A Computational Model for Measuring Trust in Mobile Social Networks Using Fuzzy Logic

With the development of the Internet and new computing tools such as smartphones and tablets, many community members make part of their social activities involve spending time in virtual environments and social networks, using them as the most widely used information resources. In recent years, various social networks have been created, such as Facebook and Twitter, and users can work on them. With the development of communication tools and new technologies, mobile social networks have been expanding, resulting in a combination of social and mobile networks. In social networks, information diffuses and users affect each other^[1]. Users can find and interact with friends on these networks and use their distributed services. For example, when a user is looking for a good traditional restaurant in another city, they can receive suggestions from their friends or friends of friends. In this regard, one of the most important issues is the level of trust taken towards other users. In fact, in mobile social networks, trust criteria are used to distinguish between friends and other network users. Therefore, cooperation based on trust in such networks can reduce the vulnerability of these networks and, in fact, the success rate of such environments depends on the level of trust among its users^{[2, 3]}. Trust has many characteristics, such as subjectivity, dynamism, symmetry, context, transitivity, etc. Depending on the different domains in which trust is used, different aspects of those characteristics are taken into account.

Applying trust in such networks has different challenges and problems^{[4, 5]}. The most important problem is that trust should be presented in the form of a computational model. In this regard, design and creation of a computational model is not an easy task. The reason is that trust is a cognitive and subjective feature with different meanings in different domains^[6–8]. For example, on the Amazon site, users use the star sign to indicate the usefulness of other users′ comments, or on another site, the number of file downloads can be considered as a criterion for determining the quality of files. In Twitter^[9], real friends and suggested friends are distinct, and the numbers of tweets that exist between the two users are used to distinguish them.

Displaying trust as a computational model requires its own design and modeling. It should also be noted that mobile social networks have their own characteristics in comparison with traditional social networks and real life^[10]. For example, in real life, there are a limited number of friends, but in a social network such as Facebook, a user can have thousands of friends. In addition, the way in which trust is formed in different environments is also different. For example, in real life, people′s trust in each other develops over a relatively long period of time, but in social networks, there is a need for a solution that can, in a shorter time, provide the trust that one user can have towards other users. In real life, trust is also gained through face-to-face experiences and appointments. But, on mobile social networks, there are virtual interactions and relationships. Hence, regarding the existence of thousands of potential friends in mobile social networks, it is necessary to design a trusted model through which, based on the computing power of existing tools, it can calculate the amount of trust to be taken towards users^[6–10].

Another serious problem in this area is the inference of trust between two people who are not friends. Most of the time, users benefit from services provided by individuals who do not have direct contact with them and communicate with them through their friends. It has also been shown that, in online communities, the number of two-by-two communication connections is relatively small in relation to the potential total number of two by two communications^{[9, 10]}. In other words, the number of friends of a user includes a limited number of users of an online community. Therefore, a method should be designed to build trust between people of a community that are not necessarily friends. Models created in this area are generally designed based on the "friend-friend" relationship^[11]. Different users may have contradictory judgments of an entity^[12]. Therefore, the dynamics mechanism is needed to define the trust class. Most previous studies have not focused much on this topic, which may lead to incorrect and unfair outputs for decision making. Classification approaches can handle some of these problems^[13]. However, in these approaches, we need to define class labels before the classification step.

In this research, a fuzzy clustering method has been applied to calculate trust in mobile social networks. The fuzzy clustering is the process of grouping elements into fuzzy sets where the membership function is defined by a fuzzy propositional function. Given that users may belong to more than one cluster, a fuzzy method is used to show users′ membership in each cluster. After establishing the groups and determining the amount of membership for them, in each cluster, the amount of trust is calculated between each user pair. Also, in the proposed method, it is possible that, if needed, the trust is also computed between the two users that are not in the same cluster.

The structure of the paper is as follows: In Section 2, a review of relevant research is presented. In Section 3, the Saadi Foundation′s dataset which is used in this paper is introduced. In Section 4, the trust inference model is presented. Finally, in Section 5, the implementation, evaluation, and results are presented.

Modeling trust has been investigated in several researches such as P2P networks^[14], cloud service selection^[15], social networks^[16], etc. Moreover, trust can be applied in various domains including information diffusion^[1,17], IoT^[18], and Blockchain technology^[19]. The challenges of trust management systems have been investigated, in which the way of displaying trust in online systems is also shown^[20]. In relation to the topic of trust, various review articles have been presented focusing on specific aspects of trust. In [21], the security aspect has taken into account in which it is based on observed behaviors, and, in this regard, in [22], a review of the types of attacks and possible defenses in systems based on reputation has been made. In [23], a new security metric in a cloud environment is introduced and a new algorithm to calculate trust is presented. In [24], a review of trust inference methods is completed. These methods provide a mechanism for determining trust inference in the absence of direct communication between users. Moreover, four types of attacks in relation to local trust and its vulnerabilities have been investigated.

