This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. We present a brief overview on intuitionistic fuzzy sets which cuts across some definitions, operations, algebra, modal operators and normalization on intuitionistic fuzzy set. One of the remarkable generalizations of fuzzy sets was intuitionistic fuzzy sets given by k. This book describes a set of hybrid fuzzy models showing how to use them to deal with incomplete andor vague information in different kind of decisionmaking problems. An intuitionistic fuzzy graph method for finding the shortest paths in. D such that the intuitionistic fuzzy sub graph induced by s. This book reports on advanced concepts in fuzzy graph theory, showing a set of tools that can be successfully applied to understanding and modeling illegal human trafficking. Intuitionistic fuzzy sets are sets whose elements have degrees of membership and nonmembership. He gave the notion of intuitionistic fuzzy relation and discussed intuitionistic fuzzy graphs which were further studied in 6. Graph theory 4, 5, 7, 9 has wide applications in several branches of.
Intuitionistic fuzzy real time multigraphs for communication. This result tried for some fuzzy labeling graphs such as butterfly graph, book graph, wheel graph, caterpillar. In this paper, the intuitionistic fuzzy organizational and neural network models, intuitionistic fuzzy neurons in medical diagnosis, intuitionistic fuzzy digraphs in vulnerability assessment of gas pipeline networks, and. Use features like bookmarks, note taking and highlighting while reading fuzzy graph theory with applications to human trafficking studies. An intuitionistic fuzzy graph method for finding the shortest paths.
However, there are relatively books available on the very same topic. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the concept of independence and domination in fuzzy graphs, as well as directed fuzzy networks, incidence graphs and many more. Research article intuitionistic fuzzy planar graphs nouraalshehri 1 andmuhammadakram 2 department of mathematics, faculty of sciences girls, king abdulaziz university, jeddah, saudi arabia department of mathematics, university of the punjab, new campus, lahore, pakistan correspondence should be addressed to n ouraalshehri. Software development in intuitionistic fuzzy relational.
After introducing the intuitionistic fuzzy numbers operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral. Mordeson, 9783030094942, available at book depository with free delivery worldwide. This book describes a set of fuzzy graphbased models, offering basic tools to construct and apply them for solving different kind of complex and decisionmaking problems, including simulation of disease, best location problem, suitable path problem, object recognition, and more. Based on the authors research, it offers a concise introduction to important models, ranging from rough fuzzy digraphs and intuitionistic fuzzy rough models to bipolar fuzzy. The second one is that the underlying graph of an intuitionistic fuzzy threshold graph is a split graph, and conversely, a given split graph can be used to construct an intuitionistic fuzzy threshold graph. Theoretical advances and applications of fuzzy logic and soft computing pp 310 cite as. Domination in graph theory plays an important role in modeling and optimization of computer and telecommunication networks, transportation networks, ad hoc networks and scheduling problems, molecular physics, etc. The notion of paired domination in intuitionistic fuzzy graph using strong arcs is also studied.
Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. Complex intuitionistic fuzzy graphs with application in cellular. Research on the theory of intuitionistic fuzzy sets has a vast opening in. Atanassov f uzzy graphs are furthe r generalized into intuitionistic fuzz y graphs in which the vertices and the edges have degree of nonmembership values. Fuzzy graph theory with applications to human trafficking by john n. Fuzzy graph theory with applications to human trafficking.
Project scheduling method using triangular intuitionistic. Buy fuzzy graph theory with applications to human trafficking. The intuitionistic fuzzy set ifs theory is based on. The concepts of covering and matching in an intuitionistic fuzzy graph using strong arcs are introduced and established many interesting properties on it. Karunambigai and parvathi 3 introduced intuitionistic fuzzy graph as a special case of atanassovs ifg. In this paper, the intuitionistic fuzzy organizational and neural network models, intuitionistic fuzzy neurons in medical diagnosis. Out of several higherorder fuzzy sets, ifs first introduced by atanassov 1 have been. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book gives a special emphasis to applications of the theory. Intuitionistic fuzzy number and its arithmetic operation. Covering and paired domination in intuitionistic fuzzy graphs. Professors mordeson and nair have made a real contribution in putting together a very com prehensive book on.
Neutrosophic set a generalization of the intuitionistic fuzzy set journal of defense resources management no. Novel applications of intuitionistic fuzzy digraphs in. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. The fuzzy graph theory as a generalization of eulers graph theory was first introduced by. V is said to be intuitionistic fuzzy point set dominating set of g if for every s. Chapter ii intuitionistic fuzzy directed graphs the theory of graph plays a vital role for solving combinatorial problems in di. Nasir et al novel properties of intuitionistic fuzzy competition graphs intuitionistic fuzzy competition graphs are discussed in 23, 20. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. The intuitionistic point set fuzzy domination number. It is featured in the series studies in fuzziness and soft computing under volume 35.
Iii matrix representations of intuitionistic fuzzy graphs in this section, the properties of the power of an intuitionistic fuzzy graph and the relationship between the index matrix of an intuitionistic fuzzy graph and power of an intuitionistic fuzzy graph have been analysed. Complex intuitionistic fuzzy graphs have many applications in database theory, expert systems, neural networks, decision making problems, gisbased road networks, facility location problems and so on. Parvathi and thamizhendhi 11 introduced and analyzed the theory of domination on join, cartesian product, lexicographic product. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs. Fuzzy graph theory is finding an increasing number of applications. Intuitionistic fuzzy graph theory was introduced by krassimir t atanassov in 1. Fuzzy graph theory with applications to human trafficking studies in fuzziness and soft computing book 365 kindle edition by mordeson, john n. As a result, a kind of representations of intuitionistic fuzzy graphs and intuitionistic fuzzy complete graphs are given. Mordeson, 9783319764535, available at book depository with free delivery worldwide. Li and yi defined an intuitionistic fuzzy matroid by using an indirect approach and study their properties, which is the first time of the combination of matroids and intuitionistic fuzzy sets 34. The book introduces the basic definitions and properties of the intuitionistic fuzzy sets, which are. The focus of this book is on establishing theories and methods of both decision and game analysis in management using in. This book reports on advanced concepts in fuzzy graph theory, showing a set of tools. Buy fuzzy graph theory with applications to human trafficking studies in.
In this paper, the concept of coloring the intuitionistic fuzzy graph introduced with. Next, categorical goodness of intuitionistic fuzzy graphs is illustrated by proving that the category of intuitionistic fuzzy graphs and homomorphisms between them is isomorphicclosed, complete, and cocomplete. In the open literature, there are many papers written on the subject of fuzzy graph theory. Part of the studies in fuzziness and soft computing book series studfuzz, volume 35 the intuitionistic fuzzy set ifs theory is based on. Intuitionistic fuzzy sets from ifigenia, the wiki for. The main theorem in this section is g1 g2 is balanced if and only if dg1dg2dg1 g2. The present research work is a continuous study of 4. Zhang 4 discussed various colorings of graph and its properties in their book. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Akram and akmal defined intuitionistic fuzzy graph structures 5 and operations on. The theory of intuitionistic fuzzy graphs ifgs was introduced by krassimir t atanassov 1, 12. Krassimir atanassov 1 introduced the concept of intuitionistic fuzzy graph ifg in 1994. In this chapter we present in brief, the theory of fuzzy set introduced by zadeh 11 and the theory of intuitionistic fuzzy set introduced by atanassov 710.
Following the above mathematical approach, we combine two very powerful techniques, namely complex intuitionistic fuzzy sets and graph theory, and introduce the notion of complex intuitionistic fuzzy graphs. Operations on intuitionistic fuzzy graph structures. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the. This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in intervalvalued intuitionistic fuzzy environments, and their applications in multiattribute. An intuitionistic fuzzy graph structure ifgs is a generalization of an intuitionistic fuzzy graph. Ping zhang 4 discussed various colorings of graph and its properties in their book. Intuitionistic fuzzy sets are the valuable generalization of fuzzy sets. Part of the advances in soft computing book series ainsc, volume 42. Graph theory has numerous applications in modern sciences and technology. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. Complex intuitionistic fuzzy graphs with application in. Hybrid soft computing models applied to graph theory. Some operations including union, join, cartesian product, cross product, lexicographic product, strong product and composition on intuitionistic.
Parvathi introduced intuitionistic fuzzy graph as a special case of. Project scheduling method using triangular intuitionistic fuzzy numbers and. Novel properties of intuitionistic fuzzy competition graphs. Read decision and game theory in management with intuitionistic fuzzy sets by dengfeng li available from rakuten kobo. In this book, readers will find discussions on some of the ifs extensions for example, intervalvalues ifss, temporal ifss and others and applications e. Abstractin this paper, we introduced energy of fuzzy labeling graph and its denoted by ef. Many problems of practical interest can be modeled and solved by using graph algorithms.
He is the author of eight books published from india and uk and these are written. Szmidt and kacpryzk introduced the hamming distance between intuitionistic fuzzy sets and proposed a similarity measure based on the distance. In general, graph theory has a wide range of applications in diverse fields. A study on point set domination of intuitionistic fuzzy graphs. Also, there are many applications of domination in fuzzy and intuitionistic fuzzy sets for solving problems in vague situations. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs.
Pdf perfect intuitionistic fuzzy graphs researchgate. Intuitionistic fuzzy sets have been introduced by krassimir atanassov 1983 as an extension of lotfi zadehs notion of fuzzy set, which itself extends the classical notion of a set in classical set theory, the membership of elements in a set is assessed in binary terms according to a. Ranking of intuitionistic fuzzy numbers by new distance. Fuzzy graph theory with applications to human trafficking studies. Intuitionistic fuzzy graphs with categorical properties. Research article intuitionistic fuzzy planar graphs. In last few years, di erent methods for ranking ifns have been introduced79,10,12,23. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book.
After rosenfeld 20 the fuzzy graph theory increases with its various. Theory and applications is the title of a book by krassimir atanassov, published in springer physicaverlag publishing house in november 1999 under isbn 3790812285. The concept of intuitionistic fuzzy graph structure is introduced and investigated in this paper. Intuitionistic fuzzy aggregation and clustering by zeshui.
We combine complex intuitionistic fuzzy sets with the graph theory. The purpose of the book is to present a continuation of studies conducted focusing mainly on measures that evaluate intuitionistic fuzzy sets. Theoretical advances and applications of fuzzy logic and soft computing pp 3 10 cite as. This book is the outcome of about eight years of work performed by the author largely in the field of intuitionistic fuzzy set theory and more in depth on intuitionistic fuzzy measures presented from a point of view characteristic for pure mathematics. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets. Decision and game theory in management with intuitionistic. In this paper, the definition of complement of an intuitionistic fuzzy graph ifg is given and some properties of selfcomplementary. Matrix representations of intuitionistic fuzzy graphs. We extend the concept of fuzzy labeling graph to the energy of fuzzy labeling graph ef lg. In recent years, a mathematical approach of blending different aspects is on the way, which as a result gives a more generalized approach. In this research article, we present some new properties of intuitionistic fuzzy competition graphs. Applicationof ifgraphsandifrelationmethodsarealsodeveloped. Chromatic excellence,chromatic number,intuitionistic fuzzy graph, vertex. Intuitionistic fuzzy sets are generalization of fuzzy sets.
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