Karate Club Research Articles

Community detection in social networks using machine learning: a systematic mapping study

AbstractOne of the important issues in social networks is the social communities which are formed by interactions between its members. Three types of community including overlapping, non-overlapping, and hidden are detected by different approaches. Regarding the importance of community detection in social networks, this paper provides a systematic mapping of machine learning-based community detection approaches. The study aimed to show the type of communities in social networks along with the algorithms of machine learning that have been used for community detection. After carrying out the steps of mapping and removing useless references, 246 papers were selected to answer the questions of this research. The results of the research indicated that unsupervised machine learning-based algorithms with 41.46% (such as k means) are the most used categories to detect communities in social networks due to their low processing overheads. On the other hand, there has been a significant increase in the use of deep learning since 2020 which has sufficient performance for community detection in large-volume data. With regard to the ability of NMI to measure the correlation or similarity between communities, with 53.25%, it is the most frequently used metric to evaluate the performance of community identifications. Furthermore, considering availability, low in size, and lack of multiple edge and loops, dataset Zachary’s Karate Club with 26.42% is the most used dataset for community detection research in social networks.

The Relationship of Power Lemb Agility and Hip Joint Fitness to the Results of the Mawashi Geri Kick in the Sport Branch of Karate

Athletes often practice, not all of them have mastered the mawashi geri kick technique, the lack of effective leg power, agility and flexibility of the hip joint when the athlete performs the mawashi geri kick attack has an effect on the athlete's performance not being optimal. The aim of this research was to determine "the relationship between leg power, agility and hip joint flexibility on the results of mawashi geri kicks in the sport of karate". The research method uses quantitative descriptive methods with a correlational approach. The population in this study were Sukabumi City BKC athletes with a sampling technique using purposive sampling, so the research sample was 14 athletes who took part in the West Java BKC Provincial Championship. The results of the research show that: 1) there is a significant relationship between leg power and the results of the mawashi geri kick in the sport of karate, which is 53.80%. 2) there is a significant relationship between agility (X2) and the results of the mawashi geri kick in the sport of karate (Y) which is 55.40%. 3) there is a significant relationship between hip joint flexibility (X3) and the results of the mawashi geri kick in karate (Y) which is 55.60%. There are three independent variables, namely leg power, agility and hip joint flexibility, which together have a significant influence on the results of the mawashi geri kick in the sport of karate at the Bandung Karate Club (BKC) Sukabumi City, amounting to 74.50%.

Large-scale group decision-making involving community representatives: A perspective of combining strong and weak ties

In the era of social media, the issue of large-scale group decision-making (LSGDM) is becoming increasingly prominent. The complexity of large group interactions increases rapidly with the expansion of the group size. Current research has often used cluster analysis to reduce the dimensionality of LSGDM, but the decision agents following dimensionality reduction are not clearly defined, which hinders the practical application of LSGDM methods. This paper studies the LSGDM through the context of community representatives which are determined by combining strong and weak ties. The participation of such representatives in subsequent decision-making can reduce negotiation costs and efficiently form a consensus from both global and local perspectives. To identify these community representatives, this study improves the traditional Laplacian centrality, calculates the local and global centrality of individuals, and defines metrics for measuring representatives. The opinion dynamics model is used to verify the effectiveness of the LSGDM model with community representatives. The karate club network is used to illustrate the application of the proposed LSGDM model. Simulation and comparative analysis results show that the proposed model takes less time to reach consensus than traditional ones. Furthermore, there is no complete linear relationship between the representative size and the time taken to reach group consensus.

Karate Sporu Yapan Kişilerin Karate Sporuna Olan İlgi Düzeylerinin İncelenmesi

This study aims to determine the participants’ level of involvement who are engaged in karate in Adana and whether this involvement differs according to the demographic variables of the people. The data were collected from karate clubs in Adana via a survey. Analyses were carried out on 268 valid surveys. According to the analysis results, the participants' involvement in karate shows significant differences according to marital status, age, how many years karate has been practised, how often karate is practised and going out of province for karate purposes. Besides, while the dimension with the highest mean of the scale of involvement in karate sport is "Attraction" (x̄=4,54), the dimension with the lowest average is "Identity Expression" (x̄=3.57). Lastly, the general average of the scale items is x̄=4,01. Based on this, it can be interpreted that the participants' interest in karate is generally high. These results highlight the positive tendencies of individuals involved in karate and underline the attractiveness and importance of the activity in their lives.

