PROBABILISTIC CLUSTERING: CPP-TRI WITH DENDROGRAMS TO SUPPORT DEFENSE PLANNING

This research proposes a hybrid multicriteria decision-support approach that integrates the Probabilistic Composition of Preferences for sorting (CPP-TRI) with agglomerative hierarchical clustering. The objective is to expand the analytical capacity of Defense and security planning through two complementary perspectives on alternatives: vertical classification by priority or severity levels and horizontal refinement based on structural similarity. The proposal addresses a limitation of ordinal classifications which, although they rank alternatives under uncertainty, may generate internally heterogeneous and operationally limited classes. In the first stage, performance evaluations are transformed into random variables using Beta-PERT distributions, incorporating minimum, mode, maximum, and shape values. CPP-TRI compares the distributions of alternatives with reference profiles and assigns them to ordered classes according to joint probabilities of exceeding or failing to exceed those profiles. In the second stage, Euclidean distance and Ward’s method are applied to form highly cohesive groups; dendrograms allow the exploration of different cut points and levels of granularity, while the Dunn index validates group separation and compactness. The entire modeling process was implemented in R, supporting the reproducibility of the procedure. The method’s effectiveness was examined through two case studies. In Civil Defense, S2iD data from 2023-2024 were analyzed for 62 municipalities in Amazonas State, normalized according to human damage, material damage, and economic losses. CPP-TRI classified the municipalities into high-, medium-, and low-severity categories, while latitude and longitude clustering identified spatially proximate subgroups within each class. In the maritime security case, indicators from the Maritime Security Index and the Maritime Power of Nations enabled the classification and grouping of countries according to capabilities, vulnerabilities, and security levels, placing Brazil within strategic affinity blocs and revealing recurring affinities across both applications. The results show that combining probabilistic classification and clustering reduces class heterogeneity and transforms multidimensional data into operational intelligence. In Amazonas, the model supports functional regionalization, the pre-positioning of supplies, team specialization, and response planning beyond administrative boundaries. In the maritime domain, it supports the identification of cooperation partners, the harmonization of protocols, and the formulation of defense policies. The approach provides a transparent and replicable tool to guide resource allocation under uncertainty while preserving decision-makers’ judgment in choosing the level of aggregation. As limitations, the quality of the modeling depends on Beta-PERT estimates, and the choice of the dendrogram cut point retains a discretionary component. Future studies may incorporate time series and automatically optimize this cut point.