The intuitionistic point set fuzzy domination number. Point set domination number of a graph is introduced by e. Research article intuitionistic fuzzy planar graphs. Intuitionistic fuzzy cycles and intuitionistic fuzzy trees.
Notes on intuitionistic fuzzy sets is an international scientific journal, specialized in the theory and application of intuitionistic fuzzy sets and logics as an interdisciplinary field at the cross point between. The first definition of intuitionistic fuzzy graphs was proposed by atanassov2. Alhawary 32 introduced the concept of balanced fuzzy graphs. Pdf the structure of an intuitionistic fuzzy graph ifg depends mainly on its arcs, as in crisp graphs. Intuitionistic fuzzy competition graphs springerlink. Intuitionisticfuzzysetspast,presentandfuture krassimirt. Ranking of intuitionistic fuzzy numbers by new distance. The concept of strong arcs in fuzzy graphs was discussed in 8. Point set domination of intuitionistic fuzzy graphs. A note on intuitionistic fuzzy logics acta philosophica.
If vd contains dominating set d of g then d is called an inverse dominating set of g with respect to d. Some theorems related to the above concepts are studied and this concept is useful in. Roy2 1 department of mathematics, siliguri institute of technology, p. In the following, we will describe those aspects of intuitionistic fuzzy sets which will be needed in our next discussion. In future we will study some more properties and applications of. A study on point set domination of intuitionistic fuzzy graphs. Software development in intuitionistic fuzzy relational. Fuzzy logic in classical logic, a statement is either true or false fuzzy logic consists of statements which have a degree of truth between 1 and 0 for an element e, a fuzzy proposition e is p is defined by a. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Pdf constant intuitionistic fuzzy graphs karunambigai. These arcs are used to study the structure of complete ifg and constant ifg. Operations on intuitionistic fuzzy graph structures. Intuitionistic fuzzy number and its arithmetic operation.
The bound on this number are obtained for some standard intuitionistic fuzzy graphs. Graph theory has numerous applications in modern sciences and technology. It is claimed that the method may play a major role in many application areas of computer science, communication network. An intuitionistic fuzzy graph structure ifgs is a generalization of an intuitionistic fuzzy graph. In last few years, di erent methods for ranking ifns have been introduced79,10,12,23. The structure of an intuitionistic fuzzy graph ifg depends mainly on its arcs, as in crisp graphs. Novel applications of intuitionistic fuzzy digraphs in. Intuitionistic fuzzy graphs with categorical properties. Intuitionistic fuzzy graphs are more convenient than fuzzy graphs, which is useful in the traffic density and telecommunication systems. After introducing the intuitionistic fuzzy numbers operational laws and. Intuitionistic fuzzy sets have only loosely related membership and nonmembership values unlike classical zadeh 16 fuzzy sets. On direct sum of two intuitionistic fuzzy graphs dr.
Chountas and alzebdi 9 presented an intuitionistic fuzzy version of a tree in graph theory. The global domination number of a graph was discussed by e. The concept of intuitionistic fuzzy graph structure is introduced and investigated in this paper. The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Pdf strong intuitionistic fuzzy graphs muhammad akram. The concept of intuitionistic fuzzy graphs was introduced by shannon and atanassov 16, they investigated some of their properties in 17. Research article intuitionistic fuzzy planar graphs nouraalshehri 1 andmuhammadakram 2 department of mathematics, faculty of sciences girls, king abdulaziz university, jeddah, saudi arabia. Pdf domination in product intuitionistic fuzzy graphs. Pdf intuitionistic fuzzy sets are generalization of fuzzy sets. A v 0forevery v in v, then the intuitionistic fuzzy set a is just zadehs fuzzy set. Since intuitionistic fuzzy models give more precision, flexibility, and compatibility to the system as compared to the fuzzy models, we have investigated some properties of intuitionistic fuzzy cycles.
Complementary nil domination in intuitionistic fuzzy graph. Global domination set in intuitionistic fuzzy graph. In this paper c we also define inverse dominating set, inverse. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. Lakshmi department of mathematics, velammal college of engineering and technology, madurai625009 abstract.
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 graphs was introduced by shannon and atanassov 16, they investigated some of their properties in. Matrix representations of intuitionistic fuzzy graphs. In general, graph theory has a wide range of applications in diverse fields. Introduction the purpose of this note it to outline the salient features of intuitionistic fuzzy logic, which is a branch of symbolic. Applicationof ifgraphsandifrelationmethodsarealsodeveloped. In this paper, two generalizations of intuitionistic fuzzy competition graphs as intuitionistic. Semi global dominating set of intuitionistic fuzzy graphs. Firstly, three kinds of new product operations called direct product. In this paper, the definition of complement of an intuitionistic fuzzy graph ifg is. An ifs is a generalization of the classical fuzzy set which defines. We present a brief overview on intuitionistic fuzzy sets which cuts across some definitions, operations.
The nodes of intuitionistic fuzzy digraph in figure 2 represent the employee and its power in terms of degree of membership and nonmembership which can be interpreted as percentage. Chapter ii intuitionistic fuzzy directed graphs the theory of graph plays a vital role for solving combinatorial problems in di. In this paper, we have defined the intuitionistic fuzzy graphs of second type and its subgraph. Intuitionistic fuzzy competition graph as a generalization of competition graph is introduced. Pdf we introduce the notion of intuitionistic fuzzy edge graph g v, b, where v is a crisp vertex set and b is an intuitionistic fuzzy relation on. Notes on intuitionistic fuzzy sets from ifigenia, the wiki.