## Hongqiang Jiao* , Xinxin Wang** and Wanning Ding*## |

Linguistic values | The cloud numbers |
---|---|

Very low(VL) | (0.1, 0.0394, 0.014) |

Low (L) | (0.3, 0.0394, 0.014 |

Medium (M) | (0.5, 0.0394, 0.014) |

Relatively high (RH) | (0.7, 0.0394, 0.014) |

Very high(VH) | (0.9, 0.0394, 0.014) |

The trust assessment method by a cloud model is as follows:

Through a study of various objective weight allocation schemes, it was found that the evaluation results obtained by objective methods such as the entropy weight method are not ideal and cannot effectively reflect the subjective intentions of decision-makers. This paper designs a subjective weight allocation algorithm that can effectively distribute the weights of evaluation indicators according to the subjective intentions of decision-makers.

For the set of evaluation indicators [TeX:] $$A=\left\{A_{l}, A_{2}, \cdots, A_{M}\right\}$$, assuming that P decision-makers decide the weight of the indicator together, we use [TeX:] $$A_{i j}(i \in[1, P], j \in[1, M])$$to denote the indicator set placed by the ith decision-maker at the jth position. The decision-makers can choose one location to place any number of indicators, and can place the already placed indicator repeatedly in other locations. Taking the weight of five indicators determined by two decision-makers as an example, the ranking of indicators is as follows:

[TeX:] $$\begin{array}{l} A_{11}=\left\{A_{2}\right\}, A_{12}=\left\{A_{3}\right\}, A_{13}=\left\{A_{1}\right\}, A_{14}=\left\{A_{4}\right\} \\ A_{21}=\left\{A_{2}\right\}, A_{22}=\left\{A_{2}, A_{3}\right\}, A_{23}=\left\{A_{1}, A_{3}\right\}, A_{24}=\left\{A_{1}, A_{3}, A_{4}\right\} \end{array}$$

If decision-maker [TeX:] $$Q_{i}$$ places an indicator j at a certain location k, then we set the [TeX:] $$a_{kj}$$ value to 1. Otherwise, we set it to 0. Then, according to the ranking of the two groups of aforementioned indicators, we obtain the quantitative decision matrix[TeX:] $$A_{k j}^{i}$$ of each decision-maker.

An example is presented here. Two decision-makers’ quantitative decision matrixes are as follows:

[TeX:] $$A_{k j}^{1}=\left(a_{k j}^{1}\right)_{4 \times 4}=\left[\begin{array}{llll} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right] \quad A_{k j}^{2}=\left(a_{k j}^{2}\right)_{4 \times 4}=\left[\begin{array}{llll} 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 1 \end{array}\right]$$

We assume that decision-makers have different decision-making powers and set the weights of P decision-makers as [TeX:] $$P_{W}=\left(\omega_{1}, \omega_{2}, \ldots, \omega_{P}\right)$$. A simple case is that they have the same decision-making power. We synthetically calculate the common decision-making matrix of P decision-makers by using each decision-maker’s quantitative decision matrix.

Consider that the two decision-makers have the same decision-making powers. We obtain the common decision-making matrix as follows:

[TeX:] $$T_{k j}=\left(t_{k j}\right)_{4 \times 4}=\left[\begin{array}{llll} 0 & 2 & 0 & 0 \\ 0 & 1 & 2 & 0 \\ 2 & 0 & 1 & 0 \\ 1 & 0 & 1 & 2 \end{array}\right]$$

To improve the computational efficiency, we design a linear descent method of position importance. This is not limited to the method we provide as long as the method satisfies the monotonic descent.

[TeX:] $$I_{k}$$denotes the importance of the kth location. We obtain a vector Z by the product of the common decision-making matrix, and [TeX:] $$I_{k}:$$ M denotes the number of evaluation indicators.

By (2), we obtain [TeX:] $$I_{1}=1$$,[TeX:] $$I_{2}=0.75$$,[TeX:] $$I_{3}=0.5$$,and [TeX:] $$I_{4}=0.25$$. These four numbers can express the importance of the four locations.

