How do you find the fuzzy triangular number?
the real line.
- Definition 2.3. Triangular Fuzzy Number A fuzzy number ˜
- A= (a, b, c)is called triangular.
- fuzzy number if its membership function is given by µ˜
- A(x) =
- x−a.
- b−a, a ≤x≤b;
- c−x.
- c−b, b ≤x≤c;
What is triangular fuzzy matrix?
Abstract. In this paper, some elementary operations on triangular fuzzy numbers (TFNs) are defined. We also define some operations on triangu-lar fuzzy matrices (TFMs) such as trace and triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented.
What is triangular fuzzy set?
A triplet ( m 1 , m 2 , m 3 ) is known as Triangular Fuzzy Number, where “ m 1 ” represents smallest likely value, “m 2 ” the most probable value, and “ m 3 ” the largest possible value of any fuzzy event.
How do you add two fuzzy numbers?
Fuzzy counterpart of real numbers is presented. Fuzzy membership functions, which satisfy conditions similar to the quasi-convexity are considered. An extra feature, called the orientation of the curve of fuzzy membership function, is introduced.
Why do we use triangular fuzzy numbers?
This gave us several times in past the impulse to apply principles of fuzzy logic for assessing human skills using as tools the corresponding system’s total uncertainty, the COG defuzzification technique and recently developed variations of it.In the present paper we use the Triangular Fuzzy Numbers (TFNs) as an …
What is triangular membership function?
Triangular membership functions feature, which is used in this paper, is characterized by a mathematical simplicity. It is specified by three parameters {a, b, c} where for each value x the membership function µ A (x) is described as shown in figure 1. These parameters values are obtained from experts’ knowledge.
How many fuzzy numbers are there?
In this section, we have discussed three types of fuzzy numbers, viz., Triangular Fuzzy Number (TFN), Trapezoidal Fuzzy Number (TrFN), and Gaussian Fuzzy Number (GFN).
How is membership function determined in fuzzy?
Membership functions (MFs) are the building blocks of fuzzy set theory, i.e., fuzziness in a fuzzy set is determined by its MF. Accordingly, the shapes of MFs are important for a particular problem since they effect on a fuzzy inference system. They may have different shapes like triangular, trapezoidal, Gaussian, etc.
How is fuzzy membership function calculated?
Formally, a membership function for a fuzzy set A on the universe of discourse X is defined as µA: X → [0, 1], where each element of X is mapped to a value between 0 and 1. This value, called membership value or degree of membership, quantifies the grade of membership of the element in X to the fuzzy set A.
How to multiply two fuzzy numbers?
Multiplication operation on fuzzy numbers is defined by the extension principle. Based on extension principle, nonlinear programming method, analytical method, computer drawing method and computer simulation method are used for solving multiplication operation of two fuzzy numbers.
What are the arithmetic operators on fuzzy numbers?
The arithmetic operators on fuzzy numbers are basic content in fuzzy mathematics. Multiplication operation on fuzzy numbers is defined by the extension principle. The procedure of addition or subtraction is simple, but the procedure of multiplication or division is complex.
What are the applications of the fuzzy set theory?
The fuzzy set theory has been applied in many fields such as operation research, control theory and management sciences etc. The fuzzy numbers and fuzzy values are widely used in engineering applications because of their suitability for representing uncertain information.
Who invented the fuzzy number system?
INTRODUCTION The concept of fuzzy sets, which was introduced by Zadeh [l], led to the definition of the fuzzy number and its implementation in fuzzy control and approximate reasoning problems. The basic arithmetic structure for fuzzy numbers was developed by Mizumoto and Tanaka [2,3], Nahmias [4], Dubois and Prade [5,6], Li [7], and Ma et al. [8].