fuzzy set

mathematics

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July 16, 2026

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A fuzzy set is a mathematical concept where an object can be a member of a set, not a member, or any degree of partial membership in between. This contrasts with traditional sets, where membership is absolute. Fuzzy logic, built upon fuzzy sets, allows statements to have degrees of truth, ranging from 0 (completely false) to 1 (completely true).123

This approach is useful for concepts that are not precisely defined, such as "high temperature" or "old person," by assigning a membership value between 0 and 1. Fuzzy logic is applied in various fields, including control systems for consumer electronics, linguistics, and medical diagnosis, enabling systems to make approximate reasoning and fine adjustments based on practical knowledge.2

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fuzzy logic
Fuzzy sets
Most concepts used in everyday language, such as “high temperature,” “round face,” or “aquatic animal,” are not clearly defined. In 1965 Lotfi Zadeh, an engineering professor at the University of California at Berkeley, proposed a mathematical definition of those classes that lack precisely…
Read More
Most concepts used in everyday language, such as “high temperature,” “round face,” or “aquatic animal,” are not clearly defined. In 1965 Lotfi Zadeh, an engineering professor at the University of California at Berkeley, proposed a mathematical definition of those classes that lack precisely…
Read More