Conceptual Graphs Research Articles

Topological numbers in uniform intuitionistic fuzzy environment and their application in neural network

Intuitionistic Fuzzy sets combine the ideas of uniformity, membership, and non-membership grades of the elements. Similarly, Intuitionistic Fuzzy Graphs are the generalization of simple fuzzy graphs. Depending on the uniformity of the fuzzy graphs (USIF) they can be categorized in different ways via membership values. From the idea of uniform fuzzy topological indices, we have developed the concepts of uniform intuitionistic fuzzy topological indices for uniform intuitionistic fuzzy graphs. This idea provides a more adaptable and nuanced representation of structural properties in graphs or networks. According to the theory of fuzzy topological indices, the importance of topological indices changes depending on the circumstance and the specific problem at hand. When the interactions between nodes are uncertain but not always hesitant, fuzzy graph theory and its adjusted topological indices are sufficient to capture and assess the underlying structure. In such cases where uncertainty is more complicated and hesitation is a major problem then there are better ways to address by intuitionistic fuzzy graph theory and the topological indices that go along with it. This article, developed the concept of uniform intuitionistic fuzzy graphs afresh and proposed Intuitionistic Fuzzy Topological Indices. We determine these indices using the topological indices and labeling of crisp graphs, rather than relying on the degrees of intuitionistic fuzzy graphs and edge portions. This approach is then applied to find intuitionistic fuzzy topological indices. Also, we have provided the MATLAB algorithm to illustrate the concept of IF labeling of cellular neural networks of any order. An example is given to explain the idea and approach towards one kind of uniform intuitionistic fuzzy graph represented by Cellular Neural Networks and graphical plots of the indices involved are also made.

Role of Rectangular and Square Matrix in Graph Theory

Graph theory is one of the topics studied in modern mathematics and the concept of graph in mathematics was discussed from the past to the present. For example, graph relations and functions have many uses. The 18th century is the beginning of modern graph theory. From the 19th century onwards, graph theory was discussed for its application in various fields, which is a field of research at this time. Graph theory and matrix are two important and well-known topics in modern mathematics, so in this article the role of rectangular and square matrix in graph theory is discussed. The main purpose of preparing this article is to study rectangular and square matrix in graph theory. The research method in this article is library that was followed by using academic articles in libraries and the Internet. The findings obtained from this study show that the matrix adjacent to the graph is a square matrix and the occurrence matrix is ​​a rectangular matrix.

Complex Fuzzy Dynamical Graphs and their Applications in Signals Processing

In this paper we introduce the concepts of complex fuzzy dynamic graphs, complex fuzzy diagonal matrices and complex fuzzy Laplacian matrices. We use these graphs and their laplacian matrices as mathematical framework for applications in Sciences, especially signals processing. We define absolute average eigenvalues of the Complex Laplacian matrices and explore the properties of these matrices with their eigenvalues. We develop an algorithm using the absolute eigenvalues of the Laplacian matrices and apply this algorithm to signal and systems. Our study begins by establishing the theoretical foundation of complex fuzzy dynamic graphs, highlighting their role to model within dynamic systems including two dimensional uncertainties. We investigates the complex fuzzy Laplacian matrices obtain from these graphs. Our main focus is on the absolute eigenvalues of these matrices, which hold a vital role into the graph’s structural characteristics and behavior. In the context of signals processing, the research demonstrates how these absolute eigenvalues serve as essential matrices for system characterization. This study presents novel methods to analyze signals on complex fuzzy dynamic graphs. These methods are particularly relevant in scenarios where signals are influenced by dynamic and uncertain environments.

Development of navigation systems in optimal utilization of transportation routes in topology helm graphs using graph labeling

Graph theory plays a vital role in many fields. The graph concept models many relationships and processes in physical, biological, social, transportation, and information systems. One of the essential fields in graph theory is graph labeling. Graph labeling is widely used in various applications such as coding theory, x-ray crystallography, radar, astronomy, circuit design, addressing of communication networks, database management, etc. In this research, we will examine a form of topology of transportation routes based on graph labeling. The topology of the transportation routes that will be studied is a modified of helm graph. This research aims to determine the total vertex irregularity strength of the modified helm graph denoted by Hn for n≥3. The lower bound is obtained based on the properties of the graph Hn using the existing supporting theorem. The upper bound is obtained by labeling the vertices and edges of the graph Hn in some simple cases. From this labeling, total vertex irregular labeling will be constructed for any n. Based on the results of this research, the total vertex irregularity strength of the graph Hn is

Hydrogen-bonding-enhanced green wearable sensors with high generation performance and low Young's modulus

A conceptual graph of the hydrogen-bonding-enhanced green wearable sensors with high generation performance and low Young's modulus.

