<![CDATA[Agricultural productivity can be constrained by fertilizer management that does not account for spatial variability in soil nutrient conditions. This study develops a hybrid Gaussian Mixture Model (GMM)–Fuzzy Sugeno framework to transform probabilistic soil phosphorus (P) and potassium (K) patterns into spatially differentiated point-level fertilizer prescriptions within a Geographic Information System (GIS). Thirty sampling locations were evaluated in each paddy and maize cultivation field in Bangkalan Regency. Soil P and K were measured directly using a portable NPK sensor, whereas nitrogen (N) requirements were determined independently from crop-specific target-yield criteria and cultivation-area measurements. GMM parameters were estimated using the Expectation-Maximization (EM) algorithm, and candidate mixture orders were assessed using maximized log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and silhouette coefficients. The EM algorithm converged at iteration 42 for paddy and iteration 9 for maize. Both AIC and BIC selected a three-component model for paddy and maize, although the resulting component separation differed between crops, with silhouette coefficients of 0.16199 and 0.43309, respectively. The selected components were subsequently characterized by their P–K profiles, and posterior responsibilities were used as normalized firing strengths in the Fuzzy Sugeno inference layer. The hybrid framework generated spatially referenced, differentiated point-level prescriptions, with mean SP-36 and KCl rates of 72.334 and 68.432 kg/ha for paddy and 87.485 and 76.637 kg/ha for maize, respectively. The corresponding coefficients of variation were 26.45% and 30.13% for paddy and 16.34% and 33.07% for maize. In contrast, the conventional Fuzzy Sugeno formulation produced uniform SP-36 and KCl rates of 100 kg/ha across the investigated points. The results demonstrate that GMM posterior responsibilities can be propagated into the Sugeno inference layer to retain probabilistic component association and generate spatially differentiated fertilizer prescriptions. However, the study evaluates computational behaviour, probabilistic assignment, and prescription differentiation rather than agronomic effectiveness; the analysis is limited to two fields, one growing season, and 30 sampling locations per crop, without independent validation of yield response, nutrient uptake, fertilizer efficiency, or dose safety. Further multi-season and field-scale agronomic validation is therefore required before the generated prescriptions can be interpreted as validated fertilizer recommendations.]]>
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