Abstract
In 1994, Zhang (Proceedings of FUZZ-IEEE, 1998) [195], (Proceedings of IEEE conference, 1994) [71] introduced the concept of bipolar fuzzy sets as a generalization of the notion of Zadeh’s fuzzy sets. A bipolar fuzzy subset of a set is a pair of functions one from the set into the interval [0, 1] and the other into the interval [ - 1, 0 ]. In a bipolar fuzzy set, the membership degree 0 of an element can be interpreted that the element is irrelevant to the corresponding property, the membership degree in (0, 1] of an element indicates the intensity that the element satisfies the property, and the membership degree in [ - 1, 0) of an element indicates the element does not satisfy the property. Fuzzy and possibilistic formalisms for bipolar information have been proposed in Dubios et al. Inf Pro Man Unc IPMU’04, 2002, [71] because bipolarity exists when dealing with spatial information in image processing or in spatial reasoning applications.
| Original language | English (US) |
|---|---|
| Title of host publication | Studies in Fuzziness and Soft Computing |
| Publisher | Springer Verlag |
| Pages | 271-306 |
| Number of pages | 36 |
| 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
Bipolar fuzzy graphs. / Mathew, Sunil; Mordeson, John N.; Malik, Davender S.
Studies in Fuzziness and Soft Computing. Vol. 363 Springer Verlag, 2018. p. 271-306 (Studies in Fuzziness and Soft Computing; Vol. 363).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Bipolar fuzzy graphs
AU - Mathew, Sunil
AU - Mordeson, John N.
AU - Malik, Davender S.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - In 1994, Zhang (Proceedings of FUZZ-IEEE, 1998) [195], (Proceedings of IEEE conference, 1994) [71] introduced the concept of bipolar fuzzy sets as a generalization of the notion of Zadeh’s fuzzy sets. A bipolar fuzzy subset of a set is a pair of functions one from the set into the interval [0, 1] and the other into the interval [ - 1, 0 ]. In a bipolar fuzzy set, the membership degree 0 of an element can be interpreted that the element is irrelevant to the corresponding property, the membership degree in (0, 1] of an element indicates the intensity that the element satisfies the property, and the membership degree in [ - 1, 0) of an element indicates the element does not satisfy the property. Fuzzy and possibilistic formalisms for bipolar information have been proposed in Dubios et al. Inf Pro Man Unc IPMU’04, 2002, [71] because bipolarity exists when dealing with spatial information in image processing or in spatial reasoning applications.
AB - In 1994, Zhang (Proceedings of FUZZ-IEEE, 1998) [195], (Proceedings of IEEE conference, 1994) [71] introduced the concept of bipolar fuzzy sets as a generalization of the notion of Zadeh’s fuzzy sets. A bipolar fuzzy subset of a set is a pair of functions one from the set into the interval [0, 1] and the other into the interval [ - 1, 0 ]. In a bipolar fuzzy set, the membership degree 0 of an element can be interpreted that the element is irrelevant to the corresponding property, the membership degree in (0, 1] of an element indicates the intensity that the element satisfies the property, and the membership degree in [ - 1, 0) of an element indicates the element does not satisfy the property. Fuzzy and possibilistic formalisms for bipolar information have been proposed in Dubios et al. Inf Pro Man Unc IPMU’04, 2002, [71] because bipolarity exists when dealing with spatial information in image processing or in spatial reasoning applications.
UR - http://www.scopus.com/inward/record.url?scp=85040000691&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85040000691&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-71407-3_8
DO - 10.1007/978-3-319-71407-3_8
M3 - Chapter
VL - 363
T3 - Studies in Fuzziness and Soft Computing
SP - 271
EP - 306
BT - Studies in Fuzziness and Soft Computing
PB - Springer Verlag
ER -