Interval-valued Fuzzy Graph Research Articles

Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem

Cubic fuzzy graphs (CFGs) offer greater utility as compared to interval-valued fuzzy graphs and fuzzy graphs due to their ability to represent the degree of membership for vertices and edges using both interval and fuzzy number forms. The significance of these concepts motivates us to analyze and interpret intricate networks, enabling more effective decision making and optimization in various domains, including transportation, social networks, trade networks, and communication systems. This paper introduces the concepts of vertex and edge connectivity in CFGs, along with discussions on partial cubic fuzzy cut nodes and partial cubic fuzzy edge cuts, and presents several related results with the help of some examples to enhance understanding. In addition, this paper introduces the idea of partial cubic α-strong and partial cubic δ-weak edges. An example is discussed to explain the motivation behind partial cubic α-strong edges. Moreover, it delves into the introduction of generalized vertex and edge connectivity in CFGs, along with generalized partial cubic fuzzy cut nodes and generalized partial cubic fuzzy edge cuts. Relevant results pertaining to these concepts are also discussed. As an application, the concept of generalized partial cubic fuzzy edge cuts is applied to identify regions that are most affected by trade deficits resulting from street crimes. Finally, the research findings are compared with the existing method to demonstrate their suitability and creativity.

Automatic Construction of Interval-Valued Fuzzy Hindi WordNet using Lexico-Syntactic Patterns and Word Embeddings

A computational lexicon is the backbone of any language processing system. It helps computers to understand the language complexity as a human does by inculcating words and their semantic associations. Manually constructed famous Hindi WordNet (HWN) consists of various classical semantic relations (crisp relations). To handle uncertainty and represent Hindi WordNet more semantically, Type- 1 fuzzy graphs are applied to relations of Hindi WordNet. But uncertainty in the crisp membership degree is not considered in Type 1 fuzzy set (T1FS). Also collecting billions (5,55,69,51,753 relations in HWN) of membership values from experts (humans) is not feasible. This paper applied the concept of Interval-Valued Fuzzy graphs and proposed Interval- Valued Fuzzy Hindi WordNet (IVFHWN). IVFHWN automatically identifies Interval- Valued Fuzzy relations between words and their degree of membership using word embeddings and lexico-syntactic patterns. The experimental results for the word sense disambiguation problem show better outcomes when IVFHWN is being used in place of Type 1 Fuzzy Hindi WordNet and classical Hindi WordNet.

A Survey on Interval-valued Fuzzy Graphs

Interval-valued fuzzy graphs (IVFGs) belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of an IVFG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. IVFGs are well-articulated, useful and practical tools to manage the uncertainty preoccupied in all real-life difficulties where not sure facts, figures and explorations are explained. In this paper, the concepts of neighbourly irregular intervalvalued fuzzy graphs, neighbourly totally irregular interval-valued fuzzy graphs, and highly irregular interval-valued fuzzy graphs are introduced and several examples are presented.

Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications

Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.

A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application

Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, such as biological sciences. In different applications, they present an appropriate construction means. There were limitations in the definition of fuzzy graphs (FGs), which prompted us to propose a new definition for IVFGs. Some interesting properties related to the new IVFGs are investigated, and enough conditions under which the level graph on IVFGs is equivalent are obtained. Therefore, in this study, we present the properties of a level graph (LG) of an IVFG, and four operations, the Cartesian product (CP), composition (CO), union, and join, are investigated on it. Today, in a treatment system, one of the issues that can be very valuable and important to the quality of service to patients is finding qualified and efficient people in each department, which is not an easy task. But the interval-valued fuzzy graph, as an important fuzzy graph, can help us by considering the ability of each person in the form of intervals of numbers and the effectiveness of each one on the other (according to the relationships between them) in order to find the most worthy people. So, an application of IVFG to find the most effective person in a hospital information system has been introduced.

