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What is fuzzy function?
membership function is the one of the fuzzy function which is used to develope the fuzzy set value . the fuzzy logic is depends upon membership function
What is fuzzy set?
= http://en.wikipedia.org/wiki/Fuzzy_set = = Fuzzy set =Jump to: navigation, searchFuzzy sets are sets whose elements have degrees of membership. Fuzzy sets have been introduced by Lotfi A. Zadeh (1965) as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition - an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1.
Difference between fuzzy set theory and crisp set theory?
The fundamental difference is that in fuzzy set theory permits the gradual assessment of the membership of elements in a set and this is described with the aid of a membership function valued in the real unit interval [0, 1]. Better, the degree of membership of the elements of a set can take values ranging between 0 and 1 allowing for a ranking of membership. Conversely, crisp set theory is a classical bivalent set so that the membership function only takes values 0 or 1. In this case, one can know only if an element of the set have or not a particular characteristic and a ranking of membership is not possible.
What is the difference between fuzzy set and L-fuzzy set?
A fuzzy set (class) A in X is characterized by a membership (characteristic)function fA : X--> [0,1] which associates with each point in X a realnumber in the interval [0, 1], with the value of fA(x) at x representingthe "grade of membership" of x in A. Thus, the nearer the value offA(x) to unity, the higher the grade of membership of x in A. When Ais a set in the ordinary sense of the term, its membership function cantake only two values 0 and 1, with fA(x) = 1 or 0 according as xdoes or does not belong to A. Thus, in this case fA(x) reduces to thefamiliar Characteristic function of a set A. (When there is a need todifferentiate between such sets and fuzzy sets, the sets with two-valuedcharacteristic functions will be referred to as ordinary sets or simply sets. )On the other hand , an L-fuzzy set A in X is characterized by the membership function fA :L--> L , where L is a complete lattice with an involutive order preserving operation N : L--> L.
What is fuzzy complement?
A fuzzy complement is a concept in fuzzy set theory that represents the degree to which an element does not belong to a fuzzy set. Unlike classical set theory, where an element is either in a set or not, fuzzy sets allow for varying degrees of membership, typically represented by values between 0 and 1. The fuzzy complement of an element's membership degree is calculated as one minus that degree, effectively reflecting the uncertainty or partial membership in the context of fuzzy logic. This concept is crucial for applications in areas such as decision-making, control systems, and artificial intelligence where ambiguity and vagueness are inherent.
What is zadeh's extension principle?
The extension principle is a basic concept in the fuzzy set theory that extends crisp domains of mathematical expressions to fuzzy domains. Suppose f(.) is a function from X to Y and A is a fuzzy set on X defined as: A=ma(x1)/x1 + ma(x2)/x2 + ...... + ma(xn)/xn Where ma is the Membership Function of A. the + sign is a fuzzy OR (Max) and the / sign is a notation (indicated the variable xi in discourse domain X - NOT DIVISION) Then the extension principle states that the image of fuzzy set A under the mapping f(.) can be expressed as a fuzzy set B, B=f(A)=ma(x1)/y1 + ma(x2)/y2 + ...... + ma(xn)/yn where yi = f(xi) , i = 1,2,3,....,n
Is not the difference between a crisp set and a fuzzy set?
Yes, the difference between a crisp set and a fuzzy set lies in how elements are classified. In a crisp set, an element either belongs to the set or it does not, resulting in a binary classification (0 or 1). In contrast, a fuzzy set allows for partial membership, where elements can have degrees of belonging ranging from 0 to 1. This flexibility enables fuzzy sets to handle uncertainty and vagueness in data more effectively.
When you call fuzzy set as fuzzy graph?
fuzzy graph is not a fuzzy set, but it is a fuzzy relation.
What is fuzzy theory?
Fuzzy theory, or fuzzy set theory, is a mathematical framework for dealing with uncertainty and imprecision in data and reasoning. Unlike classical set theory, which defines strict membership criteria, fuzzy theory allows for degrees of membership, enabling more nuanced representations of concepts. This approach is widely applied in various fields, such as control systems, artificial intelligence, and decision-making, where binary true/false evaluations are insufficient. By incorporating vagueness, fuzzy theory provides a more flexible way to model real-world situations.
What is defuzzification?
Defuzzification is the process of converting a fuzzy set into a crisp value, typically used in fuzzy logic systems. It involves selecting a single representative value from the fuzzy output set, enabling practical decision-making or control actions. Common methods of defuzzification include the centroid method, which calculates the center of gravity of the fuzzy set, and the maximum method, which selects the highest membership value. This step is crucial for translating the imprecise, qualitative information from fuzzy logic into precise, quantitative results.
What do you get if you plant three Hot Silly Peppers?
It may be possible to get Fuzzy the Furi. You do not get free membership. 001 Fuzzy the Furi [Moshi] Any 3 Hot Silly Peppers Fuzzy is found in the Moshi Magazine. It is thought that Fuzzy is possibly part of a new set of Moshlings to come out in the future. Fuzzy may not be available or may only be available to those who have a Furi Monster.
Different between crisp set and fuzzy set?
In short, for a crisp set (subset) elements of the set definitely do belong to the set, while in a fuzzy set (subset) elements of the set have a degree of membership in the set. To make things clearer:Suppose we have a reference set X={x_1, ...} and a subset Y={y_1, ...} of X. If Y represents a crisp subset of X, then for all x_n belonging to X, x_n either belongs or Y or does not belong to Y. We can write this by assigning a function C which takes each member of X to 1 iff it belongs to Y, and 0 iff it does not belong to Y. E. G. Suppose we have the set {1, 2, 3, 4, 5}. For the crisp subset {1, 2, 4} we could write this in terms of a function C which takes 1 to 1, 2 to 1, 3 to 0, 4 to 1, and 5 to 0, or we can write {(1, 1), (2, 1), (3, 0), (4, 1), (5, 1)}.For a fuzzy subset F of a reference set X the elements of F may belong to F to a degree in between 0 and 1 (as well as may belong to F to degree 0 or 1). We can write this by assigning a function M which takes each member of X to a number in the interval of real numbers from 0 to 1, [0, 1] to represent its degree of membership. Here "larger" numbers represent a greater degree of membership in the fuzzy subset F. For example, for the reference set {1, 2, 3, 4, 5} we could have a function M which takes 1 to .4, 2 to 1, 3 to .6, 4 to .2, and 5 to 0, or {(1, .4), (2, 1), (3, .6), (4, .2), (5, 0)}, with 3 having a greater degree of membership in F than 4 does, since .6>.2.