In the modeling of trust, various dimensions of it can be considered. One of these dimensions is the scale. Trust can be displayed numerically or in the form of a category. Trust values can be either continuous or discrete. For example, in systems that use ratings, trust is expressed discretely^[25]. Conversely, in systems that utilize similarity criteria or use probabilistic criteria in trust calculation, continuous trust data is used^{[26, 27]}. Another way to display trust is to use range values instead of using specified values. This method of displaying trust is used in approaches that use fuzzy logic^{[13, 28, 29]}.

Another dimension of trust is the trust label. For example, trust can have different values at different times, so, in that case, trust will have a timestamp^{[30, 31]}. These labels can be used to defend against some attacks^[30]. Another label is the context. A product or service can be good in one context, but bad in another. For example, a detergent can be good for washing dishes, but not good for washing hands and face. In influence networks, individuals′ views about topics may result in disagreeing opinions^[32]. So, various studies have been conducted taking into account the context of trust^{[31, 33, 34]}.

There are different approaches to calculate trust values. Some use probability to calculate trust. In this approach, trust can be defined by the possibility that the trusted person acts as expected by the trustee^[35]. Much research on calculating trust has used probabilistic approaches^{[36, 37]}. In suggesting systems, similarity between users, the similarity between goods and services, and rating behaviors are used to provide suggestions. This criterion in trust management systems is also used to calculate trust^[38–42]. In [3, 43–46], the trust model is proposed using the user profile that is appropriate for online communities.

Trust is not a definite property, and therefore some studies^{[13, 47, 48]} use the fuzzy logic approach to display trust. It is difficult to build an efficient algorithm to identify the structure of a mobile social network. In [49], initial research has been conducted on the use of fuzzy relations in social network analysis and a new method for identifying similar communities is presented, which uses the idea of using the central indicator to find social boundaries. In [50], for the first time, the relationship between fuzzy similarities was found on a pair of nodes in a social network.

In this paper, the social network dataset of the Saadi Foundation has been used. The Saadi Foundation was created in 2013 to strengthen and expand Persian language and literature abroad and to create synergy and coherence in activities related to this field and exploits the existing capacities. In this foundation, courses aimed at enhancing language skills of learners in all components of the language (writing, speaking, reading, listening and pronunciation) as well as creating a network of Persian learners and continuous professional training are considered.

Due to the extensive presence of Persian learning students from different parts of the world at the Saadi Foundation, the social network of the Saadi Foundation is designed to facilitate the communication between them. These students come from 39 different countries in this social network. Table 1 shows the names of the countries of the Farsi learners in the social network.

In this paper, a fuzzy clustering approach is used to cluster users. Then an inference method is used to calculate trust between users. Profile information such as age, level of Persian speaking, registration date is used in the clustering process. In the clustering process, users may become a member of various clusters. Therefore, fuzzy logic is used to show users′ membership in each cluster.

A brief introduction to fuzzy logic is presented in Section 4.1. Then the clustering process step and trust inference model are presented in Sections 4.2 and 4.3 respectively.

Fuzzy logic can handle uncertainties in various domains such as social networks, expert systems, and so forth. In fuzzy set theory, linguistic terms, symbolic and numerical values are mapped to each other. Fuzzy variables and fuzzy sets are two main parts of the fuzzy logic which represent linguistic terms and their ranges respectively. Finally, the defuzzification process returns a crisp value as an output.

Fuzzy set A is represented as follows:

A = {(x, µ_A(x))| x $\in $ X}

where µA(x) is called the membership function for the fuzzy set A. X is referred to as the universe of discourse. The membership function associates each element x $\in $ X with a value in the interval [0,1].

For example, when we talk about the term youthful age, there are uncertainties about it. The fuzzy set defined below can be associated to the term youthful age (as a fuzzy variable):

The defuzzification step calculates the output based on input fuzzy sets and rules. It can be done in several ways:

1) Center of sums method

2) Center of gravity

3) Center of area

4) Weighted average method

5) Maxima methods.

Center of gravity is one the widely used methods in this step and is calculated using following formula:

where x_i indicates the sample element, µ(x_i) is the membership function, and n represents the number of elements in the sample. In this paper, this method is used in the defuzzification step.

In this paper, the fuzzy C-means clustering approach is used to cluster users. Variables age, date of registration, and level of Persian speaking are used in this process.

Age: According to psychology, age groups are dived into four groups: teen, young adult, middle-aged and elderly^{[51, 52]}. Age intervals and fuzzy membership of young group are shown in Table 2 and Fig. 1 respectively.

Figure 1.  Fuzzy membership functions related to the age criterion

Language speaking level: In this social network, exams are used to identify the speaking level of learners. Therefore, a score is obtained for each user.

