Control and Optimization in Applied Mathematics

In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Current Issue

By Issue

By Author

By Subject

Author Index

Keyword Index

About Journal

Aims and Scope

Editorial Board

Publication Ethics

Indexing and Abstracting

Related Links

FAQ

Peer Review Process

Journal Metrics

News

Fuzzy Number-Valued Fuzzy Graph

Document Type : Research Article

Authors

1 Department of Mathematics, Payame Noor University (PNU) Tehran, Iran

2 Department of mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcs‎. ‎In this study‎, ‎some properties of the graph on fuzzy number-value fuzzy graph were examined‎. ‎First‎, ‎we define the Cartesian product‎, ‎composition‎, ‎union and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitions‎. ‎We also introduced the notion of homomorphism‎, ‎weak isomorphism,weak co-isomorphism‎, ‎isomorphism‎, ‎complete‎, ‎weak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.

Keywords

Main Subjects

References
[1] Adabitabar Firozja M.‎, ‎Firouzian S‎. ‎(2015)‎. ‎``Fuzzy number-valued fuzzy relation"‎, ‎International Journal of Industrial Mathematics‎, ‎7(4)‎, ‎Article ID IJIM-00654‎, ‎7 pages‎.
[2] Akram M‎. ‎(2011)‎. ‎``Bipolar fuzzy graphs"‎, ‎Information Sciences‎, ‎181‎, ‎5548-5564‎.
‎[3] Akram M.‎, ‎Dudek W‎. ‎A‎. ‎(2011)‎. ‎``Interval-valued fuzzy graphs"‎, ‎Computers and Mathematics with Applications‎, ‎61‎, ‎289-299‎.
[4] Akram M‎. ‎(2013)‎. ‎``Bipolar fuzzy graphs with applications"‎, ‎Knowledge-Based Systems‎, ‎39‎, ‎1-8‎.
[5] Bede B.‎, ‎Stefanini L‎. ‎``Generalized Differentiability of Fuzzy-valued Functions"‎, ‎Fuzzy Sets and Systems (to appear)‎: ‎$http://ideas.repec.org/p/urb/wpaper/1209.html$‎.
[6] Bede B‎. ‎(2013)‎. ‎``Mathematics of Fuzzy Sets and Fuzzy Logic"‎, ‎Springer‎.
[7] Coroianu L‎. ‎(2012)‎. ‎``Lipschitz functions and fuzzy number approximations"‎, ‎Fuzzy Sets and Systems‎, ‎200‎, ‎116-135‎.
[8] Friedrich E.‎, ‎Martin N‎. ‎(2012)‎. ‎``Colouring fuzzy circular interval graphs"‎, ‎European Journal of Combinatorics‎, ‎33‎, ‎893-904‎.
[9] Fullier R‎. ‎``Neural Fuzzy Systems"‎, ‎ISBN‎: ‎951-650-624-0‎, ‎ISSN‎: ‎0358-5654‎.
[10] Liu X.‎, ‎Wang X.‎, ‎Pedrycz W‎. ‎(2015)‎. ‎``Fuzzy clustering with semantic interpretation"‎, ‎Applied Soft Computing‎, ‎26‎, ‎21-30‎.
[11] Pedraza T.‎, ‎Rodríguez-López J.‎, ‎Romaguera S‎. ‎(2014)‎. ‎``Convergence of fuzzy sets with respect to the supremum metric"‎, ‎Fuzzy Sets and Systems‎, ‎245‎, ‎83-100‎.
[12] Otadi M‎. ‎(2014)‎. ‎``Fully fuzzy polynomial regression with fuzzy neural networks"‎, ‎Neuro computing‎, ‎142‎, ‎486-493‎.
[13] Roldán A.‎, ‎Martínez-Morenoa J.‎, ‎Roldán C‎. ‎(2014)‎. ‎``Some applications of the study of the image of a fuzzy number‎: ‎Countable fuzzy numbers‎, ‎operations‎, ‎regression and a specificity-type ordering"‎, ‎Fuzzy Sets and Systems‎, ‎257‎, ‎204-216‎.
[14] Rosenfeld A‎. ‎(1975)‎. ‎``Fuzzy graphs"‎, ‎In L‎. ‎A‎. ‎Zadeh‎, ‎K‎. ‎S‎. ‎Fu and M‎. ‎Shimura‎, ‎Eds.‎, ‎Fuzzy Sets and Their Applications‎, ‎Academic press‎, ‎NewYork‎.
[15] Susana M.‎, ‎Teresa M.‎, ‎Javier R.‎, ‎Javier Y‎. ‎(2005)‎. ‎``Colouring fuzzy graphs"‎, ‎Omega‎, ‎33‎, ‎211-221‎.
[16] Sunil M.‎, ‎Sunitha M‎. ‎S‎. ‎(2009)‎. ‎``Types of arcs in a fuzzy graph"‎, ‎Information Sciences‎, ‎179‎, ‎1760-1768‎.
[17] Stefanini L‎. ‎(2010)‎. ‎``A generalization of Hukuhara difference and division for interval and fuzzy arithmetic"‎, ‎Fuzzy Sets and Systems‎, ‎161‎, ‎1564-1584‎.
[18] Yang H‎. ‎L.‎, ‎Li S‎. ‎G.‎, ‎Yang W‎. ‎H.‎, ‎Lu Y‎. ‎(2013)‎. ‎``Notes on ‘‘ Bipolar fuzzy graphs’’‎ ", ‎Information Sciences‎, ‎242‎, ‎113–121‎.
[19] Zadeh L‎. ‎A‎. ‎(1965)‎. ‎``Fuzzy sets"‎, ‎Information and Control‎, ‎8‎, ‎338-353‎.
Control and Optimization in Applied Mathematics
Volume 1, Issue 2 - Serial Number 2
Autumn-Winter 2016
October 2016
Pages 77-86
Files
Share
How to cite
Statistics