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Competition graphs under complex Pythagorean fuzzy information

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Abstract

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is useful model to deal the vagueness with the degrees whose ranges are extended from real to complex subset with unit circle. This set deals with vagueness and periodicity more precisely as compared to complex fuzzy set and complex intuitionistic fuzzy set. In this paper, we propose a new graph, complex Pythagorean fuzzy competition graph by combining the complex Pythagorean fuzzy information with competition graph. We also investigate the two extensions of complex Pythagorean fuzzy competition graphs, namely, complex Pythagorean fuzzy k-competition and complex Pythagorean fuzzy p-competition graphs. Moreover, we present complex Pythagorean fuzzy neighborhood graphs and m-step complex Pythagorean fuzzy competition graphs. In addition, we illustrate an application of complex Pythagorean fuzzy competition graphs with algorithm to highlight the importance of these graphs in real life.

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References

  1. Akram, M., Habib, A.: \(q\)-Rung picture fuzzy graphs: a creative view on regularity with applications. J. Appl. Math. Comput. 61(1–2), 235–280 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  2. Akram, M., Luqman, A.: A new decision-making method based on bipolar neutrosophic directed hypergraphs. J. Appl. Math. Comput. 57(1–2), 547–575 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  3. Akram, M., Luqman, A.: Fuzzy hypergraphs and related extensions. In: Studies in Fuzziness and Soft Computing. Springer, Berlin (2020). https://doi.org/10.1007/978-981-15-2403-5

  4. Akram, M., Ilyas, F., Borumand Saeid, A.: Certain notions of Pythagorean fuzzy graphs. J. Intell. Fuzzy Syst. 36(6), 5857–5874 (2019)

    Article  Google Scholar 

  5. Akram, M., Sarwar, M.: Novel applications of \(m\)-polar fuzzy competition graphs in decision support system. Neural Comput. Appl. 30(10), 3145–3165 (2018)

    Article  Google Scholar 

  6. Akram, M., Naz, S.: A novel decision-making approach under complex Pythagorean fuzzy environment. Math. Comput. Appl. 24(3), 73 (2019)

    MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  8. Alkouri, A.M., Salleh, A.R.: Some operations on complex Atanassov’s intuitionistic fuzzy sets. AIP Conf. Proc. 157(1), 987–993 (2013)

    Article  MATH  Google Scholar 

  9. Alkouri, A.M., Salleh, A.R.: Complex Atanassov’s intuitionistic fuzzy relation. Abstr. Appl. Anal. 2013, 287382 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Alshehri, N.O., Akram, M.: Bipolar fuzzy competition graphs. ARS Combin. 121, 385–402 (2015)

    MathSciNet  MATH  Google Scholar 

  11. Atanassov, K.T.: Intuitionistic fuzzy sets. Intuitionistic Fuzzy Sets, pp. 1–137 (1999)

  12. Brigham, R.C., McMorris, F.R., Vitray, R.P.: Tolerance competition graphs. Linear Algebra Appl. 217, 41–52 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cohen, J.E., Stephens, D.W.: Food Webs and Niche Space, vol. 11. Princeton University Press, Princeton (1978)

    Google Scholar 

  14. Cho, H.H., Kim, S.R., Yunsun, N.: The \(m\)-step competition graph of a digraph. Discret. Appl. Math. 105(1–3), 115–127 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Euler, L.: Solutio problems ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae. 8(1736): 128–140

  16. Hamidi, M., Saeid, A.B.: Trans. Combin. 8(2), 21–43 (2019)

    Google Scholar 

  17. Hamidi, M., Saied, A.B.: Creating and computing graphs from hypergraphs. Kragujevac J. Math. 43(1), 139–164 (2019)

    MathSciNet  Google Scholar 

  18. Habib, A., Akram, M., Farooq, A.: q-Rung orthopair fuzzy competition graphs with application in the soil ecosystem. Mathematics 7(1), 91 (2019)

    Article  MathSciNet  Google Scholar 

  19. Isaak, G., Kim, S.R., McKees, T.A., McMorris, F.R., Roberts, F.S.: 2-Competition graphs. SIAM J. Discret. Math. 5(4), 524–538 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kim, S.R., McKee, T.A., McMorris, F.R., Roberts, F.S.: p-Competition graphs. Linear Algebra Appl. 217, 167–178 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lundgren, J.R.: Food webs, competition graphs, competition-common enemy graphs and niche graphs. Applications of Combinatorics and Graph Theory to the Biological and Social Sciences 17, 221–243 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Luqman, A., Akram, M., Al-Kenani, A.N., Alcantud, J.C.R.: A study on hypergraph representations of complex fuzzy information. Symmetry 11(11), 1381 (2019)

