Concept Of Fuzzy Graph Research Articles

An integrated description of election information using domination and dual domination in picture fuzzy graph

The concept of the fuzzy graph (FG) and the simplification of its type have been designed with many real-world concerns, decision-making, network problems, and other types of impression in mind. This article is essentially a generalization of fuzzy graph theory with their association in settings where four organizations of membership grade are characterized by imprecision. The contemporary idea of domination in picture fuzzy graph (PFG) is given the generalization of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination is unit on the innovative idea of picture fuzzy graph. This article is the main focus on the graph of the picture fuzzy set. Additionally, this research paper concludes with the concept of domination theory (DT) and double domination theory (DDT) in the concept of environment. Obviously, the framework of picture fuzzy graph is purposed and their connected theory is obtained together with presented examples. Supplementary the domination theory (DT) in the picture fuzzy graph. A few order, strength, cardinality, and domination of completeness, neighbors in a picture fuzzy graph, and the DDS and given some examples are likewise studied in the concept of picture fuzzy graph in the environment. The application of the politician campaign is novel exploiting the projected study and curious how to double dominate would relationship with the politician campaign. Finally, a comparison between the current effort and the prior effort is made, and the advantages of the work done in the context of a picture fuzzy graph are discussed.

Inverse Graphs in m-Polar Fuzzy Environments and Their Application in Robotics Manufacturing Allocation Problems with New Techniques of Resolvability

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 α-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.

Bipolar-valued hesitant fuzzy graph and its application.

In the real-world scenario, one has to find a dominating person in a social network, conferences, meetings or any group discussion. The fuzzy graph (network) is one of the most powerful tools to find the strongest influential person in a network. This paper aims to develop a concept of fuzzy graphs (FGs) in the setup of bipolar-valued hesitant fuzzy sets (BVHFs). The concept of bipolar-valued hesitant fuzzy graph (BVHFG) is different from the concept of bipolar fuzzy graph (BFG). BVHFG is the generalization of hesitant fuzzy graph (HFG), which not only considers the satisfaction degree of units in a network but also considers the satisfaction degree to some implicit counter property of units with several bipolar fuzzy values. We first introduce the definition of BVHFG, represented by another class of imprecise membership grades that refers to BVHF membership grades. We shall subsequently see the scope of BVHF membership grades in BVHFG is greater than the scope of bipolar-valued membership grades in BFG. In addition, we also discuss the basic operations and functional properties of BVHFGs. Finally, we propose a numerical method to find the most dominating person using our proposed work. As the proposed method of ranking considers the degree of hesitation as well as bipolarity, this method has the edge over earlier work. To establish the importance of our method, we also find domination degrees for HFG and BVHFG using the same example and show that there is a significant change in the ranking of dominating persons.

Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

The concept of fuzzy graph (FG) and its generalized forms has been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems, and so on. This paper is based on some developments in generalization of FG theory to deal with situation where imprecision is characterized by four types of membership grades. A novel concept of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of FG, intuitionistic fuzzy graph (IFG), and picture fuzzy graph (PFG) based on the recently introduced concept of T-spherical fuzzy set (TSFS). The significance and novelty of proposed concept is elaborated with the help of some examples, graphical analysis, and results. Some graph theoretic terms are defined and their properties are studied. Specially, the famous Dijkstra algorithm is proposed in the environment of TSFGs and is applied to solve a shortest path problem. The comparative analysis of the proposed concept and existing theory is made. In addition, the advantages of the proposed work are discussed over the existing tools.

Material selection model using spherical Dombi fuzzy graph approach

In this research paper, the properties of Spherical Dombi Fuzzy Graph (SDFG) are discussed through examples. Moreover, we present a technique for selection of materials for a given technical unit based on Spherical Dombi Fuzzy Graph concept. The Spherical Dombi Fuzzy graph is developed considering material aspects and their priority for the application. We observed that the material selection model based on SDFG gives more space than fuzzy set, intuitionistic fuzzy set and picture fuzzy set concepts.

1-Quasi Total Fuzzy Graph and Its Total Coloring

The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.

Analysing Asymmetrical Associations using Fuzzy Graph and Discovering Hidden Connections in Facebook

The fuzzy graph theory to analyse the relationship strength in Social Networks has gain significant potential in last few years and has seen applications in areas like Link Prediction, calculating Reciprocity, discovering central nodes etc. In this paper, we propose a framework to analyse and quantify the degree of strength of asymmetric relationships and predict hidden links in social networks using fuzzy logic. Till now, the work in fuzzy social relational networks has been limited to symmetric relationships. However, in this paper, we consider the scenario of asymmetric relations. The proposed approach is for web 2.0 application <em>Facebook</em>. Our contribution is three fold. First, the measurement of the strength of asymmetric relationship between nodes on the basis of social interaction using the concept of fuzzy graph. Second, a hybrid approach for prediction of missing links between two nodes on the basis of similarity of attributes of user profiles such as demographic, topology and network transactional data. Third, we perform fuzzy granular computing on attribute ‘strength of relationship’ and categorise into four granules namely <em>{socially close friends, socially near friends, socially far friends, socially very far friends}</em> based on the results of supervised learning conducted over dataset. Similarly, actual outcome for predicted links is categorised into three granules namely <em>Accept, Not accept and May be.</em> The proposed approach has predicted relationship strength with mean absolute error of 9.26% whereas the proposed approach for Link prediction has provided 64% correct predictions.

Fuzzy autocatalytic set (FACS) as fuzzy vector space

Dynamic model of clinical waste incineration process in Malacca has been successfully developed using Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type 3. FACS combines the concept of fuzzy graph and autocatalytic set and has been proven to yield more precise results than using crisp graph. Next, the graph of its process has been transformed from non-coordinated FACS to coordinated FACS in Euclidean space. Some mathematical structures related to the transformation are adjacency, transition and Laplacian matrices of FACS. Furthermore, it is found that FACS to be primitive, irreducible and aperiodic. The set of adjacency matrices of FACS of Fuzzy Graph Type 3 is predicted to be seen as fuzzy vector space, and the set of Euclidean distance matrices represent coordinated FACS is also expected to be fuzzy vector space as well. As a recently developed theory, FACS has great capabilities in generating new mathematical theories and structures that would enrich the theory itself. this study is made to attempt the formulation of new algebraic structure in FACS which is fuzzy vector space.

A Note on the Fusion of Two Vertices in a Fuzzy Graph

The concept of fuzzy sets was introduced by L. A. Zadeh in 1965. The concept of fuzzy graph was introduced by A. Rosenfeld [5] in 1975. Many of the crisp graph concepts have been extended to fuzzy graph theory. Here we define the fusion of two vertices in a fuzzy graph and investigate some properties and also give fusion algorithm for effective connectedness and for adjacency matrix.