Improving modularity score of community detection using memetic algorithms

<abstract> <p>With the growth of online networks, understanding the intricate structure of communities has become vital. Traditional community detection algorithms, while effective to an extent, often fall short in complex systems. This study introduced a meta-heuristic approach for community detection that leveraged a memetic algorithm, combining genetic algorithms (GA) with the stochastic hill climbing (SHC) algorithm as a local optimization method to enhance modularity scores, which was a measure of the strength of community structure within a network. We conducted comprehensive experiments on five social network datasets (Zachary's Karate Club, Dolphin Social Network, Books About U.S. Politics, American College Football, and the Jazz Club Dataset). Also, we executed an ablation study based on modularity and convergence speed to determine the efficiency of local search. Our method outperformed other GA-based community detection methods, delivering higher maximum and average modularity scores, indicative of a superior detection of community structures. The effectiveness of local search was notable in its ability to accelerate convergence toward the global optimum. Our results not only demonstrated the algorithm's robustness across different network complexities but also underscored the significance of local search in achieving consistent and reliable modularity scores in community detection.</p> </abstract>

A social network group decision making framework with opinion dynamics considering opinion reliability

Opinion dynamics play an important role in the consensus reaching process (CRP) when tackling social network group decision making (SNGDM) problems. Opinion reliability can be regarded as an important characteristic of expert to indicate the reliability of experts’ opinions in social trust network. However, it has rarely been considered into the opinion evolution process in SNGDM. To explore the impact of opinion reliability on group consensus reaching, a SNGDM framework with opinion dynamics considering opinion reliability is proposed in this paper. Firstly, opinion reliability of experts in social trust network is defined, and the comprehensive trust degree based on the social network structure and individual characteristic is proposed. Secondly, trust propagation and aggregation mechanisms are designed to obtain the social trust matrix. Thirdly, considering opinion similarity and opinion reliability, social network evolution rules and opinion evolution rules based on the extended Hegselmann-Krause (HK) model are presented. Finally, the proposal is applied to two numerical experiments about supplier performance evaluation and Zachary's karate club, and the simulation and comparison analyses are provided to demonstrate the convergence and illustrate the feasibility and effectiveness of the proposed model.

Efficient Spectral Graph Convolutional Network Deployment on Memristive Crossbars

Graph Neural Networks (GNNs) have attracted increasing research interest for their remarkable capability to model graph-structured knowledge. However, GNNs suffer from intensive data exchange and poor data locality, which will cause critical performance and energy bottlenecks under conventional complementary metal oxide semiconductor (CMOS)-based von-Neumann computing architectures (graphics processing unit (GPU), central processing unit (CPU)) for the “Memory Wall” issue. Fortunately, memristive crossbar-based computation has emerged as one of the most promising neuromorphic computing architectures, which has been widely studied as the computing platform for convolutional neural network (CNNs), recurrent neural network (RNNs), spiking neural network (SNNs), etc. This paper proposes the deployment of spectral graph convolutional networks (GCNs) on memristive crossbars. Further, based on the structure of GCNs (extremely high sparsity and unbalanced non-zero data distribution) and the neuromorphic characteristics of memristive crossbar circuit, we propose the acceleration method that consists of Sparse Laplace Matrix Reordering and Diagonal Block Matrix Multiplication. The simulated experiment on memristor crossbars achieves 90.3% overall accuracy on the supervised learning graph dataset (QM7), and compared with the original computation, the proposed acceleration computing framework (with half-size diagonal blocks) achieves a 27.3% reduction of memristor number. Additionally, on the unsupervised learning dataset (Karate club), our method shows no loss of accuracy with half-size diagonal block mapping and reaches a 32.2% reduction of memristor number.