    Article  Google Scholar 

  23. Luqman, A., Akram, M., Smarandache, F.: Complex neutrosophic hypergraphs: new social network models. Algorithms 12(11), 234 (2019)

    Article  Google Scholar 

  24. Nasir, M., Siddique, S., Akram, M.: Novel properties of intuitionistic fuzzy competition graphs. J. Uncertain Syst. 2(1), 49–67 (2017)

    Google Scholar 

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

    Article  Google Scholar 

  26. Raychaudhuri, A., Roberts, F.S.: Generalized competition graphs and their applications. Methods Oper. Res. 49, 295–311 (1985)

    MathSciNet  MATH  Google Scholar 

  27. Rosenfeld, A.: Fuzzy graphs. In: Fuzzy Sets and their Applications to Cognitive and Decision Processes. Academic Press, (1975), 77–95

  28. Sahoo, S., Pal, M.: Intuitionistic fuzzy competition graphs. J. Appl. Math. Comput. 52(1–2), 37–57 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Samanta, S., Akram, M., Pal, M.: \(m\)-step fuzzy competition graphs. J. Appl. Math. Comput. 47(1–2), 461–472 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  30. Samanta, S., Pal, M.: Fuzzy \(k\)-competition graphs and p-competition fuzzy graphs. Fuzzy Inf. Eng. 5(2), 191–204 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  31. Samanta, S., Pal, M., Pal, A.: Some more results on fuzzy k-competition graphs. Int. J. Adv. Res. Artif. Intell. 3(1), 60–67 (2014)

    MATH  Google Scholar 

  32. Sarwar, M., Akram, M.: Novel concepts of bipolar fuzzy competition graphs. J. Appl. Math. Comput. 54(1–2), 511–547 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Sarwar, M., Akram, M., Alshehri, N.: A new method to decision-making with fuzzy competition hypergraphs. Symmetry 10(9), 404 (2018)

    Article  MATH  Google Scholar 

  34. Scott, D.D.: The competition-common enemy graph of a digraph. Discret. Appl. Math. 17(3), 269–280 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sonntag, M., Teichert, H.M.: Competition hypergraphs. Discret. Appl. Math. 143(1–3), 324–329 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  37. Ullah, K., Mahmood, T., Ali, Z., Jan, N.: On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. (2019). https://doi.org/10.1007/s40747-019-0103-6

    Article  Google Scholar 

  38. Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57-61 (2013)

  39. Yaqoob, N., Gulistan, M., Kadry, S., Wahab, H.: Complex intuitionistic fuzzy graphs with application in cellular network provider companies. Mathematics 7(1), 35 (2019)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  41. Zhan, J., Akram, M., Sitara, M.: Novel decision-making method based on bipolar neutrosophic information. Soft Comput. 23(20), 9955–9977 (2019)

    Article  Google Scholar 

  42. Zhan, J., Masood, H., Akram, M.: Novel decision-making algorithms based on intuitionistic fuzzy rough environment. Int. J. Mach. Learn. Cybern. 10(6), 1459–1485 (2019)

    Article  Google Scholar 

  43. Zhang, G., Dillon, T.S., Cai, K.Y., Ma, J., Lu, J.: Operation properties and d-equalities of complex fuzzy sets. Int. J. Approx. Reason. 50(8), 1227–1249 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  44. Zhang, K., Zhan, J., Wu, W.Z.: Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making. Fuzzy Sets Syst. 383, 92–126 (2019)

    Article  MathSciNet  Google Scholar 

  45. Zhang, L., Zhan, J., Yao, Y.: Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf. Sci. 517, 315–339 (2020)

    Article  MathSciNet  Google Scholar 

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  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Muhammad Akram & Aqsa Sattar

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  1. Muhammad Akram
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Correspondence to Muhammad Akram.

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Akram, M., Sattar, A. Competition graphs under complex Pythagorean fuzzy information. J. Appl. Math. Comput. 63, 543–583 (2020). https://doi.org/10.1007/s12190-020-01329-4

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  • DOI: https://doi.org/10.1007/s12190-020-01329-4

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