G.Chen et al. Computer Networks 190(2021)107952 recommenders.In addition,the well-behaved recommenders may not is the recommendations provided by recommender r about trustee evaluate the trustee accurately due to insufficient interactions and thus j.Its correctness depends on the behavior of the recommender.The cannot provide precise recommendations.To solve those problems that utilization of DTand can minimize the impact of bad and the filtering algorithm cannot deal with,we apply three important imprecise recommendations and thereby improve the precision of the factors in the evaluation of the recommendation trust. recommendation trust evaluation. In human society,we usually trust information provided by people who we believe.Similarly,in the trust model,the trustor tends to 5.3.Synthesis trust use the recommendations provided by recommenders who are highly rated by the trustor.As a result,the direct trust of the trustor about Neither direct trust nor recommendation trust can comprehensively the recommender is needed in the evaluation of the recommendation reflect the trustee's trustworthiness.Hence,our trust model uses syn trust.The second important factor is the similarity of the direct trust thesis trust that is calculated by combining direct trust and recom- evaluation.Generally speaking,the trustor is more willing to receive mendation trust.Eq.(8)shows the calculation of the synthesis trust. recommendations from recommenders who have similar views with it. The similar views mean that the trustor and recommenders give similar evaluation of the direct trust to the trustee who provides the same T号=oDr9+(I-aoR9 (8) service.Eq.(4)shows how to calculate the similarity of the direct trust evaluation between the trustor and the recommender. In Eq.(8),Tdenotes the synthesis trust of trustoriabout trustee j.Its range is between 0 and 1,where 1 means complete trust while 0 59=1- ∑ESeir IDT-DTral (4) means complete distrust.DT and RT is direct trust and recommen- lSet(i,rk川 dation trust calculated by Eqs.(3)and (7).is a weight that weighs In Eq.(4),S denotes the similarity of direct trust evaluation the importance of direct trust and recommendation trust.It falls in the between trustor i and recommender rk.It falls in the interval of [0,1] interval [0.1]and the bigger it is,the more important direct trust is. where 1 means that the trustor and the recommender give exactly the The selection of is pivotal to the trust model.We adopt an adaptive same evaluation for each trustee.Ser(i.r)represents trustees common weight that can adjust automatically according to the dynamically to i and r,and ISer(i.)is the number of common trustees.Assuming hostile environment.The utilization of adaptive weight can resist trust that a recommender only gives the correct recommendations about related attacks such as bad mouthing attacks and ballot stuffing attacks part of trustees,the direct trust evaluation of the trustor and the so that improving the accuracy of trust evaluation.Eq.(9)illustrates the calculation of weight o. recommender about the same trustee may not be similar.In such a case,the similarity of the direct trust evaluation will be very small. Therefore,the trust model can resist selective misbehavior attacks by (9) 1 DTir<DTthreshold. using the factor of similarity in calculating. The last factor is the confidence level of the recommender about In Eq.(9),the calculation of is divided into two parts.The the trustee.The confidence level reflects the number of interactions principle of separate calculation is to compare DTr and DTesl between the recommender and the trustee.The higher the confidence DTr denotes the average value of direct trust of trustor i about all level is,the more the interactions between them are.Consequently,the recommenders.DT is the threshold of direct trust and is set to recommender with a high confidence level is more popular because it 0.5 by default.If DTir is less than DTreshd,will be equal to 1.It can evaluate the direct trust of the trustee accurately through sufficient means that trustor i will only use the direct trust depending on the interactions.Eg.(5)shows the calculation of the confidence level.It direct interactions with the target trustee if most of the recommenders evolves from the beta distribution standard deviation. are malicious.This way of calculating weight can prevent the trustor mistaking a good trustee as a malicious one when the proportion of 12@2+12+1) malicious recommenders is high.When DT,is equal to or greater than (5) (a%+唱+2p(a2+9+3) DT the calculation of is related to the number of interactions IN between trustor i and trustee j,and Ar that the difference between InE(5),denotes the confidence level of recommender the current time and the time of last interaction.The high number of about trusteeat time.andis the accumulated positive interactions means that the trustor has already adequately known about the trustee,so the direct trust of the trustor about the trustee is more and negative feedback given by the k'th recommenderr about target accurate.But if the trustor and the trustee have not interacted recently, trustee j.Eq.