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Łukasiewicz fuzzy logic is the extension of basic fuzzy logic BL where standard conjunction is the Łukasiewicz t-norm. It has the axioms of basic fuzzy logic plus an axiom of double negation, and its models correspond to MV-algebras. Gödel fuzzy logic is the extension of basic fuzzy logic BL where conjunction is the Gödel t-norm (that is ...
The basic idea of fuzzy logic is that a real number is assigned to each statement written in a language, within a range from 0 to 1, where 1 means that the statement is completely true, and 0 means that the statement is completely false, while values less than 1 but greater than 0 represent that the statement is "partly true", to a given ...
Fuzzy-trace theory (FTT) is a theory of cognition originally proposed by Valerie F. Reyna and Charles Brainerd [1] to explain cognitive phenomena, particularly in memory and reasoning. FTT posits two types of memory processes (verbatim and gist) and, therefore, it is often referred to as a dual process theory of memory.
Basic fuzzy logic BL is the logic of (the class of) all continuous t-norms It turns out that many logics of particular t-norms and classes of t-norms are axiomatizable. The completeness theorem of the axiomatic system with respect to the corresponding t-norm semantics on [0, 1] is then called the standard completeness of the logic.
A fuzzy control system is a control system based on fuzzy logic –a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively).
The concept of a linguistic variable in fuzzy logic connects a symbol that is typically a predicate in classical logic (e.g., "John is Bold", or in predicate logic – Bold(John)) – to linguistic values (e.g., "John is somewhat bold." or in fuzzy logic – Bold(John)=Somewhat ) – which generalizes the binary value of predicate logic in two ...
Fuzzy logic is an aspect of computing that handles approximate reasoning. Typically, binary logic allows computers to make decisions on true or false reasons (0s and 1s); however, introducing fuzzy logic allows systems to handle the unknowns between 0 and 1.
In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics , or logics of residuated lattices ; [ 1 ] it extends the logic MTL of all left-continuous t-norms.