Solving Fully Fuzzy Dual Matrix System With Optimization Problem
الموضوعات : مجله بین المللی ریاضیات صنعتیF. Babakordi 1 , M. S. Adabitabar Firozja 2
1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Science and Research
Branch, Islamic Azad University, Ghaemshahr, Iran.
الکلمات المفتاحية: Fuzzy dual matrix system, Linear Programming, Fuzzy number, Optimization, Hukuhara difference,
ملخص المقالة :
In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective function. We prove some theorems and we suggest conditions in which the fuzzy dual matrix system of AX + B = CX + D and the fuzzy matrix system of (A -H C)X = (D - H B) have the same LR fuzzy solution and we discuss about the conditions where LR fuzzy dual matrix system has crisp solution. Finally numerical examples are solved to illustrate the ability, accuracy and capability of the proposed method.
