Software development in intuitionistic fuzzy relational. The symbol v is often used instead of the symbol max. Research article novel applications of intuitionistic. Hence g is self centered intervalvalued fuzzy graph. The main theorem in this section is g1 g2 is balanced if and only if dg1dg2dg1 g2. A v 0forevery v in v, then the intuitionistic fuzzy set a is just zadehs fuzzy set. The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Research openaccess strongsumdistanceinfuzzygraphs.
In this research article, we present some new properties of intuitionistic fuzzy competition graphs. We also derived a necessary and sufficient condition for. Intuitionistic fuzzy numbers and its applications in. A is the index matrix of the intuitionistic fuzzy graph g and ak is the kth power of an intuitionistic fuzzy matrix a and conn. Self centered and self median intuitionistic fuzzy graphs, advances in fuzzy sets and systems, volume 14, number 2, 1012, 20. He gave the notion of intuitionistic fuzzy relation and discussed intuitionistic fuzzy graphs which were further studied in 6. In future we will study some more properties and applications of. The present research work is a continuous study of 4. The aim of the paper is to introduce three new intuitionistic fuzzy similarity measures. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. The definition of a self centered intuitionistic fuzzy graph and the necessary and sufficient condition for an ifg to be self centered are given. Similarly, the edges of an intuitionistic fuzzy digraph represent the influence of one person on another person, that is, end nodes of edges.
Novel applications of intuitionistic fuzzy digraphs in. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Neutrosophic set a generalization of the intuitionistic fuzzy set florentin smarandache university of new mexico abstract. Kalaivani, self centered intuitionistic fuzzy graph, world applied sciences journal 1412 2011, 19281936.
Nasir et al novel properties of intuitionistic fuzzy competition graphs intuitionistic fuzzy competition graphs are discussed in 23, 20. The concept of intuitionistic fuzzy graph structure is introduced and investigated in this paper. New intuitionistic fuzzy similarity measures and application to pattern recognition anshu ohlan department of mathematics, all india jat heroes memorial college, rohtak124001, haryana, india. 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 fuzzy set p example. We present a brief overview on intuitionistic fuzzy sets which cuts across some definitions, operations, algebra, modal operators and normalization on intuitionistic fuzzy set.
Solving multi objective linear programming problems using. In the literature, the notions of intuitionistic fuzzy sets and vague sets are. In this paper intuitionistic double layered fuzzy graph is defined with examples. A characterization of self centered complete fuzzy graph. Intuitionistic fuzzy simplex method abstract this paper deals with intuitionistic fuzzy linear programming problemsiflpps using symmetric trapezoidal intuitionistic fuzzy numbersstifns and the arithmetic operations defined on them. An intuitionistic fuzzy graph method for finding the shortest paths in networks. The intervalvalued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allow the degree of membership of a vertex to an edge to be. Isomorphism on vague graphs annals of fuzzy mathematics. Theoretical concepts of graphs are highly utilized by computer science applications.
In this paper one generalizes the intuitionistic fuzzy set ifs, paraconsistent set, and intuitionistic set to the neutrosophic set ns. Strong sum distance in fuzzy graphs pubmed central pmc. Necessary conditions for a fuzzy graph to be self centered are obtained in this section. In this paper, we have defined the intuitionistic fuzzy graphs of second type and its subgraph. Ranking of intuitionistic fuzzy numbers by new distance. Intuitionistic fuzzy lattices and intuitionistic fuzzy. The initial idea of the intuitionistic fuzzy graph ifg was also developed by atanassov 23 in 1999.
Definition 9 see 12 a bridge x, y in g is said to be. Some operations including union, join, cartesian product, cross product, lexicographic product, strong product and composition on intuitionistic. Intuitionisticfuzzysetspast,presentandfuture krassimirt. The fuzzy proposition mary is teenager is defined by the fuzzy set. Fuzzy set 19 theory plays a vital role in complex phenomena which is not effortlessly described by classical set theory. Since zadeh 35 introduced fuzzy sets fs in 1965, many approaches, 21, 22, 26 and theories 4, 5, 7, 28 treating imprecision and uncertainty have been proposed. Hence intuitionistic fuzzy sets have better modeling power than the fuzzy sets. It is featured in the series studies in fuzziness and soft computing under volume 35. Pdf self centered intervalvalued fuzzy graphs researchgate. Chapter ii intuitionistic fuzzy directed graphs the theory of graph plays a vital role for solving combinatorial problems in di. Nagoor gani and shajitha begum discussed the various types of degrees and some properties of ifg in 15.
Operations on intuitionistic trapezoidal fuzzy numbers. Selfcentered single valued neutrosophic graphs smarandache. An intuitionistic fuzzy graph structure ifgs is a generalization of an intuitionistic fuzzy graph. One of the remarkable generalizations of fuzzy sets was intuitionistic fuzzy sets given by k. Intuitionistic fuzzy number and its arithmetic operation. The motivation of the present study is to give computational algorithm for solving multi objective linear programming problem by intuitionistic fuzzy optimization approach. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. But in intuitionistic fuzzy graph, the definitions of intuitionistic fuzzy bridge and intuitionistic fuzzy cut node are not so. Intuitionistic fuzzy cycles and intuitionistic fuzzy trees. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, the definition of complement of an intuitionistic fuzzy graph ifg is given and some properties of self complementary. Strong sum distance in fuzzy graphs springerplus full text.
Introduction the concept of intuitionistic fuzzy graph structure 1 a, b, b 2. Some of its theoretical concepts were studied using different concepts in ifg. Buvaneswari, constant intuitionistic fuzzy graphs, notes on intuitionistic fuzzy sets 171 2011, 3747. Further investigate properties product intuitionistic fuzzy graphs. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. Hesitant fuzzy graphs and their applications in decision. Theory and applications is the title of a book by krassimir atanassov, published in springer physicaverlag publishing house in november 1999 under isbn 3790812285. Sunitha analyzed the properties of selfcentered fuzzy graph. Intuitionistic fuzzy graph structure, complement, self complementary, totally self complementary, strong self complementary i. Operations on intuitionistic fuzzy graph structures.
Szmidt and kacpryzk introduced the hamming distance between intuitionistic fuzzy sets and proposed a similarity measure based on the distance. The book introduces the basic definitions and properties of the intuitionistic fuzzy sets, which are. Firstly, three kinds of new product operations called direct product, lexicographic product, and strong product are defined in intuitionistic fuzzy graphs, and some important notions on intuitionistic fuzzy graphs are demonstrated by characterizing these. Matrix representations of intuitionistic fuzzy graphs. In this paper, we concentrate on a mst problem of a undirected connected fuzzy graph in which a intuitionistic fuzzy numbers, instead of a crisp real number, is used to each edge as edge weight. Pdf self centered intuitionistic fuzzy graph karunambigai m. Pdf self centered intuitionistic fuzzy graph researchgate. In fuzzy graph theory, double layered fuzzy graph and intuitionistic fuzzy graph have been defined already by different authors.
Atanassov, intuitionistic fuzzy sets, fuzzy sets and systems, 20 1986 8796. The structure of an intuitionistic fuzzy graph ifg depends mainly on its arcs, as in crisp graphs. Some of these theories, such as intuitionistic fuzzy sets ifs, intervalvalued fuzzy sets ivfs, and intervalvalued intuitionistic fuzzy sets ivifs, are. In the following, we will describe those aspects of intuitionistic fuzzy sets which will be needed in our next discussion. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. 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. In last few years, di erent methods for ranking ifns have been introduced79,10,12,23. The intuitionistic fuzzy set ifs theory is based on. As a consequence, there exists self centered fuzzy graph of radius c for each real. Intuitionistic fuzzy graphs with categorical properties.
Keywords self centered intervalvalued graph eccentricity radius diameter. Graph theory has numerous applications in modern sciences and technology. Atanassov, more on intuitionistic fuzzy sets, fuzzy sets and systems, 33 1989 3746. Later, karunambigai and parvathy presented ifgs as a special case of atanassovs ifg 24. Atanassov introduced the concept of intuitionistic fuzzy. Research article intuitionistic fuzzy planar graphs. The membership function \i aub of the union au b of the fuzzy sets a and b is defined as follows.
Novel properties of intuitionistic fuzzy competition graphs. It is shown that every complete intuitionistic fuzzy graph structure is self centered but converse is not true. First we introduce some definitions which we define below. A characterisation of self centered complete fuzzy graph is obtained and conditions under. We also present that the arithmetic operation of two or more intuitionistic fuzzy number is again an intuitionistic fuzzy number. Intuitionistic fuzzy sets are generalization of fuzzy sets. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Section 2 contains preliminaries and in section 3, strong sum distance in fuzzy graphs is defined and proved that it is a metric. Similarly, intuitionistic fuzzy lattices are more general than the fuzzy lattices. Then we introduce the concept of self centered n graphs and investigate some of their important properties. The union of fuzzy set a and b is denoted by aub and is defined as the smallest fuzzy set that contains both fuzzy set a and fuzzy set b. Based on this metric, eccentricity, radius, diameter, center in fuzzy graphs are defined. Self centered intervalvalued fuzzy graphs springerlink. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied.
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