Crisp segmentation assigns each customer to a single cluster with clear boundaries; fuzzy segmentation, through degrees of membership, allows for natural overlaps, which are essential when a customer has characteristics of multiple segments.<\/p>\n<\/figure>\n
In Italy, with its high density of heterogeneous data (demographic data that is not always up to date, social interactions that are often unstructured), the ability to model behavioural ambiguity becomes a decisive competitive advantage. Fuzzy logic allows fuzzy variables such as \u201cModerate but recent engagement\u201d or \u201cGrowing loyalty\u201d to be integrated, calibrated to real market profiles, overcoming rigid dichotomies.<\/p>\n
Detailed methodology: building an FCM model for customer segmentation<\/h3>\n
The construction of a fuzzy segmentation model in Italy requires a careful preprocessing phase and the definition of membership functions calibrated to the local context.<\/p>\n
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- Phase 1: Collection and management of partial data<\/strong>
\n Italian customer data is often fragmented: spending data is missing in some profiles, age may be approximate, and digital interactions are not always traceable.
\n \u2013 Fuzzy imputation based on profile similarity (fuzzy similarity index) is used to estimate missing values without distortion: for example, if a customer has undeclared income, similarity with similar clusters is calculated to infer a plausible value.
\n \u2013 Multivariate normalisation: fuzzy scaling techniques (e.g. fuzzy z-score) are applied to harmonise variables with different scales \u2013 age (0\u2013100), annual expenditure (10\u201310,000), engagement (0\u2013100). <\/p>\n- Phase 2: Definition and calibration of membership functions<\/strong>
\n Fuzzy functions must reflect Italian cultural and behavioural thresholds.
\n \u2013 For *Engagement*, triangular functions with a peak at 65 points are used, with a gradual transition from low (0\u201330) to medium (30\u201370) and high (>70), consistent with typical behaviours of active customers in the Italian market.
\n \u2013 For *Loyalty*, Gaussian curves are used, with a mean of around 45 and a standard deviation of 15, to capture the concentration of loyal customers in medium-to-high spending brackets.
\n \u2013 *Spending Level* is modelled using trapezoidal functions, with a low threshold of 0\u20132,000, an average of 2,000\u20138,000, and a high threshold (>8,000), in line with actual data aggregated from 50,000 AgID customers.<\/li>\n- Stage 3: Implementation of the FCM model with parametric optimisation<\/strong>
\n The Fuzzy C-Means (FCM) algorithm is used with Python libraries (scikit-fuzzy) or local software such as MATLAB with fuzzy toolboxes.
\n \u2013 Key parameter: degree of fuzzification *m* (typically 2.0\u20132.5 in Italy to balance granularity and interpretability).
\n \u2013 The number of clusters *c* is determined by analysing the fuzzy gap or entropy, verifying stability with fuzzy cross-validation on 70% of the data.
\n \u2013 Iterations until convergence: monitoring of target cost variation (fuzzy validity index) to avoid overfitting on fragmented data.<\/li>\n- Stage 4: Analysis and interpretation of clusters<\/strong>
\n Each customer receives a membership degree vector (\u03bc) between 0 and 1 for each cluster. Example output: <\/p>\n\n Customer X: \u03bc\u2081=0.72 (Cluster \u201cOccasional with Low Engagement\u201d), \u03bc\u2082=0.21 (Cluster \u201cPotential Loyal Customers\u201d), \u03bc\u2083=0.07 (Cluster \u201cPremium on the Way\u201d) \n <\/pre>\n
Cluster 1: \u201cOccasional with Low Engagement\u201d \u2013 data: low-to-medium income, fragmented spending, high propensity for coupons, low social interaction.
\n Cluster 2: \u201cLoyal Potential\u201d \u2013 age 28\u201335, average spending, strong digital engagement, low current loyalty but high purchase intent.
\n Cluster 3: \u201cPremium in Uscio\u201d \u2013 high income, high spending, personalised engagement, low price sensitivity. <\/p>\nPractical steps for integration into Italian CRM systems<\/h3>\n
- Phase 2: Definition and calibration of membership functions<\/strong>