Date of registration: Year part of registration date is extracted for this parameter.

In this paper, various criteria have been used to calculate trust between two users. These criteria which are shown in Fig. 2 can be categorized in different forms:

Figure 2.  Various types of trust

Static versus dynamic criteria: Static trust is related to the prestige and profiles of the users. Dynamic trust is related to the behavioral characteristics including interaction between users, time of interaction, and users′ location.

Direct versus indirect criteria: Direct trust is the belief in a user calculated by direct experience of trustor with trustee^[53]. Attribute trust, and prestige trust are examples of this category. Indirect trust is calculated based on user activities and the responses of other users. Participation trust and interaction trust are a kind of indirect trust.

Descriptions of these trust types are provided in Sections 4.3.1 to 4.3.7.

Users having similar characteristics may become close to each other. Variables “age”, “country”, “gender”, “registration date”, and “year of birth” are used to calculate attribute trust.

where N is the number of attributes.

Interactions between users and the number of friends may represent the prestige of users. This type of prestige is called degree prestige which shows the attitude of other users to a user. However, considering the social network as a graph, some links between users may have negative or positive prestige affect. Therefore, the number of links is not enough as a variable. So, prestige trust is defined as follows:

Interaction trust is a type of behavioral trust of a user. Length of communication, frequency of communication, and time of communication between two users is used to calculate interaction trust:

where ∆t is the length of communication, t_z represents how much time has passed from interaction z, $\rho $ is a number between 0 and 1, and n is the number of interactions.

Similar locations can lead to increased trust among users. The locations of users are identified using IP number:

Participation trust is a type of indirect trust which shows the degree which a user is involved in sharing posts at network. Participation trust is calculated as follows:

In the social network of Saadi Foundation, users can send photos or texts privately to each other. Usually, users interact with their trusted users in the closing hours of the day and at night. Therefore, based on the time of messages^[12], time trust is calculated as follows:

In social networks, each user has several friends. Two users which have a great numbers of shared friends are more likely to trust each other. Therefore, the size of shared neighbors divided by total number of friends of two users shows friends trust as follows:

In this section, the method of combination, aggregation and transition of trust values in a social network is investigated.

Trust combination. In Section 4.3, various trust values are defined. Therefore, different trust values can be acquired between two users. In this step, these values are combined to create a single trust value as follows:

Trust transition. As mentioned before, users are clustered and each user may be a member of each of the clusters regarding membership values. Considering the whole social network as a graph, two users are connected to each other if they belong to the same cluster. If two users are not connected to each other directly, we can calculate the trust value based on the intermediate users. For example, consider user A who belongs to cluster c₁, user B who belongs to clusters c₁ and c₂, and user C who belongs to cluster c₂. Therefore, two users A and C are connected to each other indirectly and the trust value is calculated considering user B as an intermediate user. The trust value between users A and B is calculated as follows:

where B_i are intermediate users.

If such path does not exist, trust value is considered zero.

Trust aggregation.

Suppose two users A and C are present in several clusters at the same time. In this case, a trust value is calculated in each cluster. Similarly, suppose two users A and C are not in the same cluster, but there are different paths between them, and a trust value is calculated per path. In this case, the trust value between the two users is obtained from the following formula:

where $ Trust\left( {A,C} \right)$ is the value of trust obtained through the cluster or path k.

In order to implement and evaluate the proposed method, the Java programming language has been used. The dataset used in this evaluation is the social network of the Saadi Foundation, which was described in Section 3. In the proposed method, there are several parameters that, given different values, can deliver different results, which are further discussed in this section according to the evaluation results. In the first stage of implementation, the initial values are attributed to the parameters. Table 3 shows these values.

In order to evaluate the proposed method, a number of Saadi Foundation users have been asked to determine their trust in other members based on a questionnaire. The abbreviations and profile of participants participating in this test are shown in Tables 4 and 5 respectively.

In general, five trust categories are considered to evaluate the trust of users as follows:

“Very low” for the calculated value of 0 to 0.2

“Low” for the calculated value of 0.2 to 0.4

“Medium” for the calculated value of 0.4 to 0.6

“High” for calculated value of 0.6 to 0.8

“Very high” for the calculated value of 0.8 to 1

Finally, the values set by users are compared with the values obtained from the proposed method. The results for each of the categories are shown in Table 6.

In many cases, the user and the proposed method have created different but close outputs. For example, the user and the proposed method have respectively created “very low” and “low” trust outputs between the two users. In the initial evaluation of performance, in these cases, these two outputs are considered different. In the new evaluation, new categories are created, in which each category is created by combination of two categories in the vicinity. The results of this evaluation are also shown in Table 7. The results are also compared with a classification approach^[13] which has used various trust criteria to calculate trust between users.

