From a model to an explained result

The library supplies explicit building blocks. Start with the physical meaning, units and allowed universe, then choose membership models and the operation that answers your question. It does not invent rules, calibrate thresholds or choose a numerical backend automatically.

Two routes through the modern API

flowchart TD
    U["Universe, units and model parameters"] --> M["Membership functions or a typed callback"]
    M --> F["ScalarFuzzySet"]
    F --> T["Named LinguisticTerm objects"]
    T --> S["LinguisticScale.Fuzzify with a selection policy"]
    S --> R["All grades, selected labels or abstention"]
    F --> C["Complement, Intersection, Union or Difference"]
    C --> D["Finite IntegrationDomain and CentroidPolicy"]
    D --> V["Centroid coordinate or an explicit numerical error"]

The temperature example follows the classification branch: one physical measurement is evaluated against every named term. The centroid example follows the composition branch: sets share a universe and produce one representative coordinate over a stated finite window. These are different questions, even if both begin with the same model.

Combine separate sensor measurements at the grade level

flowchart TD
    A["Temperature measurement in °C"] --> B["Temperature membership grade"]
    C["Vibration measurement in mm/s"] --> D["Vibration membership grade"]
    B --> E["Chosen TNormPolicy or SNormPolicy"]
    D --> E
    E --> F["Combined grade with the policy recorded"]

This is the sensor scenario. Distinct physical quantities retain their own universes. Evaluate them first, then combine their grades with an explicit scalar policy. A set-level intersection instead evaluates sets at the same coordinate on one shared universe. See operator comparisons.

The historical boundary

flowchart TD
    A["Existing 1.x consumer"] --> B["fuzzyroutines.FuzzyRoutines facade"]
    B --> C["Mutable MFunction, FuzzySet and scale adapters"]
    D["New consumer"] --> E["Immutable modern models and explicit policies"]
    C --> F["Reviewed scalar mathematics and centroid engine"]
    E --> F

The facade preserves reviewed names and call conventions. It retains a mutable object model, later-wins ties and historical naming such as supportSet for an integration window. Modern objects make universes, selection, comparison and integration policies explicit. Read historical recipes before replacing an existing call; identical mathematical intent does not guarantee identical parameter order or tie behavior.

The diagrams describe current scalar API paths. The optional NumPy prototype is an experimental workload comparison, not an automatically selected runtime. Use result records to preserve provenance and error handling to keep invalid input distinct from unresolved mathematics.