Community Detection by Node Betweenness Using Optimized Girvan-Newman Cuckoo Search Algorithm

Due to technological development, social media platforms like forums and microblogs allow people to share their experiences, thoughts, and feelings. The organization, shopping groups etc. has major discussions regarding their business advertisements and product reviews. Also, there are certain followers for particular person or group due to their interests. Here the major issue is to know who or which group in social media is more influenced. The social media analysis needs to perform for identifying influenced person in the social media. The influencer node/person detection in a certain community is already done using greedy algorithm, genetic algorithm, ant colony optimization, cuckoo search algorithms. These existing techniques takes more time for diffusion and accuracy in prediction is not satisfied by users. To overcome this issues, in this research influencer node is identified using optimized Girvan Newman Cuckoo Search Algorithm (GNCSA). First Grivan Newman is used to identify the community and perform community detection. Cuckoo search algorithm uses host bird strategy in finding cuckoo eggs in his nest. Based on the centrality measure it decides whether the node is an influencer or not. This paper proposed Influencer detection by forming community first and measures angular centrality using optimized Girvan Newman cuckoo search algorithm. Our proposed work GNCSA gives a better accuracy rate for the data sets of Dolphin 0.89, for Facebook dataset got 0.93, Twitter data set got 0.94 and for YouTube data set 0.92, karate club and football got 0.91. This proposed work increases the intracommunity of the social network and improves its performance accurately by detecting the influencer in the social network.

TÌM KIẾM CỘNG ĐỒNG MẠNG DỰA TRÊN TÍNH GÓC GIỮA HAI VÉC TƠ

Recently, the problem of community detection has attracted the attention of many scientists. Most types of networks such as computer networks, biological networks and social networks, have a community structure. Community detection helps to understand the structure and properties of that real network. There have been many algorithms with different approaches, including coordinating vertices and building appropriate distances between them. In this paper, a random walk has been used to coordinate the vertices of the graph and use the cosine of the angle between two vectors to detect network communities. The article also presents the Modularity function to evaluate graph clustering. Some experimental results on randomly generated graphs and graphs generated from the real data set Zachary's karate club network have been presented and compared with the K-means++ algorithm.

أثر برنامج تدريبي مقترح للدورة التأسيسية على المهارات التأسيسية وتركيب الجسم لدى منتسبي أندية الكاراتيه في محافظة جنين-فلسطين

The study aimed to identify the effect of a proposed training program for the foundation course of the basic skills and body composition of the members of karate clubs in the governorate of Jenin – Palestine. The researchers used the experimental approach due to its suitability to the nature and objectives of the study. To achieve this, the study was conducted on a carefully chosen sample of karate clubs (the Talented Academy of Physical Fitness and self Defense, Arrabah Karate Club and Zababdeh Karate Club). The sample consisted of 50 members, 10 of those members were of exploratory sample, and the rest 40 members were considered as a basic sample that had been divided randomly into two groups. 20 members of experimental group and 20 members of control group. The researchers used Tanita DC-360 P to measure body components and in addition to a set of tests that measure basic skills. The training program was applied for a period of (10) weeks with (3) training sessions per week. Each training session took (60) minutes. In addition, the statistical packages program was used to analyze the data. The results showed that there were differences among the members of the experimental group between the pre and post measurements of body composition and basic skills. The results also indicated that there were no statistically significant differences between the members of the experimental and control groups in the post-measurement of body composition, while the results showed that there were statistically significant differences in the post-measurement of basic skills in karate, which came in favor of the members of the experimental group. The researchers recommended to the need to take account of the training program proposed by the coaches of karate clubs (kata) in the West Bank, especially in the training phase for basic karate skills. هدفت الدراسة التعرف إلى أثر برنامج تدريبي مقترح للدورة التأسيسية على المهارات الأساسية وتركيب الجسم لدى منتسبي أندية الكاراتيه في محافظة جنين- فلسطين، واستخدم الباحثون المنهج التجريبي وذلك لملائمته لطبيعة وأهداف الدراسة، ولتحقيق ذلك أجريت الدراسة على عينة عمدية من أندية (أكاديمية الموهوبين للياقة البدنية والدفاع عن النفس، نادي عرابة للكاراتيه، نادي الزبابده للكاراتيه) حيث بلغت (50) منتسباً منها (10) منتسبين عينة استطلاعية و((40 منتسباً عينة أساسية، قسمت بشكل عشوائي لمجموعتين مجموعة تجريبية مكونة من ((20 منتسباً ومجموعة ضابطة مكونة من ((20 منتسباً، واستخدم الباحثون جهاز التانيتا (Tanita DC-360) لقياس مكونات الجسم ومجموعة من الاختبارات التي تقيس المهارات الأساسية وطبق عليهم البرنامج التدريبي لمدة (10) أسابيع بواقع ثلاث حصص تدريبية أسبوعياً زمن كل حصة تدريبية (60) دقيقة، وتم استخدام برنامج الرزم الإحصائية (SPSS) لتحليل البيانات. أظهرت النتائج وجود فروق لدى أفراد المجموعة التجريبية بين القياسين القبلي والبعدي في مكونات تركيب الجسم والمهارات الأساسية، كما أشارت إلى عدم وجود فروق دالة إحصائياً بين أفراد المجموعتين التجريبية والضابطة في القياس البعدي لمكونات تركيب الجسم، بينما أظهرت النتائج وجود فروق دالة إحصائياً في القياس البعدي للمهارات الأساسية في الكاراتيه وجاءت لصالح أفراد المجموعة التجريبية. وأوصى الباحثون بضرورة الاسترشاد بالبرنامج التدريبي المقترح من قبل مدربي أندية الكاراتيه (الكاتا) في الضفة الغربية خاصة في مرحلة التدريب على مهارات رياضة الكاراتيه الأساسية.