Using (3), we calculate the vector Z value: (1.25, 2.75, 2.25, 1).

By normalizing Z, we calculate the weight value of the index:

According to (4), the weights of the four indexes are (0.172, 0.379, 0.311, and 0.138).

The SPWA is a type of subjective weight allocation algorithm. A combination of subjective and objective weighting methods can lead to a comprehensive evaluation. A flexible weight model is advanced by combining SPWA with the entropy method. The main idea of the entropy method is that the larger the entropy, the lower the weight. We can compute the entropy En easily using a cloud model.

The entropy values of n attributes are [TeX:] $$E_{n l}, E_{n 2}, \cdots, E_{n j}(j=1,2, \cdots, n)$$.The objective weight is calculated using (5):

[TeX:] $$\omega^{5}$$denotes the subjective weight calculated by the group preference weight allocation algorithm. [TeX:] $$\omega^{\circ}$$denotes the objective weight calculated by (5). [TeX:] $$\omega$$denotes the fusion weight calculated using (6). [TeX:] $$\lambda$$is the harmonic parameter, which is set to 0.5.

Table 2.

Item_id | The index corresponding to item | The trust indexes evaluation cloud |
---|---|---|

79 | [TeX:] $$I_{1}$$Database service | [TeX:] $$C_{1}$$Database service |

87 | [TeX:] $$I_{2}$$Mobile service | [TeX:] $$C_{2}$$ (0.8142,0.2658,0.1316) |

104 | [TeX:] $$I_{3}$$Cloud communication | [TeX:] $$C_{3}$$(0.7884,0.2176,0.09) |

106 | [TeX:] $$I_{4}$$Elasticity calculation | [TeX:] $$C_{4}$$(0.8926,0.1634,0.0842) |

184 | [TeX:] $$I_{5}$$Video service | [TeX:] $$C_{5}$$(0.7484,0.2372,0.1158) |

188 | [TeX:] $$I_{6}$$Storage service | [TeX:] $$C_{6}$$(0.662,0.277,0.1158) |

223 | [TeX:] $$I_{7}$$Analysis service | [TeX:] $$C_{7}$$(0.966,0.0724,0.0846) |

224 | [TeX:] $$I_{8}$$Management and monitoring services | [TeX:] $$C_{8}$$(0.8518,0.2336,0.1162) |

225 | [TeX:] $$I_{9}$$ Application service | [TeX:] $$C_{9}$$(0.7036,0.3278,0.1758) |

We consider nine kinds of cloud services provided by Ali cloud, all of which are associated with items in the rating data (see Fig. 3). Algorithm 1 in Section 3 is used to compute the trust assessment cloud for every service. Then, the final trust assessment cloud of the cloud service is computed by method 2. The final result of trust assessment cloud C = (0.8027, 0.202, 0.099), as shown in Fig. 4. The weight is calculated as follows:

[TeX:] $$\omega=\left\{\omega_{1}, \omega_{2,}, \ldots, \omega_{9}\right\}=(0.127,0.097,0.083,0.132,0.095,0.124,0.092,0.134,0.116)$$

Table 1.

(a) | (b) | (c) |

(d) | (e) | (f) |

(g) | (h) | (i) |

Trust evaluation cloud for each service: (a) database service, (b) mobile services, (c) cloud communication service, (d) elasticity calculation, (e) video services, (f) storage services, (g) analysis service, (h) management and monitoring services, and (i) application service.

The results indicate that the trust values (0.8926 and 0.966) of cloud services S4 and S7 are very high and that the entropy values (0.1634 and 0.0724) are relatively small. This means that the uncertainty of these results is low. Thus, users can trust the cloud provider completely when using these cloud services. In sharp contrast to the aforementioned services, the trust value of service S6 is 0.662, and the entropy value is 0.277. This shows that the degree of trust is general, and the uncertainty is high. When users choose this type of cloud service, their decision needs to be considered carefully.

