offers a convenient structure on which to model uncertainty, the current methods do not have an organized mechanism to combine multiple partially ordered fuzzy soft domains, with consistency in order and hierarchical readability. This limitation restricts the development of scalable and transparent multi-domain decision systems. This paper proposes an emergence model of partially ordered fuzzy soft sets using geometry. The framework is a systematic analysis of symmetric geometries, non-symmetric but identical-layered geometries, and non-identical layered structures. A formally defined layer-contraction process with blended nodes is presented to build balanced representations with component-wise order relations and fuzzy membership semantics, in the case of heterogeneous configurations. The process of emergence is characterized on the basis of layer-wise aggregation and order-preserving fusion. The proposed model is applied to descriptor-centric message filtration by integrating three ordered fuzzy soft domains, which are extracted features, threat indicators, and signal descriptors. Empirical validation on SMS Spam Collection data demonstrates that the hybrid emergence model achieves competitive predictive accuracy with respect to baseline models (Rule-Based Filtering, Logistic Regression, Support Vector Machine, Random Forest, Neural Network, Fuzzy Soft Emergence) while retaining structural interpretability. The proposed model achieved the highest accuracy (0. 933), the strongest ROC-AUC (0. 958), an F₁ score of 0. 777, and a substantially reduced False Positive Rate (FPR = 0. 059) compared to baseline models. This contribution presents a mathematically consistent and computationally feasible framework for structured multi-domain integration into fuzzy, soft-based intelligent systems.
Wasim et al. (Sat,) studied this question.