Search Results (8)

A novel approach for analyzing the structural integrity and operational vulnerability of complex networks using intuitionistic fuzzy graphs has been modeled. While traditional fuzzy graph metrics focus primarily on existence, they fail to capture the holistic systemic impact of failures. To overcome this limitation, a scalar-based measure of nodal importance that integrates both existence (membership degree) and non-existence (non-membership degree) values of incident edges into a single critical metric has been developed. The proposed indices demonstrate enhanced sensitivity to network perturbations compared to conventional degree centrality measures, capturing latent vulnerabilities in critical infrastructure topologies. Based on this, two indices are proposed: Intuitionistic Fuzzy Degree Index and Intuitionistic Edge Interaction Index. These indices quantify the total system activity, stress dispersion, overall network cohesiveness, and potential for cascading failure propagation. When applied to synthetic core-periphery networks, the proposed indices identified critical nodes with superior discrimination capability compared to existing fuzzy graph metrics, revealing that removal of identified nodes results in system-wide connectivity degradation observable through both membership and non-membership approximations. This methodology was applied to a core-periphery communication network to analyze the systemic consequences of node removal. Experimental validation on networks of varying sizes demonstrates that the Intuitionistic Edge Interaction Index achieves robust node criticality ranking across heterogeneous network topologies with improved predictive accuracy for cascade initiation points. This work provides network analysts and engineers a quantitative tool to precisely assess criticality and inform targeted resilience strategies in uncertain, high-risk environments. Full article

The m-Polar Fuzzy Incidence Graph (m-PFIG) is an extension of the m-Polar Fuzzy Graph (m-PFG), which provides information on how vertices affect edges. This study explores the concept of matching within both bipartite and general m-polar fuzzy incidence graphs (m-PFIGs). It extends various results and theorems from fuzzy graph theory to the framework of m-PFIGs. This research investigates various operations within m-PFIGs, including augmenting paths, matching principal numbers, and the relationships among them. It focuses on identifying the most suitable employees for specific roles and achieving optimal outcomes, particularly in situations involving internal conflicts within an organization. To address fuzzy maximization problems involving vertex–incidence pairs, this study outlines key properties of maximum matching principal numbers in m-PFIGs. Ultimately, the matching concept is applied to attain these maximum principal values, demonstrating its effectiveness, particularly in bipartite m-PFIG scenarios. Full article

There are many specific risks in renewable energy (RE) investment projects, and the incidences of these risk factors are fuzzy and uncertain. In different stages of a project’s life cycle, the main risk factors frequently change. Therefore, this paper constructed a cloud dynamic Bayesian network model (Cloud-DBN) for RE operation processes; it uses the DBN graph theory to show the generation mechanism and evolution process of RE outbound investment risks, to make the risk prediction structure clear. Based on the statistical data of observation nodes, the probability of risk occurrence is deduced to ensure the scientific nature of the reasoning process. The probability of risk being low, medium, or high is given, which is highly consistent with the uncertainty and randomness of risk. An improved formula for quantitative data normalization is proposed, and an improved calculation method for joint conditional probability based on weight and contribution probability is proposed, which reduces the workload of determining numerous joint conditional probabilities and improves the practicability of the BN network with multiple parent nodes. According to the 20-year historical statistical data of observation nodes, the GM(1,1) algorithm was used to extract the transfer characteristics of observation nodes, construct the DBN network, and deduce the annual risk probability of each risk node during the operation period of the RE project. The method was applied to the wind power project invested by China in Pakistan, and the effectiveness of the method was tested. The method in this paper provides a basis for investment decisions in the RE project planning period and provides targeted risk reduction measures for the project’s operation period. Full article

The inverse in crisp graph theory is a well-known topic. However, the inverse concept for fuzzy graphs has recently been created, and its numerous characteristics are being examined. Each node and edge in m-polar fuzzy graphs (mPFG) include m components, which are interlinked through a minimum relationship. However, if one wants to maximize the relationship between nodes and edges, then the m-polar fuzzy graph concept is inappropriate. Considering everything we wish to obtain here, we present an inverse graph under an m-polar fuzzy environment. An inverse mPFG is one in which each component’s membership value (MV) is greater than or equal to that of each component of the incidence nodes. This is in contrast to an mPFG, where each component’s MV is less than or equal to the MV of each component’s incidence nodes. An inverse mPFG’s characteristics and some of its isomorphic features are introduced. The $\alpha$-cut concept is also studied here. Here, we also define the composition and decomposition of an inverse mPFG uniquely with a proper explanation. The connectivity concept, that is, the strength of connectedness, cut nodes, bridges, etc., is also developed on an inverse mPF environment, and some of the properties of this concept are also discussed in detail. Lastly, a real-life application based on the robotics manufacturing allocation problem is solved with the help of an inverse mPFG. Full article

Fuzzy topological topographic mapping ($FTTM$) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, $FTT{M}_n$, is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of $FTTM$, namely, the homeomorphisms between its components, allows the generation of new $FTTM$. The generated $FTTM$s can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated $FTTM$ and edges that connect their incidence components. A graph of pseudo degree zero, $G_0\left(FTT{M}_n^k\right),$ however, is a special type of graph where each of the $FTTM$ components differs from its adjacent. A researcher posted a conjecture on $G_0^3\left(FTT{M}_n^3\right)$ in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended $G_0^3\left(FTT{M}_n^3\right)$, namely, the conjecture on $G_0^4\left(FTT{M}_n^4\right)$ that was posed in 2018, is narrated and proven using simple mathematical induction. Full article

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are $M\left[{\gamma }_s\left(C_l(\sigma ,\varphi ,\eta )\right)\right]=\lceil \frac{l}{3}\rceil$. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization. Full article

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be done by applying a vague incidence graph (VIG), based on which the FGs may not engender satisfactory results. Similarly, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, and also other issues such as medical sciences, and traffic planning. Dominating sets (DSs) enjoy practical interest in several areas. In wireless networking, DSs are being used to find efficient routes with ad-hoc mobile networks. They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its important properties. In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc. Finally, a DS application for VIG to properly manage the COVID-19 testing facility is introduced. Full article

It is the case that, in certain applications of fuzzy graphs, a t-norm, instead of a minimum, is more suitable. This requires the development of a new theory of fuzzy graphs involving an arbitrary t-norm in the basic definition of a fuzzy graph. There is very little known about this type of fuzzy graph. The purpose of this paper is to further develop this type of fuzzy graph. We concentrate on the relatively new concept of fuzzy incidence graphs. Full article