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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