Abstract
In this paper, we define morphological topology (\(\mathcal {M}\)-topology) on intuitionistic fuzzy graph (IFG). We also define neighbourhood graph, continuity and isomorphism between \(\mathcal {M}\)-topologies.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
N. Alsheri, M. Akram, Intuitionistic fuzzy planner graphs. Discrete Dyn. Nat. Soc. 2014, 9 p. Article ID 39782
K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications (Springer-Verlag, Heidelberg, 1999)
D. Baets, E. Kerre, M. Gadan, The fundamentals of fuzzy mathematical morphology Part 1: basic concepts. Int. J. General Syst. 23, 155–171 (1995)
N. Cagman, S. Enginoglu, F. Citak, Fuzzy soft set theory and its applications. Iraninan J. Fuzzy Syst. 8(3), 137–147 (2001)
P.M. Dhanya, A. Sreekumar, M. Jathavedan, P.B. Ramkumar, Algebra of morphological dilation on intuitionistic fuzzy hypergraph IJSRSET 4(1) (2018)
P.M. Dhanya, A. Sreekumar, M. Jathavedan, P.B. Ramkumar, Document modeling and clustering using hypergraph, Int. J. Appl. Eng. Res. 12(10), 2127–2135 (2017), ISSN (0973-4562)
H. Heijmans, L. Vincent, Graph morphology in image analysis. Mathematical Morphology in Image Processing (1992), pp. 171–203
K.D. Joshy, Introduction to General Topology (Wiley, Eastern Limited, 1992)
K.G. Karunambigai, R. Parvathi, Intuitionistic fuzzy graphs. J. Comput. Intell. Theory Appl. 20, 139–150 (2006)
E. Melin, Digital geometry & Khalimsky space. Uppsala Dissert. Mathe. 54 (2008)
J.R. Munkres, Topology, 2nd edn. Pearson
A. Nagoor Gani, S. Anupriya, Spilt domination on intuitionistic fuzzy graph, in Advanced in Computational Mathematics and its Applications (ACMA) Vol. 2(2) (2012), ISSN 2167-6356
L. Najman, F. Meyer, A short tour of mathematical morphology on edge and vertex weighted graphs, Image Processing and Analysis with Graphs Theory and Practice, ed. by O. Lezoray, L. Grady, CRC Press (2012), pp. 141–174. Digital Imaging and Computer Vision. 9781439855072
L. Najman, J. Cousty, A Graph-Based Mathematical Morphology Reader (Elsevier, USA, 2014)
L. Najman, H. Talbot, Mathematical Morphology from theory to Applications (Wiley, USA, 2008)
P.B. Ramkumar, A. Jacob, Morphology on intuitionistic fuzzy soft graphs. Int. J. Adv. Res. Trends Eng. Technol. 5(Spl. issue)
A. Rosenfeld, Digital topology. American Mathe. Monthly 86(8), 621–630 (1979)
J. Serra, Image Analysis and Mathematical Morphology (Academic Press, New York, 1982)
A.M. Shyla, T.K. Mathew Varkey, Intuitionistic fuzzy soft graph. Int. J. Fuzzy Mathe. Arch. (2016)
P. Sunitha, An elementary introduction to intuitionistic fuzzy soft graphs. J. Math. Comput. Sci. 6(4), 668–681 (2016)
L. Vincent, Graphs and mathematical morphology. Signal Process 16, 365–88 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Jacob, A., Ramkumar, P.B. (2021). Intuitionistic Fuzzy Graph Morphological Topology. In: Devaney, R.L., Chan, K.C., Vinod Kumar, P. (eds) Topological Dynamics and Topological Data Analysis. IWCTA 2018. Springer Proceedings in Mathematics & Statistics, vol 350. Springer, Singapore. https://doi.org/10.1007/978-981-16-0174-3_21
Download citation
DOI: https://doi.org/10.1007/978-981-16-0174-3_21
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-0173-6
Online ISBN: 978-981-16-0174-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)