Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

Table 1

Coefficients 𝛼_𝑖𝑗, 𝛽_𝑖𝑗, 𝑐_𝑖𝑗, and 𝑑_𝑖𝑗 for the first- and second-level objectives of the BL-MOLFP problem.

	𝑓11	𝑓12	𝑓21	𝑓22	𝑓23
𝛼𝑖𝑗	−1	2	4	−4	0
𝛽𝑖𝑗	7	4	3	1	1
𝑐𝑖𝑗	(−1,0)	(−1,0)	(−1,0)	(1,0)	(−1,0)
𝑑𝑖𝑗	(0,−1)	(0,−1)	(0,−1)	(0,1)	(0,−1)
min𝐺𝑓𝑖𝑗	−0.143	−1.61	−0.308	−4	0
max𝐺𝑓𝑖𝑗	0.51	0.5	1.3333	0.2667	4
𝑔𝑖𝑗	0	−0.5	−0.3	−4	0
𝑢𝑖𝑗	0.5	0.5	1.3	0	4
𝐿𝑖𝑗	2	1	0.625	0.25	0.25
𝐿^/𝑖𝑗	0	0.5	0.1875	1	0
𝐶𝑖𝑗	(2,2)	(0.5,0.5)	(0.625,0.1875)	(−0.25,−1)	(−0.25,0.25)
𝐺𝑖𝑗	−2	4	3.0625	0	0
𝑤𝑖𝑗	2	1	1	0.25	0.25