Unsupervised Learning-based New Seed-Expanding Approach using Influential Nodes for Community Detection in Social Networks

Several recent studies focus on community structure due to its importance in analyzing and understanding complex networks. Communities are groups of nodes highly connected with themselves and not much connected to the rest of the network. Community detection helps us to understand the properties of the dynamic process within a network. In this paper, we propose a novel seed-centric approach based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and k-means algorithm to find communities in a social network. TOPSIS is used to find the seeds within this network using the benefits of multiple measure centralities. The use of a single centrality to determine seeds within a network, like in classical algorithms of community detection, doesn’t succeed in the majority of cases to reach the best selection of seeds. Therefore, we consider all centrality metrics as a multi-attribute of TOPSIS and we rank nodes based on the TOPSIS’ relative closeness. The Top-K nodes extracted from TOPSIS will be considered as seeds in the proposed approach. Afterwards, we apply the k-means algorithm using these seeds as starting centroids to detect and construct communities within a social network. The proposed approach is tested on Facebook ego network and validated on the famous dataset having the ground-truth community structure Zachary karate club. Experimental results on Facebook ego network show that the dynamic k-means provides reasonable communities in terms of distribution of nodes. These results are confirmed using Zachary karate club. Two detected communities are detected with higher normalized mutual information NMI and Adjusted Rand Index ARI compared to other seed centric algorithms such as Yasca, LICOD, etc. The proposed method is effective, feasible, and provides better results than other available state-of-the-art community detection algorithms.

Distributed Network Embedding: A Distributed Control Approach for Undirected Networks

In this paper, a new network embedding method is proposed for an effective network representation of vertices. While the existing embedding methods have embedded a set of vertices via network representation learning in a fully centralized way, we present a novel distributed network embedding (DNE) method without representation learning. By coupling first-order proximity and second-order proximity with distance embedding constraints, a distributed and explicit embedding protocol steers a set of vertices in a vector space to preserve local and global structural information of networks. The proposed method does not require representation learning process, and is distributed, explicit, and straightforward. Therefore, we expect our approach to be fast, cost-effective, especially suitable for dynamic networks, and robust for sparse networks. Lastly, numerical experiments will briefly validate the proposed embedding method using a well-known Zachary's karate club network.

Mental Imagery: Competitive Anxiety Control in Karate Kumite Athlete

This study aimed to test the effect of mental imagery training on the competitive anxiety of karate Kumite athletes. One of the benefits of mental imagery is that it can improve the athlete's ability to control psychological symptoms such as anxiety. So that athletes can show their best performance during the game. This research used quantitative methods with an experimental approach, the pretest-posttest control and an experimental group design. The population used West Java regional karate athletes, totalling 42 athletes. Using purposive sampling techniques, the samples consisted of 15 Bandung Karate Club Kumite athletes and 15 Kei Shin Kan Kumite athletes. Data were obtained using The Hogg Eco-Anxiety Scale. Based on the results of the data analysis obtained, the average experimental pretest of 25.20 and posttest of 20.00 showed a decrease in the anxiety of Kumite athletes after being given imagery training. In addition, the N-Gain scores in both groups show decreased pressure in Kumite athletes. However, the N-Gain score in the experimental group was lower than the control group (-23.60 < 3.56), and in the t-test on the N-Gain value, the score obtained the Sig. Value (2-tailed) was 0.005 < α = 0.05. So it can be concluded that imagery training affects the competitive anxiety of Kumite athletes, and there are significant differences in effectiveness in applying imagery training with conventional exercises

Maximum A Posteriori Inference of Random Dot Product Graphs via Conic Programming

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.

