Product of bipolar fuzzy graphs and their degree
The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theor...
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| Published in | International journal of general systems Vol. 45; no. 1; pp. 1 - 14 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis
02.01.2016
Taylor & Francis LLC |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1079 1563-5104 |
| DOI | 10.1080/03081079.2015.1072521 |
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| Abstract | The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs
and
using the operations Cartesian product, composition, tensor and normal product are determined. |
|---|---|
| AbstractList | The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs [Image omitted.] and [Image omitted.] using the operations Cartesian product, composition, tensor and normal product are determined. The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs [Formula omitted.] and [Formula omitted.] using the operations Cartesian product, composition, tensor and normal product are determined. The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs and using the operations Cartesian product, composition, tensor and normal product are determined. |
| Author | Borzooei, Rajab Ali Pal, Madhumangal Rashmanlou, Hossein Samanta, Sovan |
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| Cites_doi | 10.5373/jarpm.1562.092512 10.5121/ijfls.2012.2103 10.1016/S0019-9958(65)90241-X 10.1007/s13042-014-0284-7 10.1016/j.ins.2011.07.037 10.3233/IFS-141333 10.1007/s12543-013-0140-6 10.1016/0020-0255(94)90116-3 10.5120/3351-4620 10.1007/s12190-014-0785-2 10.1016/S0020-0255(71)80005-1 10.1016/j.ins.2005.01.017 |
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| SubjectTerms | Cartesian product composition Data mining degree of a vertex Fuzzy Fuzzy sets Graph theory Graphs Mathematical analysis normal product tensor product Tensors Uncertainty |
| Title | Product of bipolar fuzzy graphs and their degree |
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