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Table 6 The results of crisp and fuzzy values for the normal distribution

From: Variable demand model for periodically reviewing with allowing refunding parts of the orders

\(\beta\) Item \(Q_{mr}\) \(N_{r}\) \(E\left( {{\text{TC}}_{r} } \right)\) \(C_{or} + \left( {E\left( {{\text{TC}}_{r} } \right)/Q_{{m{\text{r}}}} } \right)\)
0.1 Item I 4847.67 0.875517 3533.53 48.51
Item II 7269.02 0.875276 16,155 136.88
Item III 9657 0.872035 13,765.9 84.95
0.3 Item I 4824.91 0.757536 3603.84 48.53
Item II 7234.77 0.757303 16,448.2 136.93
Item III 9608.93 0.754288 14,004 84.98
0.5 Item I 4765.65 0.605767 3747.14 48.57
Item II 7145.63 0.60554 17,039.1 137.05
Item III 9484.28 0.60272 14,481.2 85.05
0.7 Item I 4599.64 0.404855 4000.75 48.65
Item II 6895.85 0.404627 18,074.4 137.28
Item III 9134.18 0.401906 15,314.1 85.20
0.9 Item I 3316.37 0.115159 3807.9 48.93
Item II 4952.58 0.114599 17,181 138.13
Item III 6089.13 0.105624 15,151.7 86.01
\(\beta\) Item \(Q_{mr}\) \(N_{r}\) \(E(\widetilde{{{\text{TC}}}}_{r} )\) \(\tilde{C}_{or} + E((\widetilde{{{\text{TC}}}}_{r} ){/}\tilde{Q}_{mr} )\)
0.1 Item I 4847.68 0.875727 3495.53 48.63
Item II 7267.81 0.874992 16,261.3 136.52
Item III 9655.66 0.871915 13,827.2 85.08
0.3 Item I 4824.94 0.75772 3564.71 48.64
Item II 7233.48 0.757047 16,558.5 136.57
Item III 9607.5 0.754176 14,067.4 85.11
0.5 Item I 4765.7 0.605917 3705.81 48.68
Item II 7144.12 0.605315 17,156.4 136.69
Item III 9482.64 0.602615 14,548.6 85.18
0.7 Item I 4599.73 0.40496 3955.57 48.77
Item II 6893.73 0.404439 18,202.5 136.93
Item III 9131.89 0.401805 15,387.9 85.33
0.9 Item I 3317.17 0.115214 3766.01 49.04
Item II 4937.53 0.114233 17,299.8 137.79
Item III 6064.97 0.105205 15,220.4 86.15