Skip to main content

Decision-making with q-rung orthopair fuzzy graph structures

Abstract

The q-rung orthopair fuzzy sets being an extension of intuitionistic and Pythagorean fuzzy sets is very flexible model to express uncertain information that concerns only two attributes yes or no. In this research article, we combine the concept of graph structures with q-rung orthopair fuzzy sets, and introduce the notion of q-rung orthopair fuzzy graph structures (q-ROFGSs) that provides a broader space for membership and non-membership values. First, we define normal product of q-ROFGSs and investigate its \(\rho _{i}\)-regularity with several properties. Further, we discuss \(\rho '_{i}-m\)-partite q-ROFGSs with different conditions to be a \(\rho '_{i}-m\)-regular q-ROFGS. In addition, we present an application of m-partite q-ROFGSs in decision-making, regarding selection of best employees for sale of company products to wholesale buyers, retail buyers and online consumers.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

References

  • Akram M, Ali G (2021) Group decision-making approach under multi \((Q, N)\)-soft multi granulation rough model. Granul Comput 6(2):339–357

    Article  Google Scholar 

  • Akram M, Shahzadi G, Alcantud JCR (2021) Multi-attribute decision-making with \(q\)-rung picture fuzzy information. Granul Comput. https://doi.org/10.1007/s41066-021-00260-8

  • Akram M, Habib A, Ilyas F, Dar JM (2018) Specific types of Pythagorean fuzzy graphs and application to decision-making. Math Comput Appl 23(3):42

    MathSciNet  Google Scholar 

  • Akram M, Akmal R, Alshehri N (2016) On \(m\)-polar fuzzy graph structures. SpringerPlus. https://doi.org/10.1186/s40064-016-3066-8

    Article  MATH  Google Scholar 

  • Akram M, Sitara M (2019) Certain fuzzy graph structures. J Appl Math Comput 61(1–2):25–56

    MathSciNet  Article  Google Scholar 

  • Akram M, Sitara M, Saeid AB (2020) Residue product of fuzzy graph structures. J Multiple Valued Logic Soft Comput 34

  • Ali G, Ansari MN (2021) Multiattribute decision-making under Fermatean fuzzy bipolar soft framework. Granul Comput. https://doi.org/10.1007/s41066-021-00270-6

  • Atanassov K (1986) Intuitionistic fuzzy sets: theory and applications. Fuzzy Sets Syst 20(1):87–96

    Article  Google Scholar 

  • Cary M (2018) Perfectly regular and perfectly edge-regular fuzzy graphs. Ann Pure Appl Math 16:461–469

    Article  Google Scholar 

  • Chen SM, Ke JS, Chang JF (1990) Knowledge representation using fuzzy Petri nets. IEEE Trans Knowl Data Eng 2(3):311–319. https://doi.org/10.1109/69.60794

    Article  Google Scholar 

  • Chen SM, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872

    Article  Google Scholar 

  • Chen SM, Ko Y, Chang Y, Pan J (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):1412–1427

    Article  Google Scholar 

  • Chen SM, Wang N (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern Part B (Cybern) 40(5):1343–1358

  • Chen SM, Phuong B (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216

    Article  Google Scholar 

  • Chen SM, Hsu CC (2008) A new approach for handling forecasting problems using high-order fuzzy time series. Intell Autom Soft Comput 14(1):29–43

    Article  Google Scholar 

  • Dinesh T (2011) A study on graph structures, incidence algebras and their fuzzy analogues [Ph.D.thesis], Kannur University, Kannur, India

  • Feng F, Fujita H, Ali MI, Yager RR, Liu X (2019) Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision-making methods. IEEE Trans Fuzzy Syst 27(3):474–488

    Article  Google Scholar 

  • Feng F, Zheng Y, Sun B, Akram M (2021) Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making. Granul Comput. https://doi.org/10.1007/s41066-021-00253-7

  • Habib A, Akram M, Farooq A (2019) \(q\)-Rung orthopair fuzzy competition graphs with application in soil ecosystem. Mathematics 7:91

    Article  Google Scholar 

  • Gundogdu FK, Kahraman C (2019) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst 36(1):337–352

    Article  Google Scholar 

  • Gani AN, Ahamed MB (2003) Order and size in fuzzy graphs. Bull Pure Appl Sci 22:145–148

    MathSciNet  MATH  Google Scholar 

  • Kauffman A (1973) Introduction a la Theorie des Sous-emsembles Flous. Massonet Cie Paris, Paris

    Google Scholar 

  • Karunambigai MG, Parvathi R (2006) Intuitionistic fuzzy graphs. In: Advances in soft computing: computational intelligence, theory and applications, proceedings of the 9th fuzzy days international conference on computational intelligence, vol 20. Springer, Berlin, Heidelberg, pp 139–150

  • Liu X, Kim H, Feng F, Alcantud JCR (2018) Centroid transformations of intuitionistic fuzzy values based on aggregation operators. Mathematics 6:215

    Article  Google Scholar 

  • Liu P, Wang P (2018) Some \(q\)-rung orthopair fuzzy aggregation operators and their applications to multi-attribute decision-making. Int J Intell Syst 33:259–280

    Article  Google Scholar 

  • Naz S, Ashraf S, Akram M (2018) A novel approach to decision-making with Pythagorean fuzzy information. Mathematics 6:95

    Article  Google Scholar 

  • Radha K, Kumaravel N (2014) On Edge regular fuzzy graphs. Int J Math Arch 5(9):100–112

    Google Scholar 

  • Ramakrishnan RV, Dinesh T (2011a) On generalised fuzzy graph structures. Appl Math Sci 5(4):173–180

    MathSciNet  MATH  Google Scholar 

  • Ramakrishnan RV, Dinesh T (2011b) On generalised fuzzy graph structures II. Adv Fuzzy Math 6(1):5–12

    Article  Google Scholar 

  • Ramakrishnan RV, Dinesh T (2011c) On generalised fuzzy graph structures III. Bull Kerala Math Assoc 8(1):57–66

    MathSciNet  MATH  Google Scholar 

  • Rosenfeld A (1975) Fuzzy graphs. Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York, pp 77–95

    Chapter  Google Scholar 

  • Sampathkumar E (2006) Generalized graph structures. Bull Kerala Math Assoc 3(2):65–123

    MathSciNet  Google Scholar 

  • Sitara M, Akram M, Bhatti MY (2019) Fuzzy graph structures with application. Mathematics 7(1):63

    MathSciNet  Article  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. Proceedings of the Joint IFSAWorld Congress and NAIFPS Annual Meeting, vol 24–28. Edmonton, pp 57–61

  • Yager RR (2014) Pythagorean membership grades in multi-criteria decision-making. IEEE Trans Fuzzy Syst 22:958–965

    Article  Google Scholar 

  • Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25:1222–1230

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3(2):177–200

    MathSciNet  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muhammad Akram.

Ethics declarations

Conflict of interest:

The authors declare that they have no conflict of interest regarding the publication of the research article.

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

Verify currency and authenticity via CrossMark

Cite this article

Akram, M., Sitara, M. Decision-making with q-rung orthopair fuzzy graph structures. Granul. Comput. 7, 505–526 (2022). https://doi.org/10.1007/s41066-021-00281-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-021-00281-3

Keywords

  • q-rung orthopair fuzzy graph structure
  • \(\rho '_{i}-m\)-partite
  • \(\rho _{i}\)-regular
  • \(\rho _{i}\)-full