Article
Mathematics, Applied
Nicolas Madrid, Manuel Ojeda-Aciego
Summary: This paper discusses various ways to define the notion of inconsistency in fuzzy logic systems and provides a notion of inconsistency based on the absence of models, as well as two consistency measures that belong purely to the fuzzy paradigm. These measures coincide with the crisp notion of consistency when the set of truth values is {0, 1}, bringing back the spirit of fuzzy logic into the notion of consistency.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Mohammed Atef, Abd El Fattah El Atik, Ashraf Nawar
Summary: This paper introduces a new type of fuzzy topological graphs, investigates their properties and an edge calculation method, and explores the concept of homeomorphic between fuzzy topological graphs. It also proposes an algorithm for constructing fuzzy topological graphs and provides a new method for explaining homeomorphic between fuzzy topological graphs, to be applied in smart cities.
Article
Physics, Multidisciplinary
Shu Gong, Gang Hua
Summary: This article investigates the Wiener index on bipolar fuzzy incidence graphs, determining the lower and upper bounds for positive and negative Wiener index, and discussing the relationship between the original graph and its subgraph. The Wiener absolute index is introduced, and conclusions are drawn in terms of geodesic distance analysis. Additionally, the equality of Wiener index and Wiener absolute index for two isomorphic bipolar fuzzy incidence graphs is demonstrated.
FRONTIERS IN PHYSICS
(2021)
Article
Computer Science, Artificial Intelligence
Anushree Bhattacharya, Madhumangal Pal
Summary: This paper discusses the vertex covering problem and its modeling using fuzzy set/graph, addressing it through a series of linear and nonlinear programming problems to maximize the total number of facilities, coverage area, and efficiency while minimizing the total cost. By defining new sets for optimal decision-making and illustrating the model with an example, the paper explores the application of these methods to real-life problems.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
A. C. Guler, E. D. Yildirim, O. B. Ozbakir
Summary: This paper aims to improve the accuracy measure of a graph's subgraph and create new nano topologies on the power set of the graph's vertices and edges. It introduces Ej-neighborhoods and Cj-neighborhoods based on the vertices and edges of a simple directed graph, using j-neighborhoods for j E {out, in, n, U}. The paper applies these neighborhoods to describe Ej-approximations and Cj-approximations, investigates their properties and relationships, defines the accuracy measures of a subgraph using these approximations, and shows that Cj-accuracy measures are the highest. Furthermore, the paper generates new nano topologies using these approximations and demonstrates that these topologies may not be comparable. Finally, an application in physics is presented to show the wider applicability of the current approximations. Throughout the paper, all findings are summarized using tables.
Article
Computer Science, Artificial Intelligence
Jozsef Dombi, Tamas Jonas
Summary: In the application of fuzzy sets, the greatest uncertainty occurs when the membership grade in a fuzzy set is equal to the membership grade in the complement of this fuzzy set. The fixed point of the standard Zadeh negation is 0.5, but in the case of a strong complement operator, it may not be 0.5. This paper introduces the concept of a parametric fuzziness measure called the nu-maximal vagueness measure.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
A. Lekha, K. S. Parvathy
Summary: This paper studies the fuzzy dominating sets and their properties in fuzzy graphs, and determines the fuzzy domination number for some graphs.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2023)
Article
Mathematics, Applied
Jianhua Tu, Junyi Xiao, Rongling Lang
Summary: Given a graph G, a dissociation set is a subset of vertices inducing a subgraph with vertex degree at most 1. The dissociation polynomial is defined as D-G(lambda) = Sigma(lambda | D |)(D ∈ D(G)), where D(G) denotes the set of all dissociation sets of G. In this paper, it is proved that for any cubic graph G and any lambda ∈ (0, 1], [GRAPHICS], with equality if and only if G is a disjoint union of copies of the complete graph K-4. When lambda = 1, the value of D-G(lambda) is exactly the number of dissociation sets of G. Hence, for any cubic graph G on n vertices, |D(G)| <= |D(K-4)|(n/4) = 11(n/4).
Article
Computer Science, Artificial Intelligence
Ismat Rashid, Irfan Nazeer, Tabasam Rashid
Summary: This article investigates the connectivity concepts in intuitionistic fuzzy incidence graphs (IFIGs) and provides various examples. By classifying pairs into different types based on their strength, the fundamental structure of IFIGs is thoroughly understood. The existence of a strong intuitionistic fuzzy incidence path in an IFIG is established. Additionally, the article explores other structural properties of IFIGs and applies the concepts to real-life computer networks.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2022)
Article
Mathematics, Applied
Rupkumar Mahapatra, Sovan Samanta, Madhumangal Pal
Summary: In this study, an advanced concept of the neutrosophic planar graphs is given and investigated the generalized neutrosophic planar graphs (GNPG). The score of planarity is calculated based on the true, falsity and indeterminacy values of degree of planarity to measure the overall planarity of a GNPG. A real-life application is presented and solved by this concept of a GNPG.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
Anushree Bhattacharya, Madhumangal Pal
Summary: This paper introduces new concepts involving clique covering of a fuzzy graph for optimizing business strategy parameters. It presents four algorithms for finding necessary parameters and sets of a fuzzy graph to construct a linear programming cordon. By characterizing and solving facility location problems with this approach, the paper aims to maximize total gain and contribute to sustainable economic growth worldwide.
Article
Computer Science, Information Systems
Naeemeh Adel, Keeley Crockett, Daria Livesey, Joao Paulo Carvalho
Summary: This paper introduces an algorithm that can compare the similarity between texts containing fuzzy words and proposes a new fuzzy sentence similarity measure. The results show that this measure outperforms traditional semantic similarity measures in accounting for the presence of fuzzy words. Additionally, a fuzzy dictionary has been developed, providing a useful resource for researchers in natural language processing and fuzzy applications.
Article
Computer Science, Artificial Intelligence
Hao Zhang, Chaojie Wang, Zhengjue Wang, Zhibin Duan, Bo Chen, Mingyuan Zhou, Ricardo Henao, Lawrence Carin
Summary: In this paper, a multilevel sentence relation graph convolutional network (MuserGCN) is proposed to analyze documents by organizing their implicit topology as a graph and performing feature extraction using graph convolutional networks. A set of learnable hierarchical graphs are constructed to explore multilevel sentence relations, and multiple parallel graph convolutional networks are used to extract multilevel semantic features, which are aggregated using an attention mechanism for different document comprehension tasks. Variational inference is used to learn the graph construction and evolve the graphs dynamically to better match downstream tasks.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Computer Science, Information Systems
Muhammad Shoaib, Waqas Mahmood, Qin Xin, Fairouz Tchier, Ferdous M. O. Tawfiq
Summary: This paper introduces the extension of complex fuzzy graphs - complex picture fuzzy set (Com-PFS), and explains its development methods and primary operations in detail. Com-PFG employs three complex membership functions to provide a more accurate representation of fuzzy situations, and discusses its application in decision-making problems.
Article
Automation & Control Systems
Hong-Yu Yao, Yuan-Long Yu, Chun-Yang Zhang, Yue-Na Lin, Shang-Jia Li
Summary: This paper proposes a new dynamic graph representation learning model called FuzzyDGL, which incorporates fuzzy representation learning to handle uncertainties in dynamic graphs. Experimental results show that FuzzyDGL has strong competitiveness and generalization in tasks like link prediction and node classification.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)