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              <text>Purpose – This study examines the suitability of hard versus soft clustering approaches for customer segmentation across distinct business model types. Specifically, it evaluates whether homogeneous marketing treatment implied by K-means is justified in subscription and singular transaction contexts, and whether Fuzzy C-means (FCM) offers a more appropriate representation of behavioural overlap.  Methodology – Using the RFM (Recency–Frequency–Monetary) framework, the study applies both K-means and FCM to two datasets: the Online Retail dataset (transaction model) and the Customer Churn dataset (subscription model). RFM metrics were adapted for subscription contexts to reflect product interactions rather than discrete purchases. Clustering performance was assessed through the silhouette score (K-means) and fuzzy partition coefficient (FCM), following a consistent CRISP-DM process for data preparation, modelling, and evaluation.  Findings – Results indicate a reversal of theoretical expectations. The subscription dataset exhibited considerable behavioural overlap, with weak cluster separation, challenging the assumption of homogeneous treatment. Conversely, the transaction dataset displayed moderately strong partitions, suggesting that standardisation of product attributes may reduce behavioural heterogeneity. These findings highlight that clustering suitability depends not only on business model type but also on contextual factors such as product standardisation and tier design.  Originality – This study is the first to align the selection of hard versus soft clustering methods with business model typologies and to adapt RFM metrics for subscription contexts. By integrating FCM as a diagnostic tool for testing the validity of homogeneous treatment assumptions, it addresses a critical gap in behavioural segmentation research and provides a practical decision framework for guiding clustering choice.</text>
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                <text>Hard vs. Soft Clustering for RFM Segmentation: A Joint Evaluation of Method Suitability Across Singular Transaction and Subscription  Business Models </text>
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              <text>For portfolio managers seeking implementable portfolio optimization approaches, it is essential to evaluate the models and select the one that delivers the highest after-cost and risk-adjusted performance. This study compares traditional portfolio optimization models (Mean-Variance Optimization and the Black-Litterman model) with machine learning approaches (Random Forest and XGBoost) using the same dataset. The 30 S&amp;P 500 stocks are randomly selected, and their price data from 2015 to 2024, obtained at a monthly frequency from Yahoo Finance, are split into a training window (2015-2021), a validating window (2022), and a testing window (2023-2024). All investment strategies are long-only, fully invested, and rebalanced monthly. An equally weighted portfolio consisting of all 30 selected stocks, applying a buy-and-hold strategy, serves as the benchmark model. The model comparison involves evaluating risk-adjusted portfolio performance and predictive accuracy. The empirical test results from the testing period show that machine learning models, particularly Random Forest, can add significant value to portfolios and achieve good predictive accuracy, but they are cost-sensitive and unstable. In contrast, traditional models perform relatively poorly but are stable under different cost settings.</text>
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