Simulating imprecise data: sine–cosine and convolution methods with neutrosophic normal distribution

Aslam, Muhammad

doi:10.1186/s40537-023-00822-4

Journal of Big Data

Table 1 Random normal variate when \(\mu =[10, 12]\) and \(\sigma =[\mathrm{1,1.5}]\)

From: Simulating imprecise data: sine–cosine and convolution methods with neutrosophic normal distribution

Sr#	\({I}_{N}\)=0		\({I}_{N}\)=0.01		\({I}_{N}\)=0.02		\({I}_{N}\)=0.03		\({I}_{N}\)=0.05		\({I}_{N}\)=0.10
	\({x}_{1N}\)	\({x}_{2N}\)	\({x}_{1N}\)	\({x}_{2N}\)	\({x}_{1N}\)	\({x}_{2N}\)	\({x}_{1N}\)	\({x}_{2N}\)	\({x}_{1N}\)	\({x}_{2N}\)	\({x}_{1N}\)	\({x}_{2N}\)
1	[9.2,10.8]	[11.6,14.4]	[9.4,11]	[11.2,13.7]	[10.9,13.5]	[8.9,10.5]	[10.2,12.8]	[7.8,8.8]	[10.2,12.4]	[9.5,11.54]	[9.5,11.54]	[10.1,11.77]
2	[10, 12]	[11.3,14]	[10.5,12.8]	[8.2,9.4]	[10.6,13.1]	[8.4,9.7]	[9.6,11.7]	[8.7,10.1]	[8.9,10]	[12.2,15.06]	[12.2,15.06]	[9.1,10.73]
3	[8.2,9.3]	[9.6,11.4]	[10,12.1]	[9.5,11.3]	[10.9,13.5]	[8.6,10.1]	[11.6,14.7]	[8.6,10.4]	[11.2,13.6]	[12.4,15.61]	[12.4,15.61]	[9.2,11.9]
4	[9.9,11.9]	[11.2,13.8]	[9.2,10.8]	[9.3,10.9]	[10.6,12.8]	[10.5,12.7]	[9.1,10.8]	[9.8,11.6]	[10.4,13]	[8.9,10.59]	[8.9,10.59]	[9.3,11.51]
5	[10.3,12.5]	[10.6,12.9]	[12.7,16.1]	[10.7,13.1]	[9.9,11.8]	[11.5,14.3]	[9.9,12.1]	[8.6,10]	[11,13.4]	[10.7,13.05]	[10.7,13.05]	[10.1,12.23]
6	[10.6,12.8]	[6.8,7.2]	[9.1,10.6]	[10.6,12.9]	[10.4,12.5]	[11.8,14.8]	[10,12]	[10.6,12.8]	[9.5,11.4]	[9.5,11.24]	[9.5,11.24]	[9.5,11.7]
7	[9.9,11.9]	[11,13.6]	[11,13.5]	[10.3,12.5]	[10.4,12.5]	[10.6,12.9]	[9.6,11.4]	[10.4,12.5]	[9,10.8]	[9.2,10.57]	[9.2,10.57]	[9.5,11.06]
8	[9,10.5]	[10.5,12.7]	[9.4,11.2]	[9.7,11.5]	[11.1,13.6]	[11.3,14]	[10.3,12.4]	[9.5,11.4]	[10.9,13.2]	[12.1,15.13]	[12.1,15.13]	[9.9,11.74]
9	[10.4,12.6]	[11.8,14.7]	[11.3,14]	[9,10.6]	[8.9,10.5]	[9.3,10.8]	[10.3,12.3]	[11.4,14.1]	[11,13.5]	[10,12.05]	[10,12.05]	[9.6,10.71]
10	[10.9,13.3]	[10.7,13.1]	[10.6,12.9]	[10.2,12.3]	[10.5,13]	[8.4,9.8]	[9.1,10.5]	[11.3,13.8]	[10.9,13.3]	[10.2,12.36]	[10.2,12.36]	[9.6,11]
