Skip to main content
Log in

Pythagorean fuzzy soft decision-making method for cache replacement policy selection in fog computing

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

The cache replacement policy in fog computing is of great concern to improve CPU cache hit ratio, reduce CPU access to memory time, decrease CPU data acquisition time, and improve system efficiency. When discussing the cache replacement policy selection, the primary problem involves enormous indeterminacy. Pythagorean fuzzy soft set (PFSS), characterized by the parameterized modality of membership and non-membership, is a more useful means to depict indeterminacy. In this article, the comparison issue of Pythagorean fuzzy soft numbers (PFSNs) is managed by novel score function. Subsequently, certain properties for Pythagorean fuzzy soft matrix are explored in detail. In addition, the objective weight is determined by Criteria Importance Through Inter-criteria Correlation (CRITIC) approach while the integrated weight is calculated by simultaneously revealing subjective weight information and the objective weight preference. Then, Pythagorean fuzzy soft decision-making method based on Combined Compromise Solution (CoCoSo) is investigated for solving the low discrimination issue. Finally, the efficacy of our method is verified by the cache replacement policy selection in fog computing.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Bonomi F, Milito R, Zhu J, Addepalli S (2012) Fog computing and its role in the internet of things. In: Proceedings of the first edition of the MCC workshop on mobile cloud computing, pp 13–16

  2. Kumar G, Saha R, Rai MK, Thomas R, Kim TH (2019) Proof-of-work consensus approach in blockchain technology for cloud and fog computing using maximization-factorization statistics. IEEE Internet Things J 6(4):6835–6842

    Article  Google Scholar 

  3. Zhou Y, Tian L, Liu L, Qi Y (2019) Fog computing enabled future mobile communication networks: a convergence of communication and computing. IEEE Commun Mag 57(5):20–27

    Article  Google Scholar 

  4. Goudarzi M, Wu H, Palaniswami M, Buyya R (2021) An application placement technique for concurrent IoT applications in edge and fog computing environments. IEEE Trans Mob Comput 20(4):1298–1311

    Article  Google Scholar 

  5. Liu X, Chen W, Xia Y, Yang C (2021) SE-VFC: secure and efficient outsourcing computing in vehicular fog computing. IEEE Trans Netw Serv Manag. https://doi.org/10.1109/TNSM.2021.3080138

    Article  Google Scholar 

  6. Xiao Y, Krunz M (2021) AdaptiveFog: a modelling and optimization framework for fog computing in intelligent transportation systems. IEEE Trans Mobi Comput. https://doi.org/10.1109/TMC.2021.3080397

    Article  Google Scholar 

  7. Wang J, Li D, Hu MY (2021) Fog nodes deployment based on space-time characteristics in smart factory. IEEE Trans Ind Inf 17(5):3534–3543

    Article  Google Scholar 

  8. Mahmud R, Srirama SN, Ramamohanarao K, Buyya R (2019) Quality of experience (QoE)-aware placement of applications in fog computing environments. J Parallel Distrib Comput 132:190–203

    Article  Google Scholar 

  9. Jia G, Han G, Wang H, Wang F (2018) Cost aware cache replacement policy in shared last-level cache for hybrid memory based fog computing. Enterp Inf Syst 12(4):435–451

    Article  Google Scholar 

  10. Priya BK, Kumar S, Begum BS, Ramasubramanian N (2019) Cache lifetime enhancement technique using hybrid cache-replacement-policy. Microelectron Reliab 97:1–15

    Article  Google Scholar 

  11. Mittal S, Vetter JS (2015) EqualWrites: reducing intra-set write variations for enhancing lifetime of non-volatile caches. IEEE Trans Very Large Scale Integr VLSI Syst 24(1):103–114

    Article  Google Scholar 

  12. Wang J, Dong X, Xie Y, Jouppi NP (2013) i\(^2\)WAP: improving non-volatile cache lifetime by reducing inter-and intra-set write variations. In IEEE 19th international symposium on high performance computer architecture, pp 234–245

  13. Monazzah AMH, Farbeh H, Miremadi SG (2016) LER: least-error-rate replacement algorithm for emerging STT-RAM caches. IEEE Trans Device Mater Reliab 16(2):220–226

    Article  Google Scholar 

  14. Peneau PY, Novo D, Bruguier F, Torres L, Sassatelli G, Gamatie A (2018) Improving the performance of STT-MRAM LLC through enhanced cache replacement policy. In: International conference on architecture of computing systems, pp 168–180

  15. Yazdani M, Zarate P, Zavadskas K, Turskis Z (2019) A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Manag Decis 57(9):2501–2519

    Article  Google Scholar 

  16. Kieu PT, Nguyen VT, