### Abstract

A graph represents a particular relationship between elements of a set V. It gives an idea about the extent of the relationship between any two elements of V. We can solve this problem by using a weighted graph if proper weights are known. But in most of the situations, the weights may not be known, and the relationships are ‘fuzzy’ in a natural sense. Hence, a fuzzy relation can deal with the situation in a better way. As an example, if V represents certain locations and a network of roads is to be constructed between elements of V, then the costs of construction of the links are fuzzy. But the costs can be compared, to some extent using the terrain and local factors and can be modeled as fuzzy relations. Thus, fuzzy graph models are more helpful and realistic in natural situations.

Original language | English (US) |
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Title of host publication | Studies in Fuzziness and Soft Computing |

Publisher | Springer Verlag |

Pages | 13-83 |

Number of pages | 71 |

Volume | 363 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
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Volume | 363 |

ISSN (Print) | 1434-9922 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Computational Mathematics

### Cite this

*Studies in Fuzziness and Soft Computing*(Vol. 363, pp. 13-83). (Studies in Fuzziness and Soft Computing; Vol. 363). Springer Verlag. https://doi.org/10.1007/978-3-319-71407-3_2

**Fuzzy graphs.** / Mathew, Sunil; Mordeson, John N.; Malik, Davender S.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Studies in Fuzziness and Soft Computing.*vol. 363, Studies in Fuzziness and Soft Computing, vol. 363, Springer Verlag, pp. 13-83. https://doi.org/10.1007/978-3-319-71407-3_2

}

TY - CHAP

T1 - Fuzzy graphs

AU - Mathew, Sunil

AU - Mordeson, John N.

AU - Malik, Davender S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A graph represents a particular relationship between elements of a set V. It gives an idea about the extent of the relationship between any two elements of V. We can solve this problem by using a weighted graph if proper weights are known. But in most of the situations, the weights may not be known, and the relationships are ‘fuzzy’ in a natural sense. Hence, a fuzzy relation can deal with the situation in a better way. As an example, if V represents certain locations and a network of roads is to be constructed between elements of V, then the costs of construction of the links are fuzzy. But the costs can be compared, to some extent using the terrain and local factors and can be modeled as fuzzy relations. Thus, fuzzy graph models are more helpful and realistic in natural situations.

AB - A graph represents a particular relationship between elements of a set V. It gives an idea about the extent of the relationship between any two elements of V. We can solve this problem by using a weighted graph if proper weights are known. But in most of the situations, the weights may not be known, and the relationships are ‘fuzzy’ in a natural sense. Hence, a fuzzy relation can deal with the situation in a better way. As an example, if V represents certain locations and a network of roads is to be constructed between elements of V, then the costs of construction of the links are fuzzy. But the costs can be compared, to some extent using the terrain and local factors and can be modeled as fuzzy relations. Thus, fuzzy graph models are more helpful and realistic in natural situations.

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U2 - 10.1007/978-3-319-71407-3_2

DO - 10.1007/978-3-319-71407-3_2

M3 - Chapter

VL - 363

T3 - Studies in Fuzziness and Soft Computing

SP - 13

EP - 83

BT - Studies in Fuzziness and Soft Computing

PB - Springer Verlag

ER -