11	[9.3,11]	[10.4,12.6]	[11.3,13.9]	[11,13.6]	[9.5,11.3]	[9.6,11.3]	[9.7,11.8]	[8.8,10.2]	[10,12.2]	[9.4,11.17]	[9.4,11.17]	[9.8,11.59]
12	[9.3,10.9]	[10.3,12.4]	[10,12.1]	[8.1,9.2]	[8.9,10.4]	[10.5,12.6]	[8.7,10.1]	[10.1,11.9]	[9.3,11]	[10.4,12.4]	[10.4,12.4]	[9.8,12.5]
13	[10.5,12.8]	[11.4,14.1]	[11.5,14.2]	[10.2,12.3]	[8.7,10.1]	[10,11.9]	[9,10.7]	[9.3,10.9]	[8.6,9.8]	[11.1,13.38]	[11.1,13.38]	[7.1,8.09]
14	[9.5,11.2]	[9.4,11.1]	[9.1,10.7]	[10,11.9]	[8.4,9.7]	[9.4,11]	[9.8,11.6]	[10.8,13.1]	[9.4,11.2]	[9.6,11.32]	[9.6,11.32]	[9.8,12.41]
15	[10.4,12.5]	[10.9,13.3]	[10.3,12.6]	[9.2,10.8]	[10.2,12.2]	[10.8,13.1]	[9.5,11.1]	[11,13.4]	[8.5,10]	[9.3,10.61]	[9.3,10.61]	[11.6,14.23]
16	[9.5,11.3]	[9.9,11.9]	[9.3,10.9]	[10.8,13.2]	[10.1,12.1]	[11.4,14.1]	[10.3,12.4]	[10.4,12.5]	[8.6,10.1]	[9.3,10.55]	[9.3,10.55]	[10,11.67]
17	[11.5,14.3]	[10.2,12.3]	[9,10.5]	[9.7,11.5]	[10,11.9]	[11.5,14.2]	[12.6,15.9]	[11.2,13.8]	[10.4,12.5]	[10.6,12.83]	[10.6,12.83]	[8.2,8.88]
18	[10.6,12.9]	[10.3,12.4]	[8.6,9.9]	[10.8,13.1]	[11.1,13.7]	[10.7,13.1]	[10,12.3]	[8.8,10.2]	[8.3,9.7]	[9.5,10.84]	[9.5,10.84]	[10.9,13.1]
19	[10.9,13.4]	[10,12]	[9.3,11]	[9.6,11.4]	[9.2,10.7]	[10.6,12.8]	[9.7,11.4]	[11,13.5]	[9.8,11.6]	[10.7,12.99]	[10.7,12.99]	[9.9,11.55]
20	[8.1,9.2]	[7.8,8.6]	[11,13.5]	[10.1,12.2]	[9.2,10.9]	[9,10.5]	[10.3,12.4]	[10.3,12.4]	[10.7,13.7]	[8.1,9.57]	[8.1,9.57]	[10.8,13.41]
21	[9.8,11.7]	[11.3,14]	[9.3,10.9]	[11.2,13.7]	[10.5,12.7]	[9.6,11.4]	[10.1,12.3]	[8.9,10.5]	[10.4,12.5]	[10.7,12.93]	[10.7,12.93]	[10.6,13.46]
22	[9.5,11.2]	[10.7,13]	[11.9,14.9]	[11,13.5]	[11.1,13.7]	[10.5,12.7]	[9.8,11.6]	[11,13.4]	[9.5,11.2]	[10.6,12.66]	[10.6,12.66]	[10.3,12.3]
23	[9.2,10.8]	[10.5,12.8]	[9.7,11.6]	[11,13.5]	[8.3,9.7]	[8,8.9]	[7.4,8.2]	[9.4,10.7]	[9.4,11.1]	[10.5,12.52]	[10.5,12.52]	[10.6,13.06]
24	[7.9,8.9]	[10.5,12.7]	[8.2,9.3]	[12.1,15.2]	[10.2,12.2]	[11.5,14.3]	[9.6,11.4]	[9.9,11.8]	[8.9,10.4]	[10.1,11.86]	[10.1,11.86]	[11.3,13.71]
25	[10,12]	[11.2,13.9]	[9.8,11.7]	[10.9,13.3]	[9.6,11.5]	[8.8,10.2]	[9,10.6]	[9.9,11.7]	[9.7,11.4]	[11,13.41]	[11,13.41]	[10.4,12.32]

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