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Complex Pythagorean fuzzy threshold graphs with application in petroleum replenishment

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Abstract

The purpose of this article is to present a novel idea of complex Pythagorean fuzzy threshold graphs \((\mathcal {CPFTG}_{s})\). We introduce the relation between vertex cardinality and threshold values of a \(\mathcal {CPFTG}\). We propose that \(\mathcal {CPFTG}_{s}\) are free from alternating \(4-cycle\) and these graphs can be built up repeatedly adding an isolated or a dominating vertex. We present that the crisp graph of \(\mathcal {CPFTG}\) is a split graph \((\mathcal {SG})\). Further, the threshold dimension and threshold partition number of \(\mathcal {CPFG}_{s}\) is defined. Some basic results on threshold dimension and threshold partition number also have been discussed. Finally, an application is presented on this developed concept. Due to the wide range of complex Pythagorean fuzzy sets \((\mathcal {CPFS}_{s})\), it is obvious that \(\mathcal {CPFTG}_{s}\) are more helpful and beneficial in modeling a problem as compared to complex fuzzy threshold graphs \((\mathcal {CFTG}_{s})\) and complex intuitionistic fuzzy threshold graphs \((\mathcal {CIFTG}_{s})\).

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References

  1. Akram, M., Bashir, A., Samanta, S.: Complex Pythagorean fuzzy planar graphs. Int. J. Appl. Comput. Math. 6(3), 1–27 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  2. Akram, M., Khan, A.: Complex Pythagorean Dombi fuzzy graphs for decision making. Granul. Comput. 6, 645–669 (2021)

    Article  MathSciNet  Google Scholar 

  3. Akram, M., Naz, S.: A novel decision-making approach under complex Pythagorean fuzzy enviornment. Math. Comput. Appl. 24(3), 73 (2019). https://doi.org/10.3390/mca24030073

    Article  Google Scholar 

  4. Akram, M., Sattar, A.: Competition graphs under complex Pythagorean fuzzy information. J. Appl. Math. Comput. 63(1–2), 543–583 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Akram, M., Sattar, A., Karaaslan, F., et al.: Extension of competition graphs under complex fuzzy environment. Complex Intell. Syst. 7, 539–558 (2021)

    Article  Google Scholar 

  6. Akram, M., Ahmad, U.: Rukhsar and S. Samanta, Threshold graphs under pythagorean fuzzy information, Journal of Multiple-Valued Logic and Soft Computing (2021)

  7. Alkouri, A.U.M., Salleh, A.: Complex ituitionistic fuzzy sets. AIP Conf. Proc. 1482(1), 464–470 (2012)

    Article  Google Scholar 

  8. Andelic, M., Simic, S.K.: Some notes on the threshold graphs. Discrete Math. 310, 2241–2248 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Atanassov, K.T.: Intuitionistic fuzzy sets 20(1), 87–96 (1986)

  10. Calamoneri, T., Monti, A., Petreschi, R.: On dynamic threshold graphs and related classes. Theo. Comput. Sci. 718, 46–57 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chvatal, V., Hammer, P.L.: Set Packing problems and threshold graphs, pp. 73–21. CORR, University of Waterloo, Canada (1973)

  12. Euler, L.: Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitinae 8, 128–140 (1736)

  13. Hameed, S., Akram, M., Mustafa, N., Samanta, S.: Extension of threshold graphs under complex fuzzy environment. International Journal of Applied and Computational Mathematics (2021)

  14. Hameed, S., Akram, M., Mustafa, N., Karaaslan, F.: Extension of threshold graphs under complex intuitionistic fuzzy environment. Journal of Multiple-Valued Logic and Soft Computing (2021)

  15. Henderson, P.B., Zalcstein, Y.: A graph-theoretic characterization of the PV class of synchronizing primitives. SIAM J. Comput. 6(1), 88–108 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kaufmann, A.: Introduction a la theorie des sourensembes flous, Masson et Cie Paris (1973)

  17. Koop, G.J.: Cyclic scheduling of offweekends. Operation Res. Lett. 4, 259–263 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hyper graphs, 2nd edn. Physica Verlag, Heidelberg (1998). (2001)

