Certain computational methods for dealing with concepts that are not inherently imprecise are known as fuzzy logics. They were originally developed by the American computer scientist Lofti Zadeh. Fuzzy logics are widely discussed and used by computer scientists.
There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. In the paper,  a criterion has been formulated Fuzzy logic recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum.
A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area to the right of the function value in the inequality, including the function value.
Defuzzification The goal is to get a continuous variable from fuzzy truth values. Since, however, all output truth values are computed independently, Fuzzy logic most cases they do not represent such a set of numbers.
A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. Forming a consensus of inputs and fuzzy rules[ edit ] Since the fuzzy system output is a consensus of all of the inputs and all of the rules, fuzzy logic systems can be well behaved when input values are not available or are not trustworthy.
Weightings can be optionally added to each rule in the rulebase and weightings can be used to regulate the degree to which a rule affects the output values.
These rule weightings can be based upon the priority, reliability or consistency of each rule. These rule weightings may be static or can be changed dynamically, even based upon the output from other rules.
Early applications[ edit ] Many of the early successful applications of fuzzy logic were implemented in Japan. The first notable application was on the subway train in Sendaiin which fuzzy logic was able to improve the economy, comfort, and precision of the ride.
Propositional fuzzy logics[ edit ] The most important propositional fuzzy logics are: Monoidal t-norm-based propositional fuzzy logic MTL is an axiomatization of logic where conjunction is defined by a left continuous t-norm and implication is defined as the residuum of the t-norm.
Its models correspond to MTL-algebras that are pre-linear commutative bounded integral residuated lattices. Basic propositional fuzzy logic BL is an extension of MTL logic where conjunction is defined by a continuous t-norm, and implication is also defined as the residuum of the t-norm.
Its models correspond to BL-algebras. It has the axioms of basic fuzzy logic plus an axiom of double negation, and its models correspond to MV-algebras. It has the axioms of BL plus an axiom of idempotence of conjunction, and its models are called G-algebras.
Product fuzzy logic is the extension of basic fuzzy logic BL where conjunction is product t-norm. It has the axioms of BL plus another axiom for cancellativity of conjunction, and its models are called product algebras. This means that each formula has an evaluation.
Predicate fuzzy logics[ edit ] These extend the above-mentioned fuzzy logics by adding universal and existential quantifiers in a manner similar to the way that predicate logic is created from propositional logic. The semantics of the universal resp.
Decidability issues for fuzzy logic[ edit ] The notions of a "decidable subset" and " recursively enumerable subset" are basic ones for classical mathematics and classical logic. Thus the question of a suitable extension of them to fuzzy set theory is a crucial one.
A first proposal in such a direction was made by E. Santos by the notions of fuzzy Turing machineMarkov normal fuzzy algorithm and fuzzy program see Santos Gerla argued that the proposed definitions are rather questionable.
For example, in  one shows that the fuzzy Turing machines are not adequate for fuzzy language theory since there are natural fuzzy languages intuitively computable that cannot be recognized by a fuzzy Turing Machine.
Then, they proposed the following definitions. Then a fuzzy subset s: We say that s is decidable if both s and its complement —s are recursively enumerable. An extension of such a theory to the general case of the L-subsets is possible see Gerla The proposed definitions are well related with fuzzy logic.
Indeed, the following theorem holds true provided that the deduction apparatus of the considered fuzzy logic satisfies some obvious effectiveness property. Any "axiomatizable" fuzzy theory is recursively enumerable. In particular, the fuzzy set of logically true formulas is recursively enumerable in spite of the fact that the crisp set of valid formulas is not recursively enumerable, in general.
Moreover, any axiomatizable and complete theory is decidable. It is an open question to give supports for a "Church thesis" for fuzzy mathematicsthe proposed notion of recursive enumerability for fuzzy subsets is the adequate one.
In order to solve this, an extension of the notions of fuzzy grammar and fuzzy Turing machine are necessary. Fuzzy databases[ edit ] Once fuzzy relations are defined, it is possible to develop fuzzy relational databases.
Fuzzy querying languages have been defined, such as the SQLf by P.
These languages define some structures in order to include fuzzy aspects in the SQL statements, like fuzzy conditions, fuzzy comparators, fuzzy constants, fuzzy constraints, fuzzy thresholds, linguistic labels etc.Who are we?
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Stream ad-free or purchase CD's and MP3s now on alphabetnyc.com(17). Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based.
[Editor's Note: The following new entry by Petr Cintula, Christian G.
Fermüller, and Carles Noguera replaces the former entry on this topic by the previous author.] Fuzzy logic is intended to model logical reasoning with vague or imprecise statements like “Petr is young (rich, tall, hungry, etc.
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 .
Product Features Unfortunately, Fuzzy Logic does not come with a small stick to beat.