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Fuzzy data approximation. fuzzy logic begins with

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Fuzzylogic systems are generally used for system identification, control, and modelrecognition problems. To maximize performance, it is often necessary to performa project optimization procedure in which the variable parameters of the Fuzzysystems are tuned to maximize a given performance condition. Some imminent dataare commonly available and produce what is termed a supervised learningproblem. In this regard, we generally want to minimize the sum of error squaresin data approximation.

Fuzzylogic begins with and builds on a set of human-language rules provided by theuser. The fuzzy system changes these rules to their mathematical equivalents. This simplifies the work of the system designer and the computer and translatesinto a much more accurate representation of how systems behave in the realworld.

The additional benefits of fuzzy logic are its simplicity andflexibility. Fuzzy logic can handle problems with inaccurate and incompletedata and can model non-linear functions of random complexity. “ If you donot have a good implant model or if the system is changing, then diffusion willproduce a better solution than conventional control techniques,” says BobVarley. We can generate a fuzzy system to match any set of input and outputdata. Fuzzy Logic Toolbox makes it particularly easy to provide adaptivetechniques such as neuro-diffuse adaptive inference systems (ANFIS) and diffusesubtractive clustering.

Fuzzy logic models, called fuzzy inferencesystems, consist of a series of “ if-then” conditional rules. . Forthe designer who understands the system, we can easily write these rules andyou can provide all the rules that are essential for correctly explaining thesystem (although generally only a moderate number of rules are required). Therule-based approach and the flexible membership plan not only simplifies thecreation of fuzzy systems, but also simplifies system design and ensures thatthe system can be updated and maintained over time. It is recognized that the prepositionallogic is isomorphic to establish the theory under the association between thecomponents of these two mathematical systems. Furthermore, both systems areisomorphic to a Boolean algebra, which is a mathematical system defined byabstract entities and their axiomatic properties. The isomorphism between Boolean algebra, settheory and propositional logic ensures that each theorem in one of thesetheories has a counterpart in each of the other two theories.

These isomorphismallow us, in effect, to involve all these theories by scaling only one. We willnot spend much time reviewing the clear logic, but at some point we have tospend, especially in the concept of commitment, to achieve the concept in fuzzylogic. Fuzzy rules are the cornerstone of fuzzy logic systems. . Rules are aform of proposition. A proposition is an ordinary statement that implies, forexample, “ The ratio of the buffer is low”.

Therefore, we can have thefollowing rule: “ If the damping is low, the impulse response of the systemoscillates long before it goes out”. In traditional propositional logic, aproposition must be meaningful to call it “ true” or” false”, regardless of whether we know which of these terms appliescorrectly. Logicalreasoning is the process of combining the propositions given in otherpropositions, and then doing it repeatedly. The proposition can be combined inmany ways, deriving from three fundamental operations: the conjunction(indicated by p? q), where the simultaneous truth of two separate sentences peq is said; Disjunction(p? q), where to affirm thetruth of one or both the different proposals; the implication (p ? q) whichgenerally takes the form of an IF-THEN rule (also known as the “ productionrule”). The implicit IF part is called antecedent, while the THEN part iscalled consequential. Generate propositions using union, disjunction orimplication, a new scam The proposition can be obtained from a given prefix ofthe clause “ is false that .

..”; This is the negation operation (~ p). Furthermore, p ? q is the equivalence relation; means that both p and q aretrue or false. Fuzzyconcepts first introduced by Zadeh in the ’60s and’ 70s the focus is basicallya traditional computational logic and set theory concerns:·        True or False·        Zero or One·        In or Out (in terms of setmembership)  ·        Black or White (no grey) ·        Not the case with fuzzy logic and fuzzysetsFuzzy logic allowsconclusions to be true or false. However, there are also proposals withvariable answers, such as those that can be found by asking a group of peopleto identify a color. In these cases, the truth appears as the result ofreasoning from an inaccurate or partial knowledge in which the sampled answersare mapped into a spectrum.

Humans and animalsoften operate using fuzzy ratings in most situations. The person does notcalculate the exact values ?? for weight, density, distance, direction, heightand width of the container and the air resistance of the object to determinethe force and the projection angle of the object. Instead, the personimpulsively applies “ fuzzy” calculations quickly, based on previousexperience, to determine which force output values, direction, and verticalangle will be used to make the tone. Both degrees of truth and probabilityrange from 0 to 1 and, therefore, may seem the same at the beginning, but fuzzylogic uses degrees of truth as a mathematical model of ambiguity, whileprobability is a mathematical model of ignorance. The Basic Concepts ofFuzzy Logic are:•Approximation (“ granulation”): a color can be accurately describedusing RGB values, or it can   be roughlydescribed as “ red”, “ blue”, etc.•Degree (“ graduation”): two different colors can be described as” red”, but one is considered      more red than the other.

•Fuzzy logic tries to reflect the human way of thinking.·        Approximation (“ granulation”): a color can be accurately described using RGB values, or it can   be roughly described as “ red”,” blue”, etc..  ·        Degree (“ graduation”): twodifferent colors can be described as “ red”, but one is consideredmore red than the other.·        Fuzzy logic tries to reflect the humanway of thinking.          Implementation of Fuzzy Logic• Can be implemented insystems of different sizes and capacities, from small   microcontrollers to workstation-based networkcontrol systems.• It can be implementedin software, hardware or in a combination of both.

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