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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.
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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.
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 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 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. :)
What is the difference between the greatest and least numbers in the set of data is called?
The difference between the greatest and least numbers in a set of data is called the range.
What is the difference between the greatest and least numbers in a set of data?
The difference between the largest and smallest numbers in a data set is called the range.
What is the difference between universal set and substance set?
utterance or diffutterance what is a utterance