The results show that clustering approach has higher performance than the classification approach. Especially in “high” group, precision and recall have been increased from 43% to 49%, and from 23% to 35% respectively.

As previously stated, it is difficult to calculate trust, and due to features such as subjectivity, it is not possible to calculate it accurately. However, some of the criteria can be considered individually, and the type of users′ attitude towards each of them, albeit approximate, is obtained. Moreover, in examining the questionnaire, it is discovered that several characteristics of the users are ignored in the proposed method. These features may affect the trust calculation. In Section 5.3, previous and new criteria are investigated.

The effect of an increase in the number of friends on the level of users′ trust is shown in Fig. 3. The vertical axis and horizontal axis represent the number of users and the number of friends, respectively. The number of users who selected group “very low” to express their trust to those whose number of friends is less than 10 is far more than the number of users who selected “high” or “very high”. The users also assigned “high” and “very high” trust to those whose number of friends is more than 50. So, with the increase in the number of friends, the choices of users are decreasing in the “very low” and “low” categories and increasing in the “very high” and “high” categories.

Figure 3.  Effect of the number of friends on the trust value^[13]

In Fig. 4, the impact of the increase in the number of posts on the level of user trust has been shown. The vertical axis and horizontal axis, respectively, represent the number of users and the number of posts. The level of trust to those whose number of posts in the social network is more than 50 is “moderate”, “high” and “very high” which means the direct impact of the number of posts on trust.

Figure 4.  Effect of the number of posts criterion on the level of trust^[13]

Prestige criterion is one of the criteria whose impact is very high in the more accurate calculation of trust. This criterion was calculated using the number and quality of friends. The calculated prestige for users in the Saadi Foundation database was between 0 and 0.56. Only 6.5% of users have prestige value above 0.1. However, 83% of trust values to these users are “high” and “very high”.

The level of similarity of IP addresses has a considerable effect on the calculating trust in the social network. The results show that 63% users with more than 0.75 location trust have selected “high” and “very high” categories in order to express their trust. Moreover, 68% users with low location trust have chosen “low” and “very low” categories.

In Fig. 5, the impact of the criterion of location trust is shown. The horizontal axis represents the value of location trust among users, and the vertical axis represents the number of users. The number of users whose location trust has been calculated to be zero has selected “low” and “very low” trust categories more than any other category. Also, the number of users whose location trust has been computed one, selected “very high” and “high” trust group more than any other group.

Figure 5.  Effect of location trust on the level of trust

In Section 5.3, experiments and evaluations were conducted in relation to the calculation of trust in which various criteria were used. Regarding the results and findings, it has been found that some of these criteria have a greater impact on the effectiveness of trust calculation similar to other research^[13]. Hence, in order to improve the performance of the proposed method, in the next experiments, effective measures are used. Therefore, in the extended method, the location trust, the number of friends, the number of posts, prestige trust, and friendship variables are among the criteria used to inference the new values of trust. The following formula is used to improve the efficiency of the trust calculation:

The results of the improved method, taking into account the key criteria in the initial groups and in the merged groups, are shown in Tables 8 and 9, respectively. Moreover, results are compared with the classification approach.

As it is seen, the efficiency of the improved method has increased compared to the initial version. In other words, the use of key criteria led to a more accurate inference of trust.

In this research, various criteria for calculating trust were considered. In the evaluations conducted in the first method, it was determined that similar to the other research^[13], location trust and prestige trust have a good effect on the inference of trust. The more the location trust of a user′s is closer to one, the greater their trust is in one another. User prestige also has a direct impact on the trust of others.

Improved results were obtained by examining the responses of users to the extent of their trust in others and consideration of other features affecting their attitude to others, such as the number of common friends, friendships communication, activities, and friends. Once again, trust was calculated based on these features. So, the precision criterion is increased by a mean of 17% compared to the first method. The mean calculated precision in the first method was 39% and in the second method was 56%. The F-Measure and recall values have also been increased by an average of 4% and 7%, indicating a good performance of the improved method.

There are other methods to infer trust that can be used according to the type of application. In a future work, an effective way of calculating trust could be to identify clusters in social networks using other fuzzy clustering methods. Users in the same community are more likely to trust each other. Therefore, identifying the communities in the social networks can increase the efficiency of trust inference. In subsequent studies, the calculation of trust through other fuzzy clustering methods will be studied.

One of the important challenges in social networks is the weights of criteria which are considered in trust inference process. These weights can be different depending on the context and nature of social networks. Machine learning techniques can be used to identify these weights. Therefore, the other future work is using machine learning techniques to identify the role and weights of various trust criteria effectively.

This work was supported by the Allameh Tabataba′i University. The anonymous people who helped us to perform the empirical study are appreciated. Specially, Miss Mehdikhanloo is appreciated for providing the Saadi dataset.