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Fuzzy set

As explained in Inside AI

A fuzzy set is a set in which elements have graded rather than strictly binary membership.

A fuzzy set represents membership by degree rather than by a strict yes-or-no decision. It helps describe boundaries that are gradual, uncertain, or imprecise. section 2.4

For example, height does not divide people naturally into only tall or short groups. A person may belong to both fuzzy sets to different degrees, unlike a classical threshold that assigns binary values. section 2.4

Classifying height

Using 6 feet 2 inches as the threshold, Joe at 6 feet 3 inches is tall and not short, while Gary and Sue at 6 feet 1 inch are classified as not tall and short. The result exposes the rigidity of binary categories near the boundary. section 2.4

How Inside AI covers it

How deep it goes
Defines partial membership and contrasts it with binary thresholds, but does not develop membership-function calculations.
Examples
Uses tall-versus-short height classifications, including Joe, Gary, Sandy, and Sue, to expose threshold limitations.
What you can do after
Evaluate how binary thresholds misrepresent gradual categories and identify where graded membership is more appropriate.
How it connects
Connects fuzzy logic with classical logic, uncertainty, imprecision, decision-making, and control systems.
Cover of Inside AI
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Inside AI. The section links point to the parts of the book it draws on.