The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or obse...The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.展开更多
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
Fuzzy equations were solved by using different standard methods. One of the well-known methods is the method of α-cut. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numb...Fuzzy equations were solved by using different standard methods. One of the well-known methods is the method of α-cut. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numbers. In this article, it has been shown that the fuzzy equation , where A, X, B are fuzzy numbers can be solved by using the method of superimposition of sets. It has also been shown that the method gives same result as the method of α-cut.展开更多
文摘The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
文摘Fuzzy equations were solved by using different standard methods. One of the well-known methods is the method of α-cut. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numbers. In this article, it has been shown that the fuzzy equation , where A, X, B are fuzzy numbers can be solved by using the method of superimposition of sets. It has also been shown that the method gives same result as the method of α-cut.
