A New Method for Optimal Solution of Intuitionistic Fuzzy Transportation Problems via Generalized Trapezoidal Intuitionistic Fuzzy Numbers

Figures & data

Figure 1. A TrIFN $A=\left(l,c,d,r\right);t_A,z_A$.

Table 1. The intuitionistic fuzzy transportation table.

	1	2	…	N	$a_i$
1	$c_{11}$	$c_{12}$	…	$c_{1n}$	$a_1$
2	$c_{21}$	$c_{22}$	…	$c_{2n}$	$a_2$
…	…	…	…	…	…
$b_j$	$b_1$	$b_2$	…	$b_n$	$\sum _{i=1}^m{a}_i=\sum _{j=1}^n{b}_j$

Table 2. Data of the Example 5.1: the fuzzy transportation table.

Source	Phangnga	Phuket	Krabi	Availability
Si	$\left(3,5,7,14\right);0.6,0.3$	(2,4,8,13);0.7,0.2	(3,5,9,15);0.5,0.3	35
Yanok	$\left(2,5,8,10\right);0.8,0.2$	(3,6,9,12);0.5,0.4	(4,7,10,16);0.6,0.3	40
PhiPhi	$\left(3,6,8,13\right);0.8,0.1$	(4,8,10,15);0.6,0.2	(5,9,13,15);0.7,0.3	50
Demand	45	55	25	125

Table 3. The first iteration choose the north-west corner cell.

Source	Phangnga		Phuket	Krabi	Availability
Si	(3,5,7,14);0.6,0.3	35	(2,4,8,13);0.7,0.2	(3,5,9,15);0.5,0.3	35
Yanok	(2,5,8,10);0.8,0.2		(3,6,9,12);0.5,0.4	(4,7,10,16);0.6,0.3	40
PhiPhi	(3,6,8,13);0.8,0.1		(4,8,10,15);0.6,0.2	(5,9,13,15);0.7,0.3	50
Demand	45		55	25	125

Table 4. Last iteration by the north-west corner method.

Source	Phangnga		Phuket		Krabi		availability
Si	(3,5,7,14);0.6,0.3	35	(2,4,8,13);0.7,0.2		(3,5,9,15);0.5,0.3		35
Yanok	(2,5,8,10);0.8,0.2	10	(3,6,9,12);0.5,0.4	30	(4,7,10,16);0.6,0.3		40
PhiPhi	(3,6,8,13);0.8,0.1		(4,8,10,15);0.6,0.2	25	(5,9,13,15);0.7,0.3	25	50
Demand	45		55		25		125

Table 5. Construction of loop.

Table 6. Improved basic feasible solution.

Source	Phangnga		Phuket		Krabi		Availability
Si	(3,5,7,14);0.6,0.3	5	(2,4,8,13);0.7,0.	5	(3,5,9,15);0.5,0.3	25	35
Y anok	(2,5,8,10);0.8,0.2	40	(3,6,9,12);0.5,0.4		(4,7,10,16);0.6,0.3		40
PhiPhi	(3,6,8,13);0.8,0.1		(4,8,10,15);0.6,0.2	50	(5,9,13,15);0.7,0.3		50
Demand	45		55		25		125