Characteristics and Operations of Complex Fuzzy Graphs

IEEE Access

This paper comprises the introduction of weighted mean products of fuzzy graph structures (FGSs) to construct weighted mean fuzzy graph structures (WMFGSs) with the help of optimization parameter, and establish some novel results after validating with examples, accordingly. The notions of regular and mµ k-regular FGSs are described, where m ∈]0, 1] represents the degree of all vertices in G under mapping µ k , and develop certain properties of regular WMFGSs. In addition, we create a flowchart to present common application procedures of fuzzy graphical frameworks to classify the advanced city out of some important Pakistani cities subject to certain parameters. INDEX TERMS Fuzzy graph structure, weighted mean product, vertex degree, vertex total degree, regular fuzzy graph structure.

Complex & Intelligent Systems

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

1.1 Graph Graph theory is tremendously useful in modelling the essential features of systems with finite components. Wide applications of graphical models are in the field of railway network, telephone network, communication problems, traffic network etc. Graph theoretic models can sometimes provide a useful structure upon which analytic techniques can be used. A graph is also used to model a relationship between a given set of objects. Each object is represented by a vertex and the relationship between them is represented by an edge if the relationship is unordered and by means of a directed edge if the objects have an ordered relation between them. Relationship among the objects need not always be precisely defined criteria; when we think of an imprecise concept, the fuzziness arises. 1.2 Fuzzy graph A mathematical frame work to explain the concept of uncertainty in real life through the publication of a seminal paper is introduced by Zadeh [1]. A fuzzy set is defined mathematically by assigning to each possible individual in the universe of discourse a value, representing its grade of membership, which corresponds to the degree, to which that individual is similar or compatible with the concept represented by the fuzzy set. Rosenfeld [2] was introduced the fuzzy graph using fuzzy relation, represents the relationship between the objects by precisely indicating the level of the relationship between the objects of the given set. Also he coined many fuzzy analogous graph theoretic concepts like bridge, cut vertex and tree. Fuzzy graphs have many more applications in modelling real time systems where the level of information inherent in the system varies with different levels of precision.

Correctly determining a company's market worth during an entire year or a certain period presents a difficulty to decision-makers. In the case of the merger of companies, the need performs heavier when both the companies' owners are attracted to establishing a fair price at the optimal time to merge. The effectiveness of representing, connecting and manipulating both uncertainty and periodicity information becomes highly required. Hence, study and nhance some properties and conditions of the algebraic structure of complex hesitant fuzzy graphs. Therefore, the degree of composition between two complex hesitant fuzzy graphs is proposed. Also, the formal definitions of union, joint and complement are presented to be covered in the realm of complex hesitant fuzzy graphs. A real-life application is illustrated to show the relation between vertices and edges in the form of complex hesitant fuzzy graphs.

This paper is a study of semitotal blocks in fuzzy graphs. During the study some interesting results regarding the semitotal blocks in fuzzy graphs are obtained. It is observed that when 'B' is a block of a given fuzzy graph G:(V, σ, µ), then degree of the vertex B in semi total block fuzzy graph T STB F(G) is equal to the sum of the membership grade of the vertices in that block and the number of edges in T STB F(G) related to block B is V(B) with membership grade minimum of

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2018

Graph theory has successfully used to solve a wide range of problems encountered in diverse fields such as medical sciences, neural networks, control theory, transportation, clustering analysis, expert systems, image capturing, and network security. In past few years, a number of generalizations of graph theoretical concepts have developed to model the impreciseness and uncertainties in graphical network problems. A Pythagorean fuzzy set is a powerful tool for describing the vague concepts more precisely. The Pythagorean fuzzy set-based models provide more flexibility in handling the human judgment information as compared to other fuzzy models. The objective of this paper is to apply the concept of Pythagorean fuzzy sets to graph theory. This work introduces the notion of Pythagorean fuzzy graphs (PFGs) and describes a number of methods for their construction. We then define some basic operations on PFGs and prove some of their important properties. The work also discusses the notio...

In this study researchers propose the complete, regular and complement fuzzy graph. In these subjects we shall study some properties such that: self complementary, regular, total regular fuzzy graph and the relation between these subject. On the other hand we shall study a product fuzzy graph and what the relation between the product and the complete also the complement. We get some theorem, proposition and corollaries for these subjects.

Fuzzy Graphs are having numerous applications in problems like Network analysis, Clustering, Pattern Recognition and Neural Networks. The analysis of properties of fuzzy graphs has facilitated the study of many complicated networks like Internet. In this paper we study the structures of complement of many important fuzzy graphs such as Fuzzy cycles, Blocks etc. The complement of fuzzy graphs with a certain structural property is studied in this paper.

The authors and co-authors, listed in the order of their published neutrosophic papers: Muhammad Akram, Muzzamal Sitara, A. A. A. Agboola, B. Davvaz, F. Smarandache, Ali Hassan, Muhammad Aslam Malik, Said Broumi, Assia Bakali, Mohamed Talea, K. Hur, P. K. Lim, J. G. Lee, J. Kim, Young Bae Jun, Maryam Nasir, and A. Borumand Saeid, would like to thank Prof. Kul Hur, the Editorin-Chief of the international journal Annals of Fuzzy Mathematics and Informatics (AFMI), for dedicating the whole Vol. 14, No.1, published on 25 July 2017, to the neutrosophic theories and applications. The papers included in this volume are especially referring to neutrosophic (single-valued and interval-valued) graphs and bipolar graphs, and their applications in multi-criteria decision making (MCDM), and to neutrosophic algebraic structures, such as: category of neutrosophic crisp sets, neutrosophic quadruple algebraic hyperstructures, and neutrosophic subalgebras of BCK/BCI-algebras. We would also like to bring our gratitude to many reviewers of the neutrosophic community, from around the world, community that has grew to over eight hundred peoples (students, faculty, and researchers).