Clinical analogy resolution performance for foundation language models

Using extensive data sources to create foundation language models has revolutionized the performance of deep learning-based architectures. This remarkable improvement has led to state-of-the-art results for various downstream NLP tasks, including clinical tasks. However, more research is needed to measure model performance intrinsically, especially in the clinical domain. We revisit the use of analogy questions as an effective method to measure the intrinsic performance of language models for the clinical domain in English. We tested multiple Transformers-based language models over analogy questions constructed from the Unified Medical Language System (UMLS), a massive knowledge graph of clinical concepts. Our results show that large language models are significantly more performant for analogy resolution than small language models. Similarly, domain-specific language models perform better than general domain language models. We also found a correlation between intrinsic and extrinsic performance, validated through PubMedQA extrinsic task. Creating clinical-specific and language-specific language models is essential for advancing biomedical and clinical NLP and will ensure a valid application in clinical practice. Finally, given that our proposed intrinsic test is based on a term graph available in multiple languages, the dataset can be built to measure the performance of models in languages other than English.

System loophole of generalized noncontextuality

Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological model. However, operational indistinguishability depends on the set of operations that one may use to distinguish two procedures: we refer to this set as the reference of indistinguishability. Thus, whether or not a given experiment is noncontextual depends on the choice of reference. The choices of references appearing in the literature are seldom discussed, but typically relate to an implicit notion of a system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment? This question depends in part on one's beliefs in the universe being fundamentally continuous or fundamentally composite. To draw a coherent picture of the possible approaches one may use, we start by formulating a notion of noncontextuality for prepare-and-measure scenarios with respect to an explicit reference of indistinguishability. We investigate how verdicts of noncontextuality depend on this choice of reference, and in the process we introduce the concept of the noncontextuality graph of a prepare-and-measure scenario. We then discuss several proposals that one may appeal to in order to fix the reference to a specific choice, and we relate these proposals to different conceptions of what a system really is. With this discussion, we advocate that whether or not an experiment is noncontextual is not as absolute as often perceived. Published by the American Physical Society 2024

Study on multidimensional fuzzy graphs through modified partial ordering

This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional $t-$ norms and $t-$ conorms by providing a more general partial order that can link more components of the range set $\mathcal{J}_{\infty}\big([0,1]\big)$. More studies on various operations such as direct product, composition, tensor product, join, etc. are conducted with relevant illustrations. A novel complement operator approach is also investigated to link the multidimensional fuzzy graph and the edge-powered multidimensional fuzzy graph. Finally, defining the infimum and supremum of an arbitrary family in $\mathcal{J _{\infty}\big([0,1]\big)$ introduces many notions such as vertex degree, $min-$ vertex degree, $max-$ vertex degree, path strength, etc.

Beta and Gamma Products of Fuzzy Random Graphs with Hesitancy

Fuzzy random graphs offer a powerful framework for modeling uncertain and imprecise relationships in various real-world systems. This study introduces the concept of hesitancy fuzzy random graphs, which incorporate both fuzziness and randomness in edge and vertex memberships. Additionally, this study investigates the beta and gamma products within the context of hesitancy fuzzy random graphs. Leveraging the beta and gamma operations, this study investigates the application of combining and aggregating uncertain information from multiple sources represented by hesitancy fuzzy random graphs.

A Categorical Formalism for Conceptual Graphs

Abstract In this paper, we propose a formalism for knowledge manipulation, based on conceptual graphs, which is supported by category theory, and which can be the basis for the development of knowledge-based systems. The model we propose is an extension of the model based on conceptual graphs. In this model, the application of an inference rule between logical formulas represented by two conceptual graphs is reduced to the identification of an arrow in a category. To this end, we introduce several new notions such as: the category of conceptual graphs, the category of classes of conceptual graphs, the conceptual category of a model and the conceptual category of inference of a model.

