Comparison of WSM and Weight Product Methods with WSM-Score and Vector Approaches

Abstract

Fertilizers are essential in modern agriculture as they supply vital nutrients to plants, enhancing growth and yield. However, selecting the most appropriate fertilizer involves multiple criteria and a diverse range of available options. This study conducts a comparative analysis of two Multi-Criteria Decision-Making (MCDM) methods: the Weighted Sum Model (WSM) and the Weight Product (WP) method, supplemented by WSM-Score and vector-based approaches. The evaluation is based on four criteria price, quality, ease of availability, and fertilizer form across seven alternatives: Urea, Compost, TSP, KCL, Gandasil, NPK, and ZA. Using normalized weights from expert judgment, both methods were used to rank the alternatives. A key contribution of this study is the integration of WSM-Score and vector approaches, which enhance traditional MCDM by improving score comparability (WSM-Score) and enabling geometric interpretation of alternative positioning (vector). Results show that Compost (A2) ranks highest across all methods, indicating convergence despite differences in computational logic. WSM offers ease of interpretation, while WP better accounts for proportional differences but is more sensitive to low-performing criteria. The findings suggest that method selection should be context-dependent. Although the ranking results are consistent, the absence of empirical validation through expert comparison or field data limits the generalizability of the conclusions. Further research should include such validation to strengthen the reliability of MCDM-based decision support systems in agricultural applications.

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