(6)shows the way to calculate them and it is similar even if they interacted with each other many times long time ago,the to Eg.(2). direct trust still cannot reflect the current trustworthiness of the trustee. In such a case,we regulate the importance of the direct trust via 4t.The e-w* adaptive weight can be dynamically adjusted according to the current (6) interaction situation to adapt to the dynamically hostile environment. 6.Experimental results and analysis In Eq.(6),m is the size of the sliding window between re and j.y andare decay factors of the time decay function.andis the The detailed performance evaluation of our work is done in two main parts.In the first part,we compare our proposed system architec. positive and negative feedback at time,respectively.We combine the ture based on TTPs with the centralized architecture and the distributed three important factors explained above and give the calculation of the architecture in terms of energy consumption.In the second part,we recommendation trust in Eq.(7). first validate the effectiveness of the recommendation trust evaluation DTS.CH and the adaptive weight.Then,we compare our trust model with three (7) related models:TBSM [9],NRB [23]and NTM [4].These three related 台=1DTsc models all adopted some methods to avoid the negative impact caused by malicious nodes on trust evaluation.In TBSM [9],they established In Eq.(7),RT is the recommendation trust of trusteej calculated social relationships between nodes and used these relationships to help by trustor.is the number of recommenders after filtering.D the trustor not to use bad recommendations provided by malicious 7Computer Networks 190 (2021) 107952 7 G. Chen et al. recommenders. In addition, the well-behaved recommenders may not evaluate the trustee accurately due to insufficient interactions and thus cannot provide precise recommendations. To solve those problems that the filtering algorithm cannot deal with, we apply three important factors in the evaluation of the recommendation trust. In human society, we usually trust information provided by people who we believe. Similarly, in the trust model, the trustor tends to use the recommendations provided by recommenders who are highly rated by the trustor. As a result, the direct trust of the trustor about the recommender is needed in the evaluation of the recommendation trust. The second important factor is the similarity of the direct trust evaluation. Generally speaking, the trustor is more willing to receive recommendations from recommenders who have similar views with it. The similar views mean that the trustor and recommenders give similar evaluation of the direct trust to the trustee who provides the same service. Eq. (4) shows how to calculate the similarity of the direct trust evaluation between the trustor and the recommender. 𝑆 (𝑡) 𝑖𝑟𝑘 = 1 − ∑ 𝑙∈𝑆𝑒𝑡(𝑖,𝑟𝑘 ) |𝐷𝑇𝑖𝑙 − 𝐷𝑇𝑟𝑘 𝑙 | |𝑆𝑒𝑡(𝑖, 𝑟𝑘 )| (4) In Eq. (4), 𝑆 (𝑡) 𝑖𝑟𝑘 denotes the similarity of direct trust evaluation between trustor 𝑖 and recommender 𝑟𝑘 . It falls in the interval of [0, 1] where 1 means that the trustor and the recommender give exactly the same evaluation for each trustee. 𝑆𝑒𝑡(𝑖, 𝑟𝑘 ) represents trustees common to 𝑖 and 𝑟𝑘 , and |𝑆𝑒𝑡(𝑖, 𝑟𝑘 )| is the number of common trustees. Assuming that a recommender only gives the correct recommendations about part of trustees, the direct trust evaluation of the trustor and the recommender about the same trustee may not be similar. In such a case, the similarity of the direct trust evaluation will be very small. Therefore, the trust model can resist selective misbehavior attacks by using the factor of similarity in calculating. The last factor is the confidence level of the recommender about the trustee. The confidence level reflects the number of interactions between the recommender and the trustee. The higher the confidence level is, the more the interactions between them are. Consequently, the recommender with a high confidence level is more popular because it can evaluate the direct trust of the trustee accurately through sufficient interactions. Eq. (5) shows the calculation of the confidence level. It evolves from the beta distribution standard deviation. 𝐶 (𝑡) 𝑟𝑘 𝑗 = 1 − √√√√√ 12(𝛼 (𝑡) 𝑟𝑘 𝑗 + 1)(𝛽 (𝑡) 𝑟𝑘 𝑗 + 1) (𝛼 (𝑡) 𝑟𝑘 𝑗 + 𝛽 (𝑡) 𝑟𝑘 𝑗 + 2)2(𝛼 (𝑡) 𝑟𝑘 𝑗 + 𝛽 (𝑡) 𝑟𝑘 𝑗 + 3) (5) In Eq. (5), 𝐶 (𝑡) 𝑟𝑘 𝑗 denotes the confidence level of recommender 𝑟𝑘 about trustee 𝑗 at time 𝑡. 𝛼 (𝑡) 𝑟𝑘 𝑗 and 𝛽 (𝑡) 𝑟𝑘 𝑗 is the accumulated positive and negative feedback given by the 𝑘 ′ th recommender 𝑟𝑘 about target trustee 𝑗. Eq. (6) shows the way to calculate them and it is similar to Eq. (2). 