The Relationship of Goal Orientation, Self-Esteem, Situational Motivation and Satisfaction From Sports Among Young Karate Athletes

The main problem of the research was to determine the relationship between goal orientation, satisfaction, self-esteem, and situational motivation among young karate athletes from Republic of North Macedonia. The research was carried out on a sample of 100 respondents who are engaged in karate sport between the ages of 11 and 14 from Republic of North Macedonia. The sample is divided into two subsamples according to gender, namely 54 male respondents and 45 female respondents. The sample was drawn from several karate clubs in Republic of North Macedonia. In order to realize the goals of the research, several scales were applied to assess goal orientation, satisfaction, self-esteem and situational motivation. The obtained data were processed with appropriate parametric statistical methods. Based on the obtained results, it can be concluded that a larger number of respondents (young karate athletes) from our sample are more focused on developing and improving their competence, and less on achieving results and relying on their abilities. Interrelationships among the four subscales assessing the level of self-determination to be physically active, as expected the more proximal along the continuum are more positively correlated with task orientation than those more distal along the continuum. The research results confirm that task orientation is more positively related to more self-determined types of situational motivation (the internal motivational regulator -intrinsic motivation and the identification motivational regulator -identified regulation) and negatively related to less self-determined types of situational motivation (external motivational regulator- external regulation and guilt regulator - introjected regulation). Based on all that has been stated, it can be concluded that among young karate athletes aged 11 to 14, internal motives (i. e. fun, personal challenge, etc.) or so-called essential motives for playing sports should be promoted.

A Dynamic Community Detection Method for Complex Networks Based on Deep Self-Coding Network

Aiming at the problem of community detection in complex dynamic networks, a dynamic community detection method based on graph convolution neural network is proposed. An encoding-decoding mechanism is designed to reconstruct the feature information of each node in the graph. A stack of multiple graph convolutional layers is considered as an encoder that encodes the node feature information into the potential vector space, while the decoder employs a simple two-layer perceptron to reconstruct the initial node features from the encoded vector information. The encoding-decoding mechanism achieves a re-evaluation of the initial node features. Subsequently, an additional local feature reconstruction loss is added after the decoder to aid the goal of graph classification. Further, stochastic gradient descent is applied to solve the problem in the loss function. Finally, the proposed model is experimentally validated based on the Karate Club and Football datasets. The experimental results show that the proposed model improves the NMI metric by an average of 7.65% and effectively mitigates the node oversmoothing problem. The proposed model is proved to have good detection accuracy.

Analyzing the extremization of opinions in a general framework of bounded confidence and repulsion

In the bounded confidence framework, agents’ opinions evolve as a result of interactions with other agents having similar opinions. Thus, consensus or fragmentation of opinions can be reached, but not extremization (the evolution of opinions towards an extreme value). In contrast, when repulsion mechanisms are at work, agents with distant opinions interact and repel each other, leading to extremization. This work proposes a general opinion dynamics framework of bounded confidence and repulsion, which includes social network interactions and agent-independent time-varying rationality. We extensively analyze the performance of our model to show that the degree of extremization among a population can be controlled by the repulsion rule, and social networks promote extreme opinions. Agent-based rationality and time-varying adaptation also bear a strong impact on opinion dynamics. The high accuracy of our model is determined in a real-world social network well referenced in the literature, the Zachary Karate Club (with a known ground truth). Finally, we use our model to analyze the extremization of opinions in a real-world scenario, in Spain: a marketing action for the Netflix series “Narcos”.