Facility location problem using the concept of double domination in m-polar interval-valued fuzzy graph

Graph theory plays a crucial role in the era of computer science, medical science and information technology. The fundamental motivation behind this paper is to present some availability ideas in the m polar interval-valued fuzzy graph (m-PIVFG), which are utilized to portray the interval of the uncertainty of items. What’s more, the m-PIVFG graphs are utilized to portray the underlying connection between ideas in which the vertices and edges are of multi-poles and in the form of interval values to feature the uncertainty conditions. The dominating set involves a basic situation in graph analysis. This paper essentially adds to expanding the idea of double domination in the fuzzy graph to the m-PIVFG and getting the related extended ideas of m-PIVFG. In the interim, the ways to get the particular double dominating sets are introduced. At long last, a numeral model on ambulance service on some villages information in India is introduced to clarify the necessity of double domination in m-PIVFG in the particular application.

Some novel concepts of interval-valued picture fuzzy graphs with applications toward the Transmission Control Protocol and social networks

The Transmission Control Protocol usually involves incomplete and imperfect network states for which sophisticated analysis is needed. Fuzzy logic could be more helpful for the analysis of network state more accurately. The interval-valued picture fuzzy set being the most generalized form of fuzzy set has more capacity to analyze the network state more intelligently. In this manuscript, we present the concepts of interval-valued picture fuzzy graphs (IVPFGs) as an extension of interval-valued fuzzy graphs and picture fuzzy graphs. Since interval-valued picture fuzzy sets are the most advanced form of fuzzy sets, IVPFGs would be a more efficient tool for handling data containing uncertainties. First, basic concepts such as degree, order, and size are discussed, followed by operations such as union, intersection, Cartesian product, composition, and the ring sum of IVPFGs. Then, we provide a few relationships between the ring sum and edge deletion of IVPFGs. Special types of IVPFGs including complete IVPFGs, regular IVPFGs, complement IVPFGs, and strong IVPFGs are introduced. Concepts such as the strength of arcs, path sequence, strength of the path, and connectedness are explored in IVPFGs. Different types of strengths of connectedness are discussed based on specific types of arcs. We also provide a few structural properties of IVPFGs through these arcs. Finally, we give a clue about the potential implementation of IVPFGs, an extension of the fuzzy logic-based Transmission Control Protocol and toward social networking.

Signless Laplacian Energy of Interval-Valued Fuzzy Graph and its Applications

An interval-valued fuzzy graph (IVFG) emanates from a fuzzy graph (FG) where the membership is given in interval form. This framework give the user more flexibility in dealing with fuzzy information. In this paper, the signless Laplacian matrix of an interval-valued fuzzy-directed graph is defined. The eigenvalue, spectrum, spectral radius, and energy of an interval-valued fuzzy-directed graph associated with the signless Laplacian matrix are reported. In addition, the lower bound of the signless Laplacian energy in this graph is highlighted. Finally, these tools are employed to build an algorithm that helps in solving some real live problems.

Connected Perfect Domination of Interval-Valued Fuzzy Graphs

Connected Perfect Domination of Interval-Valued Fuzzy Graphs

Cubic Planar Graph and Its Application to Road Network

In this research article, we present the notion of a cubic planar graph and investigate its related properties. The cubic graphs are more effective than both interval-valued and fuzzy graphs as it represents the level of participation (membership degree) of vertices and edges both in interval form and as a fuzzy number. Moreover, it handles the uncertainty and vagueness more efficiently than both interval-valued fuzzy graph and fuzzy graph. The interval indicates a continuous process, whereas the point indicates a specific process. We introduce the terms cubic multigraph, cubic strong and weak edges, and degree of planarity for cubic planar graphs. Some fundamental theorems based on these concepts are also elaborated. We also propose the idea of a cubic strong and weak fuzzy faces and cubic dual graph. Some results related to these concepts are also established. Comparison with the existing method shows the worth of our proposed work.

Connectivity Index in Vague Graphs with Application in Construction

The vague graph (VG), which has recently gained a place in the family of fuzzy graph (FG), has shown good capabilities in the face of problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Connectivity index (CI) in graphs is a fundamental issue in fuzzy graph theory that has wide applications in the real world. The previous definitions’ limitations in the connectivity of fuzzy graphs directed us to offer new classifications in vague graph. Hence, in this paper, we investigate connectivity index, average connectivity index, and Randic index in vague graphs with several examples. Also, one of the motives of this research is to introduce some special types of vertices such as vague connectivity enhancing vertex, vague connectivity reducing vertex, and vague connectivity neutral vertex with their properties. Finally, an application of connectivity index in the selected town for building hospital is presented.

