Search Results (34)

Background and objectives: Large language models (LLMs) show promise in automating open-ended evaluation tasks, yet their reliability in rubric-based assessment remains uncertain. Variability in scoring, feedback, and rubric adherence raises concerns about transparency and pedagogical validity in educational contexts. This study introduces CourseEvalAI, a framework designed to enhance consistency and fidelity in rubric-guided evaluation by fine-tuning a general-purpose LLM with authentic university-level instructional content. Methods: The framework employs supervised fine-tuning with Low-Rank Adaptation (LoRA) on rubric-annotated answers and explanations drawn from undergraduate computer science exams. Responses generated by both the base and fine-tuned models were independently evaluated by two human raters and two LLM judges, applying dual-layer rubrics for answers (technical or argumentative) and explanations. Inter-rater reliability was reported as intraclass correlation coefficient (ICC(2,1)), Krippendorff’s α, and quadratic-weighted Cohen’s κ (QWK), and statistical analyses included Welch’s t tests with Holm–Bonferroni correction, Hedges’ g with bootstrap confidence intervals, and Levene’s tests. All responses, scores, feedback, and metadata were stored in a Neo4j graph database for structured exploration. Results: The fine-tuned model consistently outperformed the base version across all rubric dimensions, achieving higher scores for both answers and explanations. After multiple-testing correction, only the Generative Pre-trained Transformer (GPT-4)—judged Technical Answer contrast remains statistically significant; other contrasts show positive trends without passing the adjusted threshold, and no additional significance is claimed for explanation-level results. Variance in scoring decreased, inter-model agreement increased, and evaluator feedback for fine-tuned outputs contained fewer vague or critical remarks, indicating stronger rubric alignment and greater pedagogical coherence. Inter-rater reliability analyses indicated moderate human–human agreement and weaker alignment of LLM judges to the human mean. Originality: CourseEvalAI integrates rubric-guided fine-tuning, dual-layer evaluation, and graph-based storage into a unified framework. This combination provides a replicable and interpretable methodology that enhances the consistency, transparency, and pedagogical value of LLM-based evaluators in higher education and beyond. Full article

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article

Product Service Systems (PSS) integrate technical systems, digital infrastructure, and digital and physical services to deliver value to customers in a comprehensive way throughout the life cycle of the PSS. While the potential benefits of PSSs, such as economic efficiency and sustainability, are well-recognized, their implementation and evaluation are often hindered by significant complexities and uncertainties, particularly in the early concept phase. This paper introduces a graph-based reasoning approach that enables the evaluation of PSS concepts despite vague and uncertain understanding. By defining key characteristics in the value creation process qualitatively in distinct and probabilistic states, the graph model makes the concept executable and allows for transparent evaluation. The approach actively considers knowledge gaps and variations in the PSS concept, offering insight into how uncertainties and alternative configurations impact system performance. A case study of a PSS for metal powder recycling in additive manufacturing is conducted to validate the method, demonstrating its applicability for PSS concept evaluation. Full article

Background: Transcutaneous auricular vagus nerve stimulation (taVNS) is effective in regulating mood and high-level cognition in patients with major depressive disorder (MDD). This study aimed to investigate the efficacy of taVNS treatment in patients with MDD and an altered brain topological organization of functional networks. Methods: Nineteen patients with MDD were enrolled in this study. Patients with MDD underwent 4 weeks of taVNS treatments; resting-state functional magnetic resonance imaging (rs-fMRI) data of the patients were collected before and after taVNS treatment. The graph theory method and network-based statistics (NBS) analysis were used to detect abnormal topological organizations of functional networks in patients with MDD before and after taVNS treatment. A correlation analysis was performed to characterize the relationship between altered network properties and neuropsychological scores. Results: After 4 weeks of taVNS treatment, patients with MDD had increased global efficiency and decreased characteristic path length (Lp). Additionally, patients with MDD exhibited increased nodal efficiency (NE) and degree centrality (DC) in the left angular gyrus. NBS results showed that patients with MDD exhibited reduced connectivity between default mode network (DMN)–frontoparietal network (FPN), DMN–cingulo-opercular network (CON), and FPN–CON. Furthermore, changes in Lp and DC were correlated with changes in Hamilton depression scores. Conclusions: These findings demonstrated that taVNS may be an effective method for reducing the severity of depressive symptoms in patients with MDD, mainly through modulating the brain’s topological organization. Our study may offer insights into the underlying neural mechanism of taVNS treatment in patients with MDD. Full article

