Skip to main content
SpringerLink
Log in

Analysis of domination in the environment of picture fuzzy information

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

Picture fuzzy graph (PFG) is a useful tool in fuzzy graph theory that can be used to model a variety of real-world problems involving uncertainty caused by unknown, changing, and indeterminate data. PFG might be more fruitful at solving confusing problems than fuzzy graph (FG) and intuitionistic fuzzy graph (IFG). In this study, some interesting properties and results for the PFGs have been presented by using the concepts of strong arcs. The notions of covering in a PFG, strong node covering, strong arc covering, strong independent set, and matching number have been introduced for PFG. Moreover, we also devised the conception of paired domination, strong paired domination, and strong paired dominating set for a PFG. Furthermore, many interesting properties of these conceptions are established. Additionally, the strong paired domination numbers of complete PFG and complete bipartite PFG have been worked out. In addition, many various intriguing aspects of strong paired domination have been examined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Akram M, Akmal R (2017) Intuitionistic fuzzy graph structures. Kragujevac J Math 41:219–237

    Article  MathSciNet  MATH  Google Scholar 

  • Akram M, Davvaz B (2012) Strong intuitionistic fuzzy graphs. Filomat 26:177–196

    Article  MathSciNet  MATH  Google Scholar 

  • Akram M, Dudek WA (2011) Interval-valued fuzzy graphs. Comput Math Appl 61(2):289–299

    Article  MathSciNet  MATH  Google Scholar 

  • Akram M, Dudek WA (2013) Intuitionistic fuzzy hypergraphs with applications. Inf Sci 218:182–193

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Atanassov K (2012) Intuitionistic fuzzy relations (IFRs). On Intuitionistic Fuzzy Sets Theory, pp 147–193

  • Chartrand G (2006) Introduction to graph theory. Tata McGraw-Hill Education, New York

    Google Scholar 

  • Chen SM, Hong JA (2014) Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets and the TOPSIS method. IEEE Trans Syst Man Cybernet 44:1665–1673

    Article  Google Scholar 

  • Chen SM, Lee LW (2011) Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on interval type-2 fuzzy sets. Expert Syst Appl 38:9947–9957

    Article  Google Scholar 

  • Chen SM, Chang YC, Pan JS (2012) Fuzzy rules interpolation for sparse fuzzy rule-based systems based on interval type-2 Gaussian fuzzy sets and genetic algorithms. IEEE Trans Fuzzy Syst 21(3):412–425

    Article  Google Scholar 

  • Cuong BC, Kreinovich V (2013) Picture Fuzzy Sets-a new concept for computational computational intelligence problems. In: 2013 third world congress on information and communication technologies (WICT 2013). IEEE. pp 1–6

  • Dubois D, Prade H (2005) Interval-valued fuzzy sets, possibility theory and imprecise probability. In: EUSFLAT Conf, pp 314–319

  • Jan N, Nasir A, Alhilal MS, Khan SU, Pamucar D, Alothaim A (2021) Investigation of cyber-security and cyber-crimes in oil and gas sectors using the innovative structures of complex intuitionistic fuzzy relations. Entropy 23(9):1112

    Article  MathSciNet  Google Scholar 

  • Kauffman A (1973) Introduction a la Théorie des Sous-emsembles Flous. Masson et ice.

  • Khan SU, Nasir A, Jan N, Ma ZH (2021) Graphical analysis of covering and paired domination in the environment of neutrosophic information. Math Prob Eng 2021:1–27

    MathSciNet  Google Scholar 

  • Knyazeva M, Belyakov S, Kacprzyk J (2018) Topological ordering on interval type-2 fuzzy graph. In international conference on theory and applications of fuzzy systems and soft computing. Springer, Cham, pp 262–269

    Google Scholar 

  • Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14:808–821

    Article  Google Scholar 

  • Nasir A, Jan N, Gumaei A, Khan SU (2021a) Medical diagnosis and life span of sufferer using interval valued complex fuzzy relations. IEEE Access 9:93764–93780

    Article  Google Scholar 

  • Nasir A, Jan N, Gumaei A, Khan SU, Albogamy FR (2021b) Cybersecurity against the loopholes in industrial control systems using interval-valued complex intuitionistic fuzzy relations. Appl Sci 11(16):7668

    Article  Google Scholar 

  • Nayeem A, Pal M (2005) shortest path problem on a network with imprecise arc value. Fuzzy Optim Decis Making 4:293–312

    Article  MathSciNet  MATH  Google Scholar 

  • Pal M, Samanta Rashmanlou H (2015) some results on interval-valued fuzzy graphs. Int J Comput Sci Electron Eng 3(3):205–211

