Fuzzy Approach for Group Sequential Test

Table 4

Base and peak values {[𝑎₁,𝑎₂,𝑎₃]} of triangular shaped fuzzy numbers for group sequential test using 𝛼-cuts for 𝐾=3 and 𝑘=1,2,3.

𝛼-cut	𝑘=1
	𝑍1	𝑆1	PCV1	PCV2
0.01	[−1.23,1.265,3.761]	[−1.23,1.265,3.761]	[0.551,−1.993,−4.553]	[−0.551,1.993,4,553]
0.20	[0.013,1.265,2.561]	[0.013,1.265,2.561]	[−0.714,−1.993,−3.271]	[0.714,1.993,3.271]
0.40	[0.432,1.265,2.091]	[0.432,1.265,2.091]	[−1.113,−1.993,−2.831]	[1.113,1.993,2.831]
0.60	[0.724,1.265,1.887]	[0.724,1.265,1.887]	[−1.487,−1.993,−2.534]	[1.487,1.993,2.534]
0.80	[1.102,1.265,1.517]	[1.102,1.265,1.517]	[−1.763,−1.993,−2.266]	[1.763,1.993,2.266]
1.00	[1.265,1.265,1.265]	[1.265,1.265,1.265]	[−1.993,−1.993,−1.993]	[1.993,1.993,1.993]
𝛼-cut	𝑘=2
	𝑍2	𝑆2	PCV1	PCV2
0.01	[−1.331,1.235,3.782]	[−0.824,1.763,4.335]	[0.551,−1.993,−4.553]	[−0.551,1.993,4,553]
0.20	[−0.074,1.235,2.513]	[0.468,1.763,3.023]	[−0.714,−1.993,−3.271]	[0.714,1.993,3.271]
0.40	[0.394,1.235,2.122]	[0.967,1.763,2.645]	[−1.113,−1.993,−2.831]	[1.113,1.993,2.831]
0.60	[0.756,1.235,1.693]	[1.253,1.763,2.284]	[−1.487,−1.993,−2.534]	[1.487,1.993,2.534]
0.80	[0.997,1.235,1.486]	[1.511,1.763,1.987]	[−1.763,−1.993,−2.266]	[1.763,1.993,2.266]
1.00	[1.235,1.235,1.235]	[1.763,1.763,1.763]	[−1.993,−1.993,−1.993]	[1.993,1.993,1.993]
𝛼-cut	𝑘=3
	𝑍3	𝑆3	PCV1	PCV2
0.01	[−1.032,1.533,4.122]	[−0.274,2.325,4.923]	[0.551,−1.993,−4.553]	[−0.551,1.993,4,553]
0.20	[0.278,1.533,2.775]	[1.078,2.325,3.587]	[−0.714,−1.993,−3.271]	[0.714,1.993,3.271]
0.40	[0.684,1.533,2.356]	[1.458,2.325,3.184]	[−1.113,−1.993,−2.831]	[1.113,1.993,2.831]
0.60	[1.084,1.533,2.023]	[1.836,2.325,2.835]	[−1.487,−1.993,−2.534]	[1.487,1.993,2.534]
0.80	[1.321,1.533,1.786]	[2.079,2.325,2.586]	[−1.763,−1.993,−2.266]	[1.763,1.993,2.266]
1.00	[1.533,1.533,1.533]	[2.325,2.325,2.325]	[−1.993,−1.993,−1.993]	[1.993,1.993,1.993]