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If you're in need of professional JavaScript help, shoot me an email at hello kiro. Zero dependencies. By Kiro Risk. Include score Whether the score should be included in the result set. A score of 0 indicates a perfect match, while a score of 1 indicates a complete mismatch. Include matches Whether the matches should be included in the result set. When true , each record in the result set will include the indices of the matched characters: indices: [start, end]. These can consequently be used for highlighting purposes.

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Minimum character length When set to include matches, only the matches whose length exceeds this value will be returned. For instance, if you want to ignore single character index returns, set to 2. Sort Whether to sort the result list, by score. Tokenize When true , the algorithm will search individual words and the full string, computing the final score as a function of both.

In this case, the threshold , distance , and location are inconsequential for individual tokens, and are thus ignored. Match all tokens When true , the result set will only include records that match all tokens. Will only work if tokenize is also true. Find All Matches When true , the matching function will continue to the end of a search pattern even if a perfect match has already been located in the string.

ID The name of the identifier property. 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. 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. In this image, the meanings of the expressions cold , warm , and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions.

The vertical line in the image represents a particular temperature that the three arrows truth values gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot". The orange arrow pointing at 0. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 which can have a length of 0 or greater and a slope where the value is decreasing.

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Fuzzy logic works with membership values in a way that mimics Boolean logic. There are several ways to this. A common replacement is called the Zadeh operators :.

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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. However, an arbitrary choice table does not always define a fuzzy logic function.

In the paper, [10] a criterion has been formulated to 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.

Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable.

The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. 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. Many of the early successful applications of fuzzy logic were implemented in Japan. The first notable application was on the subway train in Sendai , in which fuzzy logic was able to improve the economy, comfort, and precision of the ride.

Fuzzy logic

In mathematical logic , there are several formal systems of "fuzzy logic", most of which are in the family of t-norm fuzzy logics. 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. 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 machine , Markov normal fuzzy algorithm and fuzzy program see Santos Successively, L. Biacino and G. Gerla argued that the proposed definitions are rather questionable.

For example, in [13] 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.

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Then, they proposed the following definitions. 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.

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Moreover, any axiomatizable and complete theory is decidable. It is an open question to give supports for a "Church thesis" for fuzzy mathematics , the 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. Once fuzzy relations are defined, it is possible to develop fuzzy relational databases. Medina, M. Vila et al. Fuzzy querying languages have been defined, such as the SQLf by P. Bosc et al. Galindo et al. 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.

Fuzzy logic and probability address different forms of uncertainty. While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, fuzzy set theory uses the concept of fuzzy set membership, i. The concept of fuzzy sets was developed in the mid-twentieth century at Berkeley [14] as a response to the lacking of probability theory for jointly modelling uncertainty and vagueness. Bart Kosko claims in Fuzziness vs.

Probability [16] that probability theory is a subtheory of fuzzy logic, as questions of degrees of belief in mutually-exclusive set membership in probability theory can be represented as certain cases of non-mutually-exclusive graded membership in fuzzy theory.

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In that context, he also derives Bayes' theorem from the concept of fuzzy subsethood. Lotfi A.

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fuzzy definition: 1. (of an image) having shapes that do not have clear edges, or ( of a sound, especially from a television, radio, etc.) not clear, usually because of. fuzzy (comparative fuzzier, superlative fuzziest) My recollection of that event is fuzzy. Not clear; unfocused. I finally threw out a large stack of fuzzy photos.

Zadeh argues that fuzzy logic is different in character from probability, and is not a replacement for it. He fuzzified probability to fuzzy probability and also generalized it to possibility theory. More generally, fuzzy logic is one of many different extensions to classical logic intended to deal with issues of uncertainty outside of the scope of classical logic, the inapplicability of probability theory in many domains, and the paradoxes of Dempster-Shafer theory.

Computational theorist Leslie Valiant uses the term ecorithms to describe how many less exact systems and techniques like fuzzy logic and "less robust" logic can be applied to learning algorithms. Valiant essentially redefines machine learning as evolutionary. In general use, ecorithms are algorithms that learn from their more complex environments hence eco- to generalize, approximate and simplify solution logic.

Like fuzzy logic, they are methods used to overcome continuous variables or systems too complex to completely enumerate or understand discretely or exactly. Compensatory fuzzy logic CFL is a branch of fuzzy logic with modified rules for conjunction and disjunction. When the truth value of one component of a conjunction or disjunction is increased or decreased, the other component is decreased or increased to compensate. This increase or decrease in truth value may be offset by the increase or decrease in another component. An offset may be blocked when certain thresholds are met.