A new methodology of solving fuzzy linear equations based on simulation
محورهای موضوعی : نظریه فازی
1 - Department of Mathematics, Urmia Branch, Islamic Azad UniversityIslamic Azad , Urmia, Iran .
کلید واژه: Fuzzy number, Defuzzification, Fuzzy linear system, Distance, Simulation.,
چکیده مقاله :
In this article, it is attempted to develop a method for solving an arbitrary general fuzzy linear system by using the weighted metric. By using of the distance between two fuzzy numbers, the best and nearest approximation fuzzy symmetric vector can be obtained. Defuzzification can replace the $n × n$ fuzzy linear system with two $n × n$ crisp linear system. Consequently, to obtain best approximation of solution for $n × n$ fuzzy linear system the researcher must solve two $n × n$ crisp linear system. Considering the existing and uniqueness of fuzzy solution to n×n linear fuzzy system is done. Numerical examples are presented to illustrate the proposed model.
In this article, it is attempted to develop a method for solving an arbitrary general fuzzy linear system by using the weighted metric. By using of the distance between two fuzzy numbers, the best and nearest approximation fuzzy symmetric vector can be obtained. Defuzzification can replace the $n × n$ fuzzy linear system with two $n × n$ crisp linear system. Consequently, to obtain best approximation of solution for $n × n$ fuzzy linear system the researcher must solve two $n × n$ crisp linear system. Considering the existing and uniqueness of fuzzy solution to n×n linear fuzzy system is done. Numerical examples are presented to illustrate the proposed model.
1. M. Friedman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems. 96 (1998) 201 - 209.
2. M. Friedman, M. Ming, A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and Systems. 109 (2000) 55 - 58.
3. W. Cong-Xing, M. Ming, Embeding problem of fuzzy number, Fuzzy Sets and Systems. 44 (1991) 33 - 36.
4. Ming Ma, A. Kandel, M. Friedman, A new approach for defuzzification, Fuzzy Sets and Systems. 111 (2000) 351 - 356.
