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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 real
number in the interval [0, 1], with the value of fA(x) at x representing
the "grade of membership" of x in A. Thus, the nearer the value of
fA(x) to unity, the higher the grade of membership of x in A. When A
is a set in the ordinary sense of the term, its membership function can
take only two values 0 and 1, with fA(x) = 1 or 0 according as x
does or does not belong to A. Thus, in this case fA(x) reduces to the
familiar Characteristic function of a set A. (When there is a need to
differentiate between such sets and fuzzy sets, the sets with two-valued
characteristic 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 else can I help you with?
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
Difference between highest and lowest number in a set of numbers?
It is called the range.
What is the difference between domain and abscissa?
Domain is a set of all abscissa in a set of points WHILE Abscissa is the x-value or the counter part of ordinate
What is the difference between Hyperion and Essbase?
Essbase is a multidimensional DBMS where Hyperion performance suite is a set of BI tools.
Difference between induction and deduction?
Induction is reasoning down to a set of principles, from facts. Deduction is going from a generalized down to particulars.
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.
What is the difference between classical set theory and fuzzy set theory?
Classical theory is a reference to established theory. Fuzzy set theory is a reference to theories that are not widely accepted.
Difference between crisp set and fuzzy set?
Let A be a crisp set defined over the universe X. Then for any element x in X,either x is a member of A or not.In a fuzzy set,it is not necessary that x is the full member of the set or not a member. It can be the partial member of the set.
When you call fuzzy set as fuzzy graph?
fuzzy graph is not a fuzzy set, but it is a fuzzy relation.
What is the difference between fuzzy number and crisp number?
Each crisp number is a single point.example 3 or 5.5 or6.But each fuzzy number is a fuzzy set with different degree of closeness to a given crisp number example,about 3,nearly 5 and a half,almost 6.
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 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 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 a difference between a collection and a set?
None. A set is a collection and a collection is a set.
What is the difference between two sets in Python?
In Python, the difference between two sets is the elements that are present in one set but not in the other set.
What is fuzzy system?
 Fuzzy inference is a computer paradigm based on fuzzy set theory, fuzzy if-then- rules and fuzzy reasoning  Applications: data classification, decision analysis, expert systems, times series predictions, robotics & pattern recognition  Different names; fuzzy rule-based system, fuzzy model, fuzzy associative memory, fuzzy logic controller & fuzzy system Fuzzy inference is a computer paradigm based on fuzzy set theory, fuzzy if-then- rules and fuzzy reasoning  Applications: data classification, decision analysis, expert systems, times series predictions, robotics & pattern recognition  Different names; fuzzy rule-based system, fuzzy model, fuzzy associative memory, fuzzy logic controller & fuzzy system
What is the difference between a system of numerals and a set of numbers?
there is a huge difference. :)
