### Abstract

The notion of a fuzzy graph was initially introduced by Kauffman (Introduction to the theory of fuzzy sets, Academic Press Inc., Orlando) in [91]. However, the development of fuzzy graph theory is due to the ground setting papers of Rosenfeld (Fuzzy sets and their applications, Academic Press, New York) [154] and Yeh and Bang (Fuzzy sets and their applications, Academic Press, New York) [186]. In Rosenfeld’s paper, basic structural and connectivity concepts were presented while Yeh and Bang introduced different connectivity parameters and discussed their application. Rosenfeld obtained the fuzzy analogs of several graph-theoretic concepts like bridges, paths, cycles, trees, and connectedness. Most of the theoretical development of fuzzy graph theory is based on Rosenfeld’s initial work.

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

Publisher | Springer Verlag |

Pages | 1-12 |

Number of pages | 12 |

Volume | 363 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
---|---|

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. 1-12). (Studies in Fuzziness and Soft Computing; Vol. 363). Springer Verlag. https://doi.org/10.1007/978-3-319-71407-3_1

**Fuzzy sets and relations.** / 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. 1-12. https://doi.org/10.1007/978-3-319-71407-3_1

}

TY - CHAP

T1 - Fuzzy sets and relations

AU - Mathew, Sunil

AU - Mordeson, John N.

AU - Malik, Davender S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The notion of a fuzzy graph was initially introduced by Kauffman (Introduction to the theory of fuzzy sets, Academic Press Inc., Orlando) in [91]. However, the development of fuzzy graph theory is due to the ground setting papers of Rosenfeld (Fuzzy sets and their applications, Academic Press, New York) [154] and Yeh and Bang (Fuzzy sets and their applications, Academic Press, New York) [186]. In Rosenfeld’s paper, basic structural and connectivity concepts were presented while Yeh and Bang introduced different connectivity parameters and discussed their application. Rosenfeld obtained the fuzzy analogs of several graph-theoretic concepts like bridges, paths, cycles, trees, and connectedness. Most of the theoretical development of fuzzy graph theory is based on Rosenfeld’s initial work.

AB - The notion of a fuzzy graph was initially introduced by Kauffman (Introduction to the theory of fuzzy sets, Academic Press Inc., Orlando) in [91]. However, the development of fuzzy graph theory is due to the ground setting papers of Rosenfeld (Fuzzy sets and their applications, Academic Press, New York) [154] and Yeh and Bang (Fuzzy sets and their applications, Academic Press, New York) [186]. In Rosenfeld’s paper, basic structural and connectivity concepts were presented while Yeh and Bang introduced different connectivity parameters and discussed their application. Rosenfeld obtained the fuzzy analogs of several graph-theoretic concepts like bridges, paths, cycles, trees, and connectedness. Most of the theoretical development of fuzzy graph theory is based on Rosenfeld’s initial work.

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U2 - 10.1007/978-3-319-71407-3_1

DO - 10.1007/978-3-319-71407-3_1

M3 - Chapter

AN - SCOPUS:85039987148

VL - 363

T3 - Studies in Fuzziness and Soft Computing

SP - 1

EP - 12

BT - Studies in Fuzziness and Soft Computing

PB - Springer Verlag

ER -