𝛼 (𝑡) 𝑟𝑘 𝑗 = ∑𝑚 𝑖=1 𝑒 −𝛾(𝑡−𝑡 𝑖 ) ∗ 𝛼 (𝑡 𝑖 ) 𝑟𝑘 𝑗 𝛽 (𝑡) 𝑟𝑘 𝑗 = ∑𝑚 𝑖=1 𝑒 −𝜎(𝑡−𝑡 𝑖 ) ∗ 𝛽 (𝑡 𝑖 ) 𝑟𝑘 𝑗 (6) In Eq. (6), 𝑚 is the size of the sliding window between 𝑟𝑘 and 𝑗. 𝛾 and 𝜎 are decay factors of the time decay function. 𝛼 (𝑡 𝑖 ) 𝑟𝑘 𝑗 and 𝛽 (𝑡 𝑖 ) 𝑟𝑘 𝑗 is the positive and negative feedback at time 𝑡 𝑖 , respectively. We combine the three important factors explained above and give the calculation of the recommendation trust in Eq. (7). 𝑅𝑇 (𝑡) 𝑖𝑗 = ∑𝑛 𝑘=1 𝐷𝑇 (𝑡) 𝑖𝑟𝑘 𝑆 (𝑡) 𝑖𝑟𝑘 𝐶 (𝑡) 𝑟𝑘 𝑗 ∑𝑛 𝑘=1 𝐷𝑇 (𝑡) 𝑖𝑟𝑘 𝑆 (𝑡) 𝑖𝑟𝑘 𝐶 (𝑡) 𝑟𝑘 𝑗 ∗ 𝐷𝑇 (𝑡) 𝑟𝑘 𝑗 (7) In Eq. (7), 𝑅𝑇 (𝑡) 𝑖𝑗 is the recommendation trust of trustee 𝑗 calculated by trustor 𝑖. 𝑛 is the number of recommenders after filtering. 𝐷𝑇 (𝑡) 𝑟𝑘 𝑗 is the recommendations provided by recommender 𝑟𝑘 about trustee 𝑗. Its correctness depends on the behavior of the recommender. The utilization of 𝐷𝑇 (𝑡) 𝑖𝑟𝑘 , 𝑆 (𝑡) 𝑖𝑟𝑘 and 𝐶 (𝑡) 𝑟𝑘 𝑗 can minimize the impact of bad and imprecise recommendations and thereby improve the precision of the recommendation trust evaluation. 5.3. Synthesis trust Neither direct trust nor recommendation trust can comprehensively reflect the trustee’s trustworthiness. Hence, our trust model uses syn￾thesis trust that is calculated by combining direct trust and recom￾mendation trust. Eq. (8) shows the calculation of the synthesis trust. 𝑇 (𝑡) 𝑖𝑗 = 𝜔𝐷𝑇 (𝑡) 𝑖𝑗 + (1 − 𝜔)𝑅𝑇 (𝑡) 𝑖𝑗 (8) In Eq. (8), 𝑇 (𝑡) 𝑖𝑗 denotes the synthesis trust of trustor 𝑖 about trustee 𝑗. Its range is between 0 and 1, where 1 means complete trust while 0 means complete distrust. 𝐷𝑇 (𝑡) 𝑖𝑗 and 𝑅𝑇 (𝑡) 𝑖𝑗 is direct trust and recommen￾dation trust calculated by Eqs. (3) and (7). 𝜔 is a weight that weighs the importance of direct trust and recommendation trust. It falls in the interval [0, 1] and the bigger it is, the more important direct trust is. The selection of 𝜔 is pivotal to the trust model. We adopt an adaptive weight that can adjust automatically according to the dynamically hostile environment. The utilization of adaptive weight can resist trust related attacks such as bad mouthing attacks and ballot stuffing attacks so that improving the accuracy of trust evaluation. Eq. (9) illustrates the calculation of weight 𝜔. 𝜔 = { 1 − 𝜃 𝑒 −𝛥𝑡𝐼𝑁 𝐷𝑇𝑖𝑟 ≥ 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 , 1 𝐷𝑇𝑖𝑟 < 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 . (9) In Eq. (9), the calculation of 𝜔 is divided into two parts. The principle of separate calculation is to compare 𝐷𝑇𝑖𝑟 and 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 . 𝐷𝑇𝑖𝑟 denotes the average value of direct trust of trustor 𝑖 about all recommenders. 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 is the threshold of direct trust and is set to 0.5 by default. If 𝐷𝑇𝑖𝑟 is less than 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 , 𝜔 will be equal to 1. It means that trustor 𝑖 will only use the direct trust depending on the direct interactions with the target trustee if most of the recommenders are malicious. This way of calculating weight can prevent the trustor mistaking a good trustee as a malicious one when the proportion of malicious recommenders is high. When 𝐷𝑇𝑖𝑟 is equal to or greater than 𝐷𝑇𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 , the calculation of 𝜔 is related to the number of interactions 𝐼𝑁 between trustor 𝑖 and trustee 𝑗, and 𝛥𝑡 that the difference between the current time and the time of last interaction. The high number of interactions means that the trustor has already adequately known about the trustee, so the direct trust of the trustor about the trustee is more accurate. But if the trustor and the trustee have not interacted recently, even if they interacted with each other many times long time ago, the direct trust still cannot reflect the current trustworthiness of the trustee. In such a case, we regulate the importance of the direct trust via 𝛥𝑡. The adaptive weight can be dynamically adjusted according to the current interaction situation to adapt to the dynamically hostile environment. 6. Experimental results and analysis The detailed performance evaluation of our work is done in two main parts. In the first part, we compare our proposed system architec￾ture based on TTPs with the centralized architecture and the distributed architecture in terms of energy consumption. In the second part, we first validate the effectiveness of the recommendation trust evaluation and the adaptive weight. Then, we compare our trust model with three related models: TBSM [9], NRB [23] and NTM [4]. These three related models all adopted some methods to avoid the negative impact caused by malicious nodes on trust evaluation. In TBSM [9], they established social relationships between nodes and used these relationships to help the trustor not to use bad recommendations provided by malicious