  19. Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37(4–5), 19–31 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mahapatra, R., Samanta, S., Pal, M.: Generalized neutrosophic planar graphs and its application. J. Appl. Math. Comput. 65(1), 693–712 (2021)

    Article  MathSciNet  Google Scholar 

  21. Mahapatra, R., Samanta, S., Pal, M.: Applications of edge colouring of fuzzy graphs. Informatica 31(2), 313–330 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mahapatra, R., Samanta, S., Pal, M., Xin, Q.: RSM index: a new way of link prediction in social networks. J. Intell. Fuzzy Syst. 37(2), 2137–2151 (2019)

    Article  Google Scholar 

  23. Mahapatra, R., Samanta, S., Pal, M., Xin, Q.: Link prediction in social networks by neutrosophic graph. Int. J. Comput. Intell. Syst. 13(1), 1699–1713 (2020)

    Article  Google Scholar 

  24. Mahapatra, T., Pal, M.: An investigation on m-polar fuzzy threshold graph and its application on resource power controlling system. J. Ambient Intell. Humaniz. Comput. (2021). https://doi.org/10.1007/s12652-021-02914-6

    Article  Google Scholar 

  25. Naz, S., Ashraf, S., Akram, M.: A novel approach to decision-making with Pythagorean fuzzy information. Mathematics 6, 1–28 (2018)

    Article  MATH  Google Scholar 

  26. Ordman, E.T.: Threshold coverings and resource allocation. In: 16th Southeastern Conference on Combinatorics, Graph Theory and Computing, (1985), pp. 99–113

  27. Pramanik, T., Pal, M., Mondal, S.: Intervel-valued fuzzy threshold graph. Pac. Sci. Rev. A: Nat. Sci. Eng. 18(1), 66–71 (2016)

    Google Scholar 

  28. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  29. Peled, U.N., Mahadev, N.V.: Threshold graphs and retaed topics. North Holland (1995)

  30. Parvathi, R., Tamizhendi, G.: Domination in intuitionistic fuzzy graphs. 14th International Conference on intuitionistic fuzzy sets 16(2), 39–49 (2010)

  31. Ramot, D., Milo, R., Fiedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)

    Article  Google Scholar 

  32. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Process, pp. 77–95. Academic Press, Cambridge (1975)

    Chapter  Google Scholar 

  33. Samanta, S., Pal, M.: Fuzzy threshold graphs, CiiT. Int. J. Fuzzy Syst. 3(12), 360–364 (2011)

    Google Scholar 

  34. Sannon, A., Atanassov, K.T.: A first step to a theory of intuitionistic fuzzy graphs. In: Lakov, D. (ed.) Proceedings of Fuzzy Based Expert Systems, pp. 59–61. Sofia (1994)

  35. Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10(1), 243–248 (2016)

    Google Scholar 

  36. Ullah, K., Mahmood, T., Ali, Z., Jan, N.: On some distance measure of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. 6, 15–27 (2019)

    Article  Google Scholar 

  37. Yager, R.R.: Pythagorean fuzzy subsets. IEEE 57–61,(2013)

  38. Yang, L., Mao, H.: Intuitionistic fuzzy threshold graphs. J. Intell. Fuzzy Syst. 36, 6641–6651 (2019)

    Article  Google Scholar 

  39. Yaqoob, N., Gulistan, M., Kadry, S., Wahab, H.: Complex intuitionistic fuzzy graphs with application in cellular network provider companies. Mathematics (2019). https://doi.org/10.3390/math7010035

    Article  Google Scholar 

  40. Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. 338, 1–22 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  41. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, P.O. Box No. 54590, Lahore, Pakistan

    Muhammad Akram, Uzma Ahmad &  Rukhsar

  2. Department of Mathematics, Faculty of Sciences, Çankiri Karatekin University, 18100, Çankiri, Turkey

    Faruk Karaaslan

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  1. Muhammad Akram
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  2. Uzma Ahmad
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  3. Rukhsar
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  4. Faruk Karaaslan
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Correspondence to Faruk Karaaslan.

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Akram, M., Ahmad, U., Rukhsar et al. Complex Pythagorean fuzzy threshold graphs with application in petroleum replenishment. J. Appl. Math. Comput. 68, 2125–2150 (2022). https://doi.org/10.1007/s12190-021-01604-y

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