A hybrid approach for predicting missing follower–followee links in social networks using topological features with ensemble learning

PurposeSocial networking platforms are increasingly using the Follower Link Prediction tool in an effort to expand the number of their users. It facilitates the discovery of previously unidentified individuals and can be employed to determine the relationships among the nodes in a social network. On the other hand, social site firms use follower–followee link prediction (FFLP) to increase their user base. FFLP can help identify unfamiliar people and determine node-to-node links in a social network. Choosing the appropriate person to follow becomes crucial as the number of users increases. A hybrid model employing the Ensemble Learning algorithm for FFLP (HMELA) is proposed to advise the formation of new follower links in large networks.Design/methodology/approachHMELA includes fundamental classification techniques for treating link prediction as a binary classification problem. The data sets are represented using a variety of machine-learning-friendly hybrid graph features. The HMELA is evaluated using six real-world social network data sets.FindingsThe first set of experiments used exploratory data analysis on a di-graph to produce a balanced matrix. The second set of experiments compared the benchmark and hybrid features on data sets. This was followed by using benchmark classifiers and ensemble learning methods. The experiments show that the proposed (HMELA) method predicts missing links better than other methods.Practical implicationsA hybrid suggested model for link prediction is proposed in this paper. The suggested HMELA model makes use of AUC scores to predict new future links. The proposed approach facilitates comprehension and insight into the domain of link prediction. This work is almost entirely aimed at academics, practitioners, and those involved in the field of social networks, etc. Also, the model is quite effective in the field of product recommendation and in recommending a new friend and user on social networks.Originality/valueThe outcome on six benchmark data sets revealed that when the HMELA strategy had been applied to all of the selected data sets, the area under the curve (AUC) scores were greater than when individual techniques were applied to the same data sets. Using the HMELA technique, the maximum AUC score in the Facebook data set has been increased by 10.3 per cent from 0.8449 to 0.9479. There has also been an 8.53 per cent increase in the accuracy of the Net Science, Karate Club and USAir databases. As a result, the HMELA strategy outperforms every other strategy tested in the study.

Comparative Analysis of Overlap Community Detection Techniques on Social Media Platform

Abstract Community structure over social media (SM) is the collaborative group of globally spread users with identical characteristics and ideologies. The collective features of SM are inherent with both the implicit and explicit nature of end-users. This paper presents an analytical and methodological community detection framework to bind passive users’ implicit and explicit nature after scrutinizing graphical data to identify seed nodes and communities. Moreover, this work provides the concept of the unsupervised machine learning approach over the graphical perspective of SM to identify the trade-off between similarity of nodes attributes and density of connections for social theories. Subsequently, this paper evaluates a comprehensive analysis of the benchmark community detection algorithm (CDA) Label Propagation Algorithm (LPA), Clique Percolation Method (CPM), Democratic Estimate of the Modular Organization of a Network (DEMON) and Non-Negative Matrix Factorization (NMF). The evaluation has been carried out over modularity and normalized mutual information of resultant structured community on six real-time SM data set. The performance of benchmark CDAs is significantly increased after incorporating social theories. NMF, DEMON, CPM and LPA gained the highest improvement over Zachary’s Karate Club data sets, i.e. approximate 26.91%, 21.68%, 18.79%, 19.96%, respectively.

Generalized fuzzy variable precision rough sets based on bisimulations and the corresponding decision-making.

Recently, the classical rough set has been extended in many ways. However, some of them are based on binary relations which only excavate “one step” information to distinguish objects. The “one step” in the binary relation means that the ordered pair of the starting and end points of the step belongs to the relation. Faced with some complex data sets, the “one step” information may be not feasible. Motivated by the notion of bisimulation in computer science, three types of bisimulation-based generalized fuzzy variable precision rough set (BGFVPRS) models are constructed. Different from many existed rough set models which are based on binary relations, the BGFVPRS models can distinguish objects by excavating the “multi-step” information of underlying relations. The related properties and relationships of BGFVPRS models are investigated. The uncertainty measure of BGFVPRS models and the reduction of fuzzy bisimulations are also discussed. Furthermore, learning from the PROMETHEE II method and combining it with our presented BGFVPRS models, a novel multiple-attribute decision-making method is provided. This method can effectively deal with complex problems including attribute data and relational data. The flexibility and effectiveness of our decision-making method are illustrated by comparative analysis and sensitivity analysis in the Zachary karate club network.