The trust value of service [TeX:] $$S_{9}$$is 0.7036 (relatively high), and the entropy value is 0.3278 (very high). This means that some people believe they can trust this service. Others believe should not trust this service because there is a large uncertainty with this kind of service. The trust of other services [TeX:] $$\left(\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{5}, \mathrm{~S}_{7}, \text { and } \mathrm{S}_{8}\right)$$ is relatively high, and the trust values are listed in Table 2. In general, users can choose these services more safely.

In this section, we compare our model with the trust evaluation method in [17]. The sample dataset is the same as in [17] (Tables 3, 4). The weight vector value is calculated by the method described in Section 4.2:

[TeX:] $$\omega=\left\{\omega_{1}, \omega_{2}, \ldots, \omega_{0}\right\}=(0.107,0.097,0.083,0.122,0.095,0.0 \mathrm{E} 94,0.092,0.084,0.116,0.110)$$

Table 4.

Database server | Type CPU cores | Memory (GB) | Storage |
---|---|---|---|

Small (S) | 4 | 8-16 | 50 GB data volume |

Medium (M) | 8 | 16-32 | 100 GB data volume |

Large (L) | 16 | 32-64 | 200 GB data volume |

Table 4.

CSP | [TeX:] $$\mathrm{SP}_{\mathrm{int}}$$ | [TeX:] $$\mathrm{SP}_{\mathrm{fp}}$$ | [TeX:] $$\mathbf{M P}_{\mathrm{sc}}$$ | [TeX:] $$\mathbf{M P}_{\mathrm{td}}$$ | [TeX:] $$\mathrm{SRW}_{\mathrm{dp}}$$ | [TeX:] $$\mathbf{R R W}_{\mathrm{dp}}$$ | [TeX:] $$\mathrm{SRW}_{\mathrm{pc}}$$ | [TeX:] $$\mathbf{R R W}_{\mathrm{pc}}$$ | [TeX:] $$\mathbf{N}_{\mathbf{l}}$$ | [TeX:] $$\mathbf{C}_{{o} \mathbf{d}}$$ |
---|---|---|---|---|---|---|---|---|---|---|

Amazon EC2 (S) | 0.1027 | 0.1120 | 0.2794 | 0.2865 | 0.1354 | 0.0964 | 0.2144 | 0.2098 | 0.0831 | 0.036 |

DigitalOcean (S) | 0.0826 | 0.1139 | 0.1962 | 0.2151 | 0.0806 | 0.0872 | 0.1401 | 0.1505 | 0.2494 | 0.0204 |

Google (S) | 0.0875 | 0.0991 | 0.2986 | 0.2937 | 0.0128 | 0.0106 | 0.2549 | 0.2206 | 0.3603 | 0.0480 |

Microsoft Azure (S) | 0.0575 | 0.0593 | 0.1195 | 0.1202 | 0.1449 | 0.1567 | 0.2133 | 0.2186 | 0.3270 | 0.0412 |

Rackspace (S) | 0.1340 | 0.1595 | 0.2343 | 0.2271 | 0.4232 | 0.1939 | 0.3024 | 0.2897 | 0.2328 | 0.1166 |

SoftLayer (S) | 0.0973 | 0.1208 | 0.2278 | 0.2129 | 0.2532 | 0.2418 | 0.2029 | 0.2864 | 0.0554 | 0.0405 |

Amazon EC2 (M) | 0.1945 | 0.2066 | 0.2834 | 0.2806 | 0.3025 | 0.0914 | 0.1920 | 0.2152 | 0.0776 | 0.0720 |

DigitalOcean (M) | 0.1728 | 0.1981 | 0.2029 | 0.2149 | 0.1021 | 0.1105 | 0.1300 | 0.1409 | 0.2162 | 0.0408 |

Google (M) | 0.1687 | 0.1767 | 0.2938 | 0.2974 | 0.0255 | 0.0212 | 0.2567 | 0.2614 | 0.3658 | 0.0960 |