SYNTHESIS OF HYDROPNEUMATIC DRIVE SYSTEM SCHEMES ON SEVEN-LINEAR DISTRIBUTORS

The purpose of the article is an in-depth study of ways to improve hydraulic and pneumatic systems using seven-line distributors. The main advantages focused on include increased efficiency, increased ease of installation, reduced hardware costs, and lower cost of the hydropneumatic actuator, these are the main components that must be guided when designing hydraulic and pneumatic circuits. When achieving these indicators, the hydraulic equipment used in the system plays an important role. Due to the idea of using extremely universal modules, the article investigated distributors with more lines than in standard solutions, namely seven-line hydraulic and pneumatic distributors. The conventional notation of the seven-line distributor is given. The minimal combinations of functions that can be implemented using seven-linear distributors are considered. It was determined what can be considered a trigger. Examples of the use of seven-line dividers in the construction of flip-flops with a dominant zero and flip-flops with a counting input are given. A detailed description of the operation of such triggers is given. The possibility of expanding the functions of the command apparatus was investigated. A detailed description of the command apparatus built on seven-line distributors is made. The definition of the concept of graph of operations is given. A graph of operations for a molding machine is built. On the basis of this graph, logical equations are constructed that describe the entire system operation process and transition states, taking into account the signals that move the system to the next state and the signals acting inside the transition. A pneumatic circuit for the molding machine was also constructed based on the obtained logic equations. A seven-line command apparatus was used to build this scheme, which demonstrates the possibilities of using a seven-line command apparatus in practical conditions. The areas of application of such command apparatus and seven-line distributors are considered.

Research and Applications of Knowledge Graphs in the Power Sector: A Review

With the rapid development of science and technology, power system has become the lifeblood of modern society, an increasingly large power system complicates the management, operation, and maintenance of the grid. In order to effectively use a large number of operating data and prior knowledge of power system, the knowledge graph is introduced into the field of power systems. This paper introduces the research and application of knowledge graph in power system and emphasizes the importance of knowledge graphs in addressing the increasing complexity of power systems and the rising demand for intelligence, the knowledge graph integrates heterogeneous data in a structured way, which helps to improve the technical level of power system management and control, especially in fault diagnosis, equipment monitoring and market transactions. This paper first introduces the basic concept, construction method and main application scenarios of knowledge graph in power system, including data management, equipment operation and maintenance, power system operation management and decision support, Through specific examples, such as a question-answering system for identifying defects in power equipment based on knowledge graphs, the identification method of transmission line missing bolts, intelligent planning of distribution network, etc., the paper shows knowledge graph can effectively improve the operation efficiency and management level of power system. Finally, the paper looks forward to the future development trend of knowledge graph in power system, points out its broad application prospects in smart grid construction, multidisciplinary cross integration and other fields, and emphasizes the importance of knowledge graph for promoting the intelligent development of power system.

Note for Neutrosophic Incidence and Threshold Graph

Uncertain Graph Theory has emerged to model the uncertainties present in real-world networks. An Incidence Graph represents the connections between vertices and edges using incidence pairs to illustrate relationships. A Threshold Graph is defined by vertex weights and thresholds, forming cliques or independent sets. We explore the concepts of the Pentapartitioned Neutrosophic Incidence Graph, Turiyam Neutrosophic Incidence Graph, Pentapartitioned Neutrosophic Fuzzy Threshold Graph, and Turiyam Neutrosophic Fuzzy Threshold Graph.

Study for General Plithogenic Soft Expert Graphs

Graph theory, a branch of mathematics, focuses on studying graphs that model relationships between objects through vertices and edges [29]. The Turiyam Neutrosophic Graph handles uncertainty by assigning four values to vertices and edges: truth, indeterminacy, falsity, and liberal state. In contrast, the Plithogenic Graph is a general structure where vertices and edges are defined by degrees of appurtenance and contradiction across multiple attributes [45]. The General Plithogenic Graph extends the Plithogenic Graph, offering a broader framework [45]. This study presents new concepts of the General Plithogenic Soft Expert Graph and the Turiyam Neutrosophic Soft Expert Graph, with the former expanding the existing Soft Expert Graph model into a more generalized structure.

On Domination and Related Concepts of Multidimensional Fuzzy Graphs and Their Applications

Domination and its associated concepts are significant ideas in fuzzy graph theory that have applications in diverse fields such as neural networks, game theory, and telecommunication. This study presents the notions of dominance and its associated research in a broader form of fuzzy graph called the multidimensional fuzzy graph. Basic results, such as the relationship between these parameters and vertices, edges, minimal sets, and so forth, are identified and illustrated with appropriate examples. The dominance number of multidimensional fuzzy graphs is determined after undergoing operations such as direct product, tensor product, composition, join, and others. Ultimately, this study displays a decision-making problem that can be efficiently addressed by utilizing the concept of the dominance number. The effectiveness of this approach is then compared to various models, like [Formula: see text]-polar fuzzy sets.

A study of novel linear Diophantine fuzzy topological numbers and their application to communicable diseases.

The idea of linear Diophantine fuzzy sets (LDFs) is a novel tool for analysis, soft computing, and optimization. Recently, the concept of a linear Diophantine fuzzy graph has been proposed in 2022. The aim of this research is to extend topological numbers to LDFSs. A real value assigned to a particular graph is known as a topological graph theoretic parameter. We extend the bound of the crisp graph toward the linear Diophantine fuzzy graph (LDFG), including the edge and vertex deletion operations via LDFG theoretic parameters. We also investigate the interesting bound of the LDFGs via LDFG theoretic parameters. Finally, for decision-making problems, we developed an algorithm by exploiting the relationship between LDFG theoretic parameters and LDFSs. Based on the established approach, we discussed a numerical example of an application of a medical diagnosis using the linear Diophantine fuzzy Sombor graph parameter and the first, fifth, and sixth versions of the linear Diophantine fuzzy Sombor graph parameters.

Contrasting Multi-Source Temporal Knowledge Graphs for Biomedical Hypothesis Generation.

Hypothesis Generation (HG) aims to expedite biomedical researches by generating novel hypotheses from existing scientific literature. Most existing studies focused on modeling static snapshots of the corpus, neglecting the temporal evolution of scientific terms. Despite recent efforts to learn term evolution from Knowledge Bases (KBs) for HG, the temporal information from multi-source KBs is still overlooked, which contains important, up-to-date knowledge. In this paper, an innovative Temporal Contrastive Learning (TCL) framework is introduced to uncover latent associations between entities by jointly modeling their co-evolution across multi-source temporal KBs. Specifically, we first construct a temporal relation graph based on PubMed papers and a biomedical relation database (such as Comparative Toxicogenomics Database (CTD)). Then the constructed temporal relation graph and a temporal concept graph (such as Medical Subject Headings (MeSH)) are used to train two GCN-based recurrent networks for learning the entity temporal evolutional embeddings, respectively. Finally, a cross-view temporal prediction task is designed for learning knowledge enriched temporal embeddings by contrasting the temporal embeddings learned from the two Temporal Knowledge Graphs (TKGs). Findings from experiments conducted on three real-world biomedical term relationship datasets demonstrate that the proposed approach is clearly superior to approaches based on single TKG, achieving the state-of-the-art performance.

Resilient Consensus for Discrete-Time Multiagent Systems With a Dynamic Leader and Time Delay: Theory and Experiment.

The ever-present cyber-attacks have posed a significant challenge to consensus of multiagent systems (MASs), due to their capability of compromising agents. These threats underscore the critical need to design control strategies that can endow MASs with resilience. In this article, we address resilient consensus problems for first- and second-order discrete-time MASs, considering the presence of malicious agents, a dynamic leader, and communication delay. First, a resilient controller is designed for first-order MASs, and sufficient conditions are derived based on existing robust graph concepts to achieve consensus with ultimately bounded error. Next, since the derived error bound grows factorially with the system scale, a novel graph structure and a modified controller are proposed to limit the growth to a linear rate. Building upon the obtained results, an estimator-based control framework is introduced to solve resilient consensus problems for second-order MASs. Finally, comparative simulations and practical experiments based on unmanned ground vehicles and unmanned-aerial-vehicles are conducted to validate the effectiveness and practicability of the proposed control methods.

Towards Nash‐Williams orientation conjecture for infinite graphs

AbstractIn 1960 Nash‐Williams proved that an edge‐connectivity of is sufficient for a finite graph to have a ‐arc‐connected orientation. He then conjectured that the same is true for infinite graphs. In 2016, Thomassen, using his own results on the auxiliary lifting graph, proved that ‐edge‐connected infinite graphs admit a ‐arc‐connected orientation. Here we improve this result for the class of one‐ended locally finite graphs and show that an edge‐connectivity of is enough in that case. Crucial to this improvement are results presented in a separate paper, by the same author of this paper, on the key concept of the lifting graph, extending results by Ok, Richter, and Thomassen.

Novel Concepts of Bipolar Picture Fuzzy Graphs With Applications in Image Segmentation and Road Maps Designs

Novel Concepts of Bipolar Picture Fuzzy Graphs With Applications in Image Segmentation and Road Maps Designs