Generally in uncertain environment we use fuzzy number. There are different types of fuzzy number. Trapezoidal fuzzy number is one of them. I want to know which advantage we will get if we use trapezoidal fuzzy number.
Trapezoidan membership functions réflex clearly the vaiation of a element. From 0 to 1, represents its membership, remain 1 being the variable, then, decreases form 1 to 0.
Because you need only 4 real numbers. Also because the upper semicontinuous function which defines a trapezoidal fuzzy number is completely determined by two linear functions.
The option to choose trapezoidal fuzzy number actually depends on the situation. I would like to take triangular fuzzy number as an example. We have three number or triplet (a,b,c). a and b denotes least likely values (lowest and highest value) and b denotes the most likely value. For trapezoidal, let say (a,b,c,d), b and c are considered as the most likely values.
For triangular, we have one most likely value but for trapezoidal we have two most likely values.
Refer to the problem we are dealing with. And the question that arises from your question: What is the application of the fuzzy number in solving our real problems ? For example:
what's the difference (not mathematically) to solve the fuzzy equation using:
1) trapezoidal fuzzy number.
2) triangular fuzzy number.
In fuzzy models and controllers we use expert knowledge. Experts use linguistic values, e.g., small, medium, high speed of a car. It is necessary to identify the mathematical models of these human concepts. In our minds, concepts are usually modeled as Gauss-like functions. The best mathematical simplification and approximation of such functions is the trapezoid function and then the triangular function. These functions are easy in identification.
see this:
https://www.science.gov/topicpages/t/trapezoidal+fuzzy+numbers
http://wairco.org/IJCCIT/April2015Paper70.pdf
Trapezoidal fuzzy numbers (a, b, c, d): Arithmetic behavior
Some physical phenomena requires trapezoidal fuzzy number in fuzzy modelling. In short depends on the problem.
Triangular fuzzy number is a subset of trapezoidal fuzzy number. At instance, suppose we denote triangular fuzzy number as (a,b,c) and trapezoidal as (a,b_1,b_2,c). A trapezoidal fuzzy number is a triangular fuzzy number when b_1=b_2.
Fuzzy numbers and more generally linguistic values are approximate assessments, given by experts and accepted by decision-makers when obtaining value that is more accurate is impossible or unnecessary. Distance between two fuzzy numbers plays an important role in linguistic decision-making. well detailed at
https://www.science.gov/topicpages/t/trapezoidal+fuzzy+numbers
Fuzzy numbers are help to find the uncertainty so uncertainty does not lies in one point so we are fixing the linguistic terms based on the membership function for example triangular fuzzy numbers are having three membership function (0,0.50,1) for that the linguistic terms are 0 low 0.50 medium and 1 is high for trapezoidal 0,0.50,0.75,1 low medium high very high for finding the vaguness trapezoidal fuzzy numbers gives the better solution compared to the triangular fuzzy number.best example is fuzzy based washing machine
a simple algorithm of arithmetic operations as well as easy and intuitive interpretation
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