    Google Scholar 

  • Parvathi R, Karunambigai MG (2006) Intuitionistic fuzzy graphs. In Computational intelligence, theory and applications. Springer, Berlin, pp 139–150

    Google Scholar 

  • Pramanik T, Samanta S, Pal M (2016a) Interval-valued fuzzy planar graphs. Int J Mach Learn Cybern 7(4):653–664

    Article  Google Scholar 

  • Pramanik T, Samanta S, Sarkar B, Pal M (2016b) Fuzzy Ø-tolerance competition graphs. Soft Comput 21:3723–3734

    Article  MATH  Google Scholar 

  • Rashmanlou H, Pal M (2013a) Some properties of highly irregular interval-valued fuzzy graphs. World Appl Sci J 27(12):1756–1773

    Google Scholar 

  • Rashmanlou H, Pal M (2013b) Balanced interval-valued fuzzy graphs. J Phys Sci 17:43–57

    MathSciNet  Google Scholar 

  • Rashmanlou H, Samanta S, Pal M, Borzooei RA (2015) A study on bipolar fuzzy graphs. J Intell Fuzzy Syst 28:571–580

    Article  MathSciNet  MATH  Google Scholar 

  • Rashmanlou H, Pal M (2014) Isometry on interval-valued fuzzy graphs. arXiv preprint http://arxiv.org/abs/1405.6003.

  • Rosenfield A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications to cognitive and decision processes, pp 77–95

  • Sahoo S, Pal M (2015) Intuitionistic fuzzy competition graph. J Appl Math Comput 52:37–57

    Article  MathSciNet  MATH  Google Scholar 

  • Sahoo S, Pal M, Rashmanlou H, Borzooei RA (2017) Covering and paired domination in intuitionistic fuzzy graphs. J Intell Fuzzy Syst 33(6):4007–4015

    Article  Google Scholar 

  • Samanta S, Pal M (2011a) Fuzzy tolerance Graphs. Int J Latest Trends Math 1:57–67

    Google Scholar 

  • Samanta S, Pal M (2011b) Fuzzy threshold graphs. CIIT Int J Fuzzy Syst 3:360–364

    Google Scholar 

  • Samanta S, Pal M (2012a) Bipolar fuzzy hyper graphs. Int J Fuzzy Logic Syst 2:17–28

    Article  Google Scholar 

  • Samanta S, Pal M (2012b) Irregular bipolar fuzzy graphs. Int J Appl Fuzzy Sets 2:91–102

    Google Scholar 

  • Samanta S, Pal M (2013) Fuzzy k-competition graphs and p-competition fuzzy graphs. Fuzzy Inf Eng 5:191–204

    Article  MathSciNet  MATH  Google Scholar 

  • Samanta S, Pal M (2015) Fuzzy planar graph. IEEE Trans Fuzzy Syst 23:1936–1942

    Article  Google Scholar 

  • Samanta S, Pal A, Pal M (2014) New concepts of fuzzy planar graphs. Int J Adv Res Artif Intell 3:52–59

    Google Scholar 

  • Samanta S, Akram M, Pal M (2015a) m-step fuzzy competition graphs. J Appl Math Comput Spring 47:461–472

    Article  MathSciNet  MATH  Google Scholar 

  • Samanta S, Pramanik T, Pal M (2015b) Fuzzy coloring of fuzzy graphs. Afrika Mathematika 27:37–50

    Article  MATH  Google Scholar 

  • Samanta S, Sarkar B, Shin D, Pal M (2016) Completeness and regularity of generalized fuzzy graphs. Springerplus 5:1979–2003

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zuo C, Pal A, Dey A (2019) New concepts of picture fuzzy graphs with the application. Mathematics 7(5):470

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Deanship of Scientific Research, King Saud University for funding through Vice Deanship of Scientific Research Chairs.

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, 29050, KPK, Pakistan

    Naeem Jan, Muhammad Asif, Abdul Nasir & Sami Ullah Khan

  2. Computer Science Department, Faculty of Applied Sciences, Taiz University, 6803, Taiz, Yemen

    Abdu Gumaei

  3. STC’s Artificial Intelligence Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh, 11543, Saudi Arabia

    Abdu Gumaei

Authors
  1. Naeem Jan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Asif
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdul Nasir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sami Ullah Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Abdu Gumaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Naeem Jan or Abdu Gumaei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jan, N., Asif, M., Nasir, A. et al. Analysis of domination in the environment of picture fuzzy information. Granul. Comput. 7, 801–812 (2022). https://doi.org/10.1007/s41066-021-00296-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-021-00296-w

Keywords

Search

Navigation