Microsoft Azure (M) | 0.0956 | 0.1128 | 0.0482 | 0.0477 | 0.1446 | 0.156 | 0.2997 | 0.2231 | 0.3326 | 0.0823 |

Rackspace (M) | 0.2307 | 0.2483 | 0.2382 | 0.2312 | 0.6158 | 0.8191 | 0.2357 | 0.2869 | 0.1607 | 0.2332 |

SoftLayer (M) | 0.1876 | 0.2159 | 0.2352 | 0.2195 | 0.0634 | 0.0328 | 0.3193 | 0.2925 | 0.0665 | 0.0751 |

Amazon EC2 (L) | 0.3501 | 0.3238 | 0.2814 | 0.2813 | 0.1521 | 0.0883 | 0.1906 | 0.2092 | 0.0610 | 0.1441 |

DigitalOcean (L) | 0.2324 | 0.2741 | 0.2003 | 0.2188 | 0.1361 | 0.1473 | 0.1132 | 0.1220 | 0.1995 | 0.7666 |

Google (L) | 0.2840 | 0.2586 | 0.2598 | 0.2761 | 0.0506 | 0.0426 | 0.2241 | 0.2659 | 0.3658 | 0.1209 |

Microsoft Azure (L) | 0.4579 | 0.4019 | 0.2533 | 0.2430 | 0.1446 | 0.1560 | 0.2997 | 0.2231 | 0.3326 | 0.1921 |

Rackspace (L) | 0.3976 | 0.3823 | 0.2376 | 0.2288 | 0.2732 | 0.1362 | 0.3084 | 0.3291 | 0.1275 | 0.4665 |

SoftLayer (L) | 0.3543 | 0.3640 | 0.2086 | 0.2053 | 0.2536 | 0.2660 | 0.2000 | 0.1773 | 0.0721 | 0.1362 |

The evaluation results are listed in Table 5 and Fig. 5.

Table 5.

CSP | NormalizedTrusti in our model | NormalizedTrusti in [17] |
---|---|---|

AmazonEC2 (S) | 0.4199 | 0.3893 |

DigitalOcean (S) | 0.3708 | 0.3425 |

Google(S) | 0.4694 | 0.4544 |

Microsoft Azure (S) | 0.3995 | 0.3782 |

Rackspace(S) | 0.6246 | 0.5769 |

SoftLayer (S) | 0.4598 | 0.4443 |

AmazonEC2 (M) | 0.5181 | 0.5079 |

DigitalOcean (M) | 0.4236 | 0.4165 |

Google(M) | 0.5462 | 0.5148 |

Microsoft Azure (M) | 0.4212 | 0.4014 |

Rackspace(M) | 0.8854 | 1 |

SoftLayer (M) | 0.4569 | 0.4297 |

AmazonEC2 (L) | 0.5695 | 0.6124 |

DigitalOcean (L) | 0.6859 | 0.5563 |

Google(L) | 0.5994 | 0.5936 |

Microsoft Azure (L) | 0.7501 | 0.7777 |

Rackspace(L) | 0.7915 | 0.7394 |

SoftLayer (L) | 0.6080 | 0.7018 |

Aiming at different cloud services, we researched the establishment of trust relationships between users and cloud computing service platforms. We concluded that the trust value cannot be accurately and effectively measured by analyzing existing trust evaluation models. To solve this problem, we designed a subjective preference weight allocation algorithm. The SPWA algorithm was used to integrate each evaluation result to obtain the trust evaluation value of the entire cloud service provider.

A flexible weight model was advanced by combining SPWA with the entropy method. The model can integrate subjective weight and objective weight. This overcomes the disadvantage of using only one traditional weight distribution scheme.

The use of the cloud model by the SPWA algorithm effectively makes the qualitative assessment of trust into a quantitative evaluation, and the evaluation results are more in line with the trust of fuzzy and subjective characteristics.

This paper did not identify the authenticity of the trust evaluation data, nor did it design reputation punishment for malicious users. Future work will enhance the model to make it more effective.

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