New Concepts of Vertex Covering in Cubic Graphs with Its Applications

Graphs serve as one of the main tools for the mathematical modeling of various human problems. Fuzzy graphs have the ability to solve uncertain and ambiguous problems. The cubic graph, which has recently gained a position in the fuzzy graph family, has shown good capabilities when faced with problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Simultaneous application of fuzzy and interval-valued fuzzy membership indicates a high flexibility in modeling uncertainty issues. The vertex cover is a fundamental issue in graph theory that has wide application in the real world. The previous definition limitations in the vertex covering of fuzzy graphs has directed us to offer new classifications in terms of cubic graph. In this study, we introduced the strong vertex covering and independent vertex covering in a cubic graph with strong edges and described some of its properties. One of the motives of this research was to examine the changes in the strong vertex covering number of a cubic graph if one vertex is omitted. This issue can play a decisive role in covering the graph vertices. Since many of the problems ahead are of hybrid type, by reviewing some operations on the cubic graph we were able to determine the strong vertex covering number on the most important cubic product operations. Finally, two applications of strong vertex covering and strong vertex independence are presented.

A Study on Interval‐Valued Fuzzy Graph with Application in Energy Industry Management

In this paper, we define the concept of level graphs on interval‐valued fuzzy graphs (IVFGs) and introduce the notions of [α, β]−[α, β]− homomorphism, isomorphism, weak isomorphism, and co‐weak isomorphism of IVFGs by [α, β]− homomorphism. Also, an application of homomorphism of IVFGs has been presented by using coloring‐FG.

INTERVAL–VALUED FUZZY GRAPH OF SEMI-GROUP

The aim of this study is to merge the interval valued (int-valued) fuzzy graphs with fuzzy graphs of semi groups. We introduce the interval-valued fuzzy graph of semigroup (IVFGS) with some suitable examples and we study some of the properties of IVFGS and isomorphism of IVFGS

Domination in Some Operations on Interval-valued Fuzzy Graphs

Domination in Some Operations on Interval-valued Fuzzy Graphs

Split Domination In Interval-valued Fuzzy Graphs

Aims / Objectives: In this paper, we introduced and investigated the concept of split domination in interval-valued fuzzy graph and denoted by γs. We obtained many results related to γs. We investigated and study the relationship of γs with other known parameters in interval-valued fuzzy graph. Finally we calculated γs(G) for some standard interval valued fuzzy graphs.

Energy of interval-valued fuzzy graphs and its application in ecological systems

Energy of interval-valued fuzzy graphs and its application in ecological systems

A novel concept of domination in m-polar interval-valued fuzzy graph and its application.

The concept of domination is one of the most significant topics in graph theory to handle unpredictable phenomena. In this study, an unprecedented idea of domination is introduced in m-polar interval-valued fuzzy graph (m-PIVFG). Domination number (DN), isolated vertex, total dominating set, independent set of domination on m-PIVFG are discussed. Some algebraic properties of domination on m-PIVFG are investigated. Weak domination, strong domination, split and non-split domination, cototal and global dominating sets on m-PIVFG are investigated with some fundamental hypotheses and models. We explore the concept of domination in m-PIVFG by solving a case study of locating new facilities to handle a catastrophe reaction activity due to the “COVID-19 pandemic” in West Bengal, India. Ultimately, conclusions and avenues of future scopes are placed at the end of this study.

An Easy-to-Understand Method to Construct Desired Distance-Like Measures

Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly.

Graphical Structures of Cubic Intuitionistic Fuzzy Information

The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such as the idea subgraphs, degree of CIFG, order of CIFG, complement of CIFG, path in CIFG, strong CIFG, and the concept of bridges for CIFGs. Furthermore, the generalization of CIFG is proved with the help of some remarks. In addition, the comparison among the existing and the proposed ideas is carried out. Finally, an application of CIFG in decision-making problem is studied, and some future study is proposed.