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) |
|---|---|
| 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 |
|---|---|
| Volume | 363 |
| ISSN (Print) | 1434-9922 |
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All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
- Computational Mathematics
Cite this
Fuzzy graphs. / Mathew, Sunil; Mordeson, John N.; Malik, Davender S.
Studies in Fuzziness and Soft Computing. Vol. 363 Springer Verlag, 2018. p. 13-83 (Studies in Fuzziness and Soft Computing; Vol. 363).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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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UR - http://www.scopus.com/inward/citedby.url?scp=85040014437&partnerID=8YFLogxK
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 -