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Research Article

On the convergence of sequences in ℝ+ through weighted geometric means via multiplicative calculus and application to intuitionistic fuzzy numbers

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Pages 442-450 | Received 23 Oct 2021, Accepted 23 Apr 2022, Published online: 09 May 2022

References

  • Grossman M, Katz R. Non-Newtonian calculus. Pigeon Cove (MA): Lee Press; 1972.
  • Stanley D. A multiplicative calculus. Primus. 1999;9(4):310–326.
  • Xu ZS, Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst. 2006;35:417–433.
  • Xu ZS. Intuitionistic fuzzy aggregation operations. IEEE Trans Fuzzy Syst. 2007;15:1179–1187.
  • Çanak İ. Necessary and sufficient conditions for geometric means of sequences in multiplicative calculus. Miskolc Math Notes. 2016;17(2):791–800.
  • Bashirov AE, Kurpınar EM, Özyapıcı A. Multiplicative calculus and its applications. J Math Anal Appl. 2008;337(1):36–48.
  • Abbas M, Ali B, Suleiman YI. Common fixed points of locally contractive mappings in multiplicative metric spaces with application. Int J Math Sci. 2015;2015:Article ID 218683.
  • Tor AH. An introduction to non-smooth convex analysis via multiplicative derivative. J Taibah Univ Sci. 2019;13(1):351–359.
  • Seadawy AR, Lu D, Yue C. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. J Taibah Univ Sci. 2017;11(4):623–633.
  • Seadawy AR, Iqbal M, Lu D. Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity. J Taibah Univ Sci. 2019;13(1):1060–1072.
  • Özkan YS, Seadawy AR, Yaşar E. Multi-wave, breather and interaction solutions to (3+1) dimensional Vakhnenko–Parkes equation arising at propagation of high-frequency waves in a relaxing medium. J Taibah Univ Sci. 2021;15(1):666–678.
  • Chen CP, Hsu JM. Tauberian theorems for weighted means of double sequences. Anal Math. 2000;26:243–262.
  • Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;20:87–96.
  • Zadeh LA. Fuzzy sets. Inform Control. 1965;8:338–353.
  • Deschrijver G, Kerre EE. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 2003;133:227–235.
  • Lei Q, Xu ZS. Derivative and differential operations of intuitionistic fuzzy numbers. Int J Intell Syst. 2015;30:468–498.
  • Móricz F, Rhoades BE. Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability. Acta Math Hungar. 1995;66(1–2):105–111.
  • Sezer SA, Çanak İ. On the core of weighted means of sequences. Afrika Mat. 2021;32:363–367.
  • Mursaleen M, Mohiuddine SA. Statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Chaos Solitons Fractals. 2009;41:2414–2421.
  • Mursaleen M, Mohiuddine SA, Edely OHH. On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces. Comput Math Appl. 2010;59(2):603–611.
  • Alghamdi MA, Alotaibi A, Lohani QMD, et al. Statistical limit superior and limit inferior in intuitionistic fuzzy normed spaces. J Inequal Appl. 2012;2012:96.
  • Lei Q, Xu ZS. Fundamental properties of intuitionistic fuzzy calculus. Knowl Based Syst. 2015;76:1–16.
  • Lei Q, Xu ZS. Intuitionistic fuzzy calculus. Cham (Switzerland): Springer; 2017.
  • Ai ZH, Xu ZS, Lei Q. Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers. Fuzzy Optim Decis Mak. 2017;16:71–87.
  • Ai ZH, Xu ZS, Lei Q. Fundamental properties with respect to the completeness of intuitionistic fuzzy partially ordered set. IEEE Trans Fuzzy Syst. 2017;25(6):1741–1751.
  • Zhang S, Xu ZS. Infinite intuitionistic fuzzy series and product. Int J Intell Syst. 2017;32(6):645–662.
  • Akram M, Ali G, Alcantud JCR. New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets. Soft Comput. 2019;23:9853–9868.
  • Zhang L, Zhan J, Xu Z, et al. Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making. Inf Sci. 2019;494:114–140.
  • Alcantud JCR, Khameneh AZ, Kilicman A. Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inf Sci. 2020;514:106–117.
  • Ma R, Liu S, Xu ZS, et al. Series based on the new order in intuitionistic fuzzy environment. J Intell Fuzzy Syst. 2021;40(1):319–330.
  • Riaz M, Hashmi MR. Linear diophantine fuzzy set and its applications towards multi-attribute decision-making problems. J Intell Fuzzy Syst. 2019;37:5417–5439.
  • Yager RR. Pythagorean membership grades in multi-criteria decision making. IEEE Trans Fuzzy Syst. 2014;22:958–965.
  • Zhang X, Xu Z. Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets. Int J Intell Syst. 2014;29:1061–1078.
  • Peng X, Yang Y. Some results for pythagorean fuzzy sets. Int J Intell Syst. 2015;30:1133–1160.