In the context of crowd innovation and the generative design driven by big language models, the exploration of personalized requirements has become a key in significantly improving product innovation, concept feasibility, and design interaction efficiency. To mine a large number of vague and unexpressed implicit requirements of personalized products, a domain knowledge graph-based method is proposed in this research. First, based on the classical theory of design science, the characteristics and categories of personalized implicit requirements are analyzed, and the theoretical basis of implicit requirement mining is formed. Next, in order to improve the practicability and construction efficiency of the domain knowledge graph, a more informative ontology is constructed, and better-performing natural language processing (NLP) models are proposed. Then, a multi-category personalized implicit requirement mining method based on a knowledge graph is proposed. Finally, a platform was developed based on the technical solution proposed in this study, and an example verification was conducted in the field of electromechanical engineering. The efficiency improvement of the training model proposed in the research was analyzed, and the practicality of implicit requirement mining methods are discussed. Full article

In this paper, we consider a wireless sensor network consisting of an unmanned aerial vehicle (UAV) acting as a sink node and a number of sensor nodes scattered uncertainly on the ground. In the network, the UAV flies to a spatial point called point of interest and hovers to collect environmental data from neighboring sensor nodes. Then, the UAV proceeds to the next point of interest. The UAV must gather data from all the sensor nodes. On the other hand, a shorter round-trip air route of the UAV is more preferred since a battery-operated UAV needs regular recharging. To satisfy the requirement and to adhere to the recommendation as well, especially in the situation where only vague locational information about sensor nodes is available, we propose a scheme that follows three steps. First, it covers the sensor field of the wireless sensor network with three categories of hexagonal tessellations. Secondly, it establishes a point of interest at the centroid of each tile. Thirdly, it constructs an air route of the UAV, which visits every point of interest along a Hamiltonian cycle on the induced graph. Next, we develop a closed-form expression for the exact flight distance attained by the proposed scheme. For comparative evaluation, we discover some optimal schemes that minimize the flight distance by completely inspecting all patterns and corroborating the property of Hamiltonicity. The flight distance along the air route constructed by the proposed scheme is found to be only slightly longer than the flight distance yielded by an optimal scheme. Furthermore, the proposed scheme is proven to be practically valid when a common multicopter is employed as the sink node. Full article

Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of $\mathcal{I}n$-pair , strong $\mathcal{I}n$-pair, $\mathcal{I}n$-cut vertex, $\mathcal{I}n$-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced. Full article

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as it enhances the space of uncertainty. It broadens the space of vague information evaluated by decision makers since graphs are the pictorial representation of information. Graphs are a tool to represent a network. To handle some real-world problems, spherical fuzzy graphs can be used more effectively as compared to picture fuzzy graphs (PFGs). In this article, we expand the notion of fuzzy Zagreb indices of the fuzzy graph to the spherical fuzzy Zagreb indices of the spherical fuzzy graph (SFG). The spherical fuzzy Zagreb matrix of SFG and Zagreb energy of SFG are defined with examples. Additionally, we develop several lower and upper bounds of the spherical Zagreb energy of SFG. In addition, we present an application of SFG by computing its Zagreb energy in the decision-making problem of choosing the best location for business purposes. Full article

This paper is devoted to the study of the double domination in vague graphs, and it is a contribution to the Special Issue “Advances in graph theory and Symmetry/Asymmetry” of Symmetry. Symmetry is one of the most important criteria that illustrate the structure and properties of fuzzy graphs. It has many applications in dominating sets and helps find a suitable place for construction. Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In the graph theory, a dominating set (DS) for a graph $G^{*}=(X,E)$ is a subset $\mathfrak{D}$ of the vertices X so that every vertex which is not in $\mathfrak{D}$ is adjacent to at least one member of $\mathfrak{D}$. The subject of energy in graph theory is one of the most attractive topics serving a very important role in biological and chemical sciences. Hence, in this work, we express the notion of energy on a dominating vague graph (DVG) and also use the concept of energy in modeling problems related to DVGs. Moreover, we introduce a new notion of a double dominating vague graph (DDVG) and provide some examples to explain various concepts introduced. Finally, we present an application of energy on DVGs. Full article

In graph theory, a “dominating vertex set” is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in the dominating set “dominate” the remaining vertices in the graph. Dominating vertex sets are important in graph theory because they can help us understand and analyze the behavior of a graph. For example, in network analysis, a set of dominant vertices may represent key nodes in a network that can influence the behavior of other nodes. Identifying dominant sets in a graph can also help in optimization problems, as it can help us find the minimum set of vertices that can control the entire graph. Now that there are theories about vagueness, it is important to define parallel ideas in vague structures, such as intuitionistic fuzzy graphs. This paper describes a better way to find dominating vertex sets (DVSs) in intuitive fuzzy graphs (IFGs). Even though there is already an algorithm for finding DVSs in IFGs, it has some problems. For example, it does not take into account the vertex volume, which has a direct effect on how DVSs are calculated. To address these limitations, we propose a new algorithm that can handle large-scale IFGs more efficiently. We show how effective and scalable the method is by comparing it to other methods and applying it to water flow. This work’s contributions can be used in many areas, such as social network analysis, transportation planning, and telecommunications. Full article

Problems of preeclampsia sign diagnosis are mostly based on symptom data with the characteristics of data collected periodically in uncertain, ambiguous, and obstetrician opinions. To reduce the effects of preeclampsia, many studies have investigated the disease, prevention, and complication. Conventional fuzzy inference techniques can solve several diagnosis problems in health such as fuzzy inference systems (FIS), and Mamdani complex fuzzy inference systems with rule reduction (M-CFIS-R), however, the computation time is quite high. Recently, the research direction of approximate inference based on fuzzy knowledge graph (FKG) has been proposed in the M-CFIS-FKG model with the combination of regimens in traditional medicine and subclinical data gathered from medical records. The paper has presented a proposed model of FKG-Pairs3 to support patients’ disease diagnosis, together with doctors’ preferences in decision-making. The proposed model has been implemented in real-world applications for disease diagnosis in traditional medicine based on input data sets with vague information, quantified by doctor’s preferences. To validate the proposed model, it has been tested in a real-world case study of preeclampsia signs in a hospital for disease diagnosis with the traditional medicine approach. Experimental results show that the proposed model has demonstrated the model’s effectiveness in the decision-making of preeclampsia signs. Full article

Vague graphs (VGs), belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. A vague fuzzy graph structure (VFGS) is the generalization of the VG. It is a powerful and useful tool to find the influential person in various relations. VFGSs can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problems where fuzzy graphs may fail to reveal satisfactory results. Moreover, VGSs are very useful tools for the study of different domains of computer science such as networking, social systems, and other issues such as bioscience and medical science. The subject of energy in graph theory is one of the most attractive topics that is very important in biological and chemical sciences. Hence, in this work, we extend the notion of energy of a VG to the energy of a VFGS and also use the concept of energy in modeling problems related to VFGS. Actually, our purpose is to develop a notion of VFGS and investigate energy and Laplacian energy (LE) on this graph. We define the adjacency matrix (AM) concept, energy, and LE of a VFGS. Finally, we present three applications of the energy in decision-making problems. Full article

In this article, we present a novel framework for edge domination in vague incidence graphs (VIG). We introduce the notion of certain types of vague incidence graphs and extend the concepts of dominations into edge and incidence domination in VIG. In particular, we propose the idea of order, size in VIG, isolated vertex, and cardinalities related to a dominating set. Additionally, the strong and weak domination for VIG were obtained and discussed with some theorems to support the context. We also initiate some definitions of edge domination and incidence domination on VIG and propose a model for the application of edge and incidence domination on VIG. Full article

A dynamic uncertain causality graph (DUCG) is a probabilistic graphical model for knowledge representation and reasoning, which has been widely used in many areas, such as probabilistic safety assessment, medical diagnosis, and fault diagnosis. However, the convention DUCG model fails to model experts’ knowledge precisely because knowledge parameters were crisp numbers or fuzzy numbers. In reality, domain experts tend to use linguistic terms to express their judgements due to professional limitations and information deficiency. To overcome the shortcomings of DUCGs, this article proposes a new type of DUCG model by integrating Pythagorean uncertain linguistic sets (PULSs) and the evaluation based on the distance from average solution (EDAS) method. In particular, experts express knowledge parameters in the form of the PULSs, which can depict the uncertainty and vagueness of expert knowledge. Furthermore, this model gathers the evaluations of experts on knowledge parameters and handles conflicting opinions among them. Moreover, a reasoning algorithm based on the EDAS method is proposed to improve the reliability and intelligence of expert systems. Lastly, an industrial example concerning the root cause analysis of abnormal aluminum electrolysis cell condition is provided to demonstrate the proposed DUCG model. Full article

We consider the problem of modeling complex systems where little or nothing is known about the structure of the connections between the elements. In particular, when such systems are to be modeled by graphs, it is unclear what vertex degree distributions these graphs should have. We propose that, instead of attempting to guess the appropriate degree distribution for a poorly understood system, one should model the system via a set of sample graphs whose degree distributions cover a representative range of possibilities and account for a variety of possible connection structures. To construct such a representative set of graphs, we propose a new random graph generator, Random Plots, in which we (1) generate a diversified set of vertex degree distributions and (2) target a graph generator at each of the constructed distributions, one-by-one, to obtain the ensemble of graphs. To assess the diversity of the resulting ensembles, we (1) substantialize the vague notion of diversity in a graph ensemble as the diversity of the numeral characteristics of the graphs within this ensemble and (2) compare such formalized diversity for the proposed model with that of three other common models (Erdos–Rényi–Gilbert (ERG), scale-free, and small-world). Computational experiments show that, in most cases, our approach produces more diverse sets of graphs compared with the three other models, including the entropy-maximizing ERG. The corresponding Python code is available at GitHub. Full article