In a control system numeric data is fuzzied, processed by fuzzy logic, then defuzzied generating a specific quantified operation.

Interesting that it worked out when fuzzy is a binary true fakes you get regular Boolean logic. So I imagine youmight say fuzzy is a superset of Boolean]n logic.

From a book I read imagine a balance beam on a knife edge. Weighted fuzzy variables are distributed along the beam. A fuzzy control system balances the beam based on the fuzzy variables. Any number of combinations of states of the fuzzy variables can balance the mean. Contrasted to a Boolean logic or algebraic function that applies a rid formula for processing variables .

https://en.wikipedia.org/wiki/Fuzzy_logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.[1] By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.

The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi Zadeh.[2][3] Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.[4]

It is based on the observation that people make decisions based on imprecise and non-numerical information, fuzzy models or sets are mathematical means of representing vagueness and imprecise information, hence the term fuzzy. These models have the capability of recognising, representing, manipulating, interpreting, and utilising data and information that are vague and lack certainty.[5]

Fuzzy logic has been applied to many fields, from control theory to artificial intelligence.

Overview[edit]

Classical logic only permits conclusions which are either true or false. However, there are also propositions with variable answers, such as one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum.[citation needed]

Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance.[6]

Applying truth values[edit]

A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled.[7]

Linguistic variables[edit]

While variables in mathematics usually take numerical values, in fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts.[8]

A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young.

Fuzzification operations can map mathematical input values into fuzzy membership functions. And the opposite de-fuzzifying operations can be used to map a fuzzy output membership function into a "crisp" output value that can be then used for decision or control purposes.