In this paper, we apply the concept of bipolar fuzzy sets to multigraphs and planar graphs. Bipolar neutrosophic models are more flexible and applicable. We consider the concept of strongest bipolar fuzzy relations on bipolar fuzzy dideals of a group and discuss some related properties. Graph theory has numerous application to problems in systems analysis, operations research, economics, and transportation. Extended bipolar fuzzy directed hypergraphs to mpolar information.
We depict certain operations on mpolar fuzzy directed hypergraphs. In the open literature, there are many papers written on the subject of fuzzy graph theory. Jan 14, 2016 a bipolar fuzzy set is a generalization of a fuzzy set. Applied computational intelligence and soft computing 2016 article. Samanta and pal introduced fuzzy tolerance graph 21, irregular bipolar fuzzy graphs 23, fuzzy k competition graphs and pcompetition fuzzy graphs 24, bipolar fuzzy hypergraphs. The bipolar fuzzy graph is a generalized structure of a fuzzy graph which gives more precision, flexibility, and compatibility with a system when compared with the fuzzy graphs. Further investigate properties product intuitionistic fuzzy graphs. Different types of products on intuitionistic fuzzy graphs sciencedirect. An mpolar fuzzy model is a generalization of the fuzzy model.
We introduce the notions of bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, bipolar fuzzy. We introduce certain notions, including bipolar fuzzy graph structure bfgs, strong bipolar fuzzy graph structure, bipolar fuzzy cycle, bipolar fuzzy tree, bipolar fuzzy cut vertex, and bipolar fuzzy. A bipolar fuzzy set is a generalization of a fuzzy set. Intuitionistic fuzzy hypergraphs cybernetics and information. It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy. In this paper, we initiate a study on bipolar, fuzzy sets in semihypergroups. Application of bipolar fuzzy sets in graph structures applied. We consider the concept of strongest bipolar anti q fuzzy relations on. It discusses applied generalized mathematical models of fuzzy sets to hypergraphs, including intuitionistic fuzzy sets, bipolar fuzzy sets, mpolar fuzzy. Fuzzy multiple domination international journal of scientific and. This paper introduces the concepts of perfect bipolar fuzzy graph, complete perfect bipolar fuzzy graph, semiperfect. Colouring of fuzzy graphs has several applications in real world.
The mpolar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An application of fuzzy hypergraphs and hypergraphs in. To deal with such types of problems, we use mathematical models that are based on bipolar fuzzy. We introduce certain notions, including bipolar fuzzy graph structure bfgs, strong bipolar fuzzy graph structure, bipolar fuzzy cycle, bipolar fuzzy tree, bipolar fuzzy cut vertex, and bipolar fuzzy bridge, and illustrate these notions by several examples. Pdf properties of bipolar fuzzy hypergraphs researchgate. Sometimes, given data in a network model are based on bipolar information rather than one sided. A hypernetwork m is a network whose underlying structure is a.
A totally regular bsvnhg is the generalization of totally regular fuzzy hypergraphs, totally regular intuitionistic fuzzy hypergraphs, totally regular bipolar fuzzy hypergraphs and totally regular single valued. In 1994, zhang initiated the concept of bipolar fuzzy sets as a generalization of fuzzy sets. Application of bipolar fuzzy sets in planar graphs. We also give characterizations of bipolar fuzzy ideal. In this paper, a new concept of colouring of fuzzy graphs has been introduced. In this paper, an effective degree of a vertex, a ordinary degree of a vertex in bipolar fuzzy graph as analogous of fuzzy graph. The dombi operations have so far not yet been applied for bipolar fuzzy sets. The bipolar fuzzy hypergraph is a hypergraph in which each vertex and edge is. Motivated from dombi operations, we have proposed bipolar fuzzy dombi weighted averaging operator, bipolar fuzzy. Some basic concepts of bipolar fuzzy set are defined.
Directed hypergraphs for bipolar neutrosophic structures. In this research paper, we apply the notion of mpolar fuzzy sets to generalize the theory of hypergraphs. A new decisionmaking method based on bipolar neutrosophic. Regular product vague graphs and product vague line graphs. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, mpolar fuzzy, pythagorean, complex pythagorean, and qrung orthopair hypergraphs, as well as singlevalued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. The operations of tnorm and tconorm introduced by dombi was known as dombi operations can have a lead of good flexibility with the general parameter. A directed hyperedge or hyperarc is an ordered pair e x,y of possibly empty disjoint subsets of vertices.
Chapter iii discusses thebipolar fuzzy line graph of a bipolar fuzzy hypergraphs. We also give characterizations of bipolar anti q fuzzy ideal. This book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. Bipolar fuzzy sets are an extension of fuzzy sets whose membership degree range is. Fuzzy hypergraphs and related extensions muhammad akram. Application of bipolar fuzzy sets in graph structures. An extension of bipolar fuzzy sets juanjuanchen, 1,2 shenggangli, 1 shengquanma, 1 andxuepingwang 3 college of mathematics and information science, shaanxi normal university, xi an, china. Application of bipolar fuzzy sets in graph structures akram. Certain concepts of bipolar fuzzy directed hypergraphs. They defined isometry on intervalvalued fuzzy graphs 14. In this paper, we discuss some properties of the self complement and self weak complement bipolar fuzzy graphs, and get a sufficient condition for a bipolar fuzzy graph to be the self weak complement bipolar fuzzy graph. We introduce the concepts of mpolar fuzzy hypergraphs, dual mpolar fuzzy hypergraphs, mpolar fuzzy line graphs and 2section of mpolar fuzzy. In this research study, we introduce the notion of mpolar fuzzy directed hypergraphs, and present some properties.
Bipolar fuzzy sets are an extension of fuzzy sets whose range of membership degree is 1,1. To deal with such types of problems, we use mathematical models that are based on bipolar fuzzy bf sets. This model is useful for multipolar information, multiagent, multiattribute and multiobject network models. An mpolar fuzzy model plays a vital role in modeling of realworld problems that involve multiattribute, multipolar information and uncertainty. Bipolar fuzzy graphs with applications sciencedirect. A hypergraph is the most developed tool for modeling various practical problems in different fields, including computer sciences, biological sciences, social networks and psychology. International journal on future revolution in computer. Then f is a bijective map defined by fx 1 x 2 for all x 1. Zhang 1994, 1998 introduced the concept of bipolar fuzzy sets.
In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. International journal of fuzzy logic systems ijfls vol. Bipolar fuzzy line graph of a bipolar fuzzy hypergraph definition 3. In this paper, specific types of bipolar fuzzy graphs have been introduced and discussed. The bipolar fuzzy graph is a generalized structure of a fuzzy graph which gives more precision, flexibility, and compatibility with a system when compared with the fuzzy. Regular and totally regular bipolar fuzzy hypergraphs. This paper introduces the concept of a bipolar fuzzy line graph of a bipolar fuzzy hypergraph and some of the properties of the bipolar fuzzy line graph of a bipolar fuzzy hypergraph are also examined. Samanta and pal have also worked on bipolar fuzzy hypergraphs. Pdf in this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs.
In this section, we describe a couple of example applications of hypergraphs. Structures on bipolar fuzzy groups and bipolar fuzzy dideals. Professors mordeson and nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs. A study on bipolar fuzzy planar graph and its application in. On mpolar fuzzy graph structures connecting repositories. It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy sets. An application of fuzzy hypergraphs and hypergraphs in granular computing. The notion of bipolar fuzzy set was initiated by lee 2000 as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. And also provide necessary and sufficient condition under which regular bipolar fuzzy hypergraphs and totally regular bipolar fuzzy hypergraphs are equivalent. Feb 01, 20 read bipolar fuzzy graphs with applications, knowledgebased systems on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, mpolar fuzzy.
And also provide necessary and sufficient condition under which regular bipolar fuzzy hypergraphs and totally regular bipolar fuzzy hypergraphs. It discusses applied generalized mathematical models of fuzzy sets to hypergraphs, including intuitionistic fuzzy sets, bipolar fuzzy sets, mpolar fuzzy sets, etc. Bipolar fuzzy line graph of a bipolar fuzzy hypergraph. We illustrate these operations by several examples. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, mpolar fuzzy, pythagorean, complex pythagorean, and qrung orthopair hypergraphs, as well as singlevalued neutrosophic, complex neutrosophic and bipolar. Some properties of bipolar fuzzy hypergraphs are investigated in. Different types of products on intuitionistic fuzzy graphs core.
We describe certain operations on bf directed hypergraphs. Mordeson and nair studied cycles and cocycles of fuzzy graphs, and studied fuzzy graphs and fuzzy hypergraphs in. Applications of bipolar fuzzy theory to hemirings 769 characterize normal bipolar fuzzy hideal of hemiring in section 6. We extend work on completeness of bipolar single valued neutrosophic hypergraphs. Bipolar neutrosophic hypergraphs, btempered bipolar neutrosophic hypergraphs, bipolar neutrosophictransversals, applications. Fuzzy hypergraphs and related extensions springerlink. Download fuzzy hypergraphs and related extensions softarchive. This paper introduces the concept of a bipolar fuzzy line graph of a bipolar fuzzy hypergraph and some of the properties of the bipolar fuzzy line graph of a. In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some basic theorems and some properties of bipolar fuzzy hypergraphs. We introduce the notions of bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, bipolar fuzzy dual graphs, and investigate some of their interesting properties. We introduce certain notions, including bipolar fuzzy graph structure bfgs, strong bipolar fuzzy graph structure, bipolar fuzzy n icycle, bipolar fuzzy n itree, bipolar fuzzy n icut vertex, and bipolar fuzzy n ibridge, and illustrate these notions by several. However, there are relatively books available on the very same topic.
Directed hypergraphs are widely used as a tool to solve and model the problems appearing in computer science and operations research. Pdf in this paper, we define some basic concepts of bipolar fuzzy hypergraphs, cut level bipolar fuzzy hypergraphs, dual bipolar fuzzy hypergraphs and. Then the weak isomorphism between these bipolar fuzzy graphs is a partial order relation. Vague graph is a generalized structure of fuzzy graph which gives more. Also, some important terms like strength cut graphs, fuzzy colour, chromatic number of fuzzy. Intervalvalued fuzzy threshold graph sciencedirect. A new decisionmaking method based on bipolar neutrosophic directed hypergraphs. Also we investigate relations between operations union, join, and complement on bipolar fuzzy. Keywords fuzzy hypergraphs, bipolar fuzzy hypergraphs, bipolar. We introduce the concepts of regular and totally regular bipolar fuzzy graphs. A special emphasis is given to mpolar fuzzy graphs at t. We provide a condition for a bipolar anti q fuzzy groups to be a bipolar anti q fuzzy dideal. Bipolar fuzzy soft lie algebras 3 in other words, a soft set over u is a parameterized family of subsets of the universe u.
The bipolar fuzzy influence graph of a social group is also developed. Regular bipolar single valued neutrosophic hypergraphs. In this research paper, we introduce the concept of bf directed hypergraphs. Intuitionistic fuzzy hypergraphs with applications. We put forward the notion of polar fuzzy set an extension of bipolar fuzzy set and point out that many concepts which have been defined based on bipolar fuzzy sets and many results related to these concepts can be generalized to the case of polar fuzzy sets see remarks 7 and 8 for details. A bipolar fuzzy hypergraph is defined to be a pair h x. Some basic theorems related to the stated graphs have also been presented. Bipolar fuzzy graphs, irregular bipolar fuzzy graphs, totally irregular bipolar fuzzy graphs. Bipolar fuzzy graphs with applications, knowledgebased.
It is demonstrated that every intervalvalued fuzzy threshold graph can be treated as an. Mathew and sunitha 6 described the types of arcs in a fuzzy graph. Pdf certain concepts of bipolar fuzzy directed hypergraphs. Pdf a hypergraph is the most developed tool for modeling various practical problems in different fields, including computer sciences, biological. There are so many related works found in 31, 33, 3537. Bipolar fuzzy line graph of a bipolar fuzzy hypergraph in. Pdf in this paper, we define some basic concepts of bipolar fuzzy hypergraphs, cut level bipolar fuzzy hypergraphs, dual bipolar fuzzy. We describe certain operations on bf directed hypergraphs, including addition, multiplication, vertexwise multiplication and structural subtraction. Let lh s, t be a line graph of a simple hypergraph. A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. Pdf in this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy. A directed hyperedge or hyperarc is an ordered pair e x,y of possibly empty disjoint.
Complement and isomorphism on bipolar fuzzy graphs. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. In this research article, we introduce the notion of mpolar fuzzy graph structure and present various operations, including cartesian product, strong product, cross product, lexicographic product, composition, union and join of mpolar fuzzy graph structures. Akram and dudek 2 studied regular bipolar fuzzy graphs, and akram 3 also discussed bipolar fuzzy graphs with applications. They also discussed intuitionistic fuzzy hypergraphs with applications 3. An mpolar fuzzy set assigns the membership degree to an object belonging to 0,1m describing the m distinct. In this paper, we defined bipolar fuzzy planar graph and bipolar fuzzy dual graph and presented several properties. Directed hypergraphs under mpolar fuzzy environment ios. Novel applications of mpolar fuzzy hypergraphs ios press. Chapter iv illustrates thedefinition of fuzzy intersection graphs. Further, we present some applications of bipolar neutrosophic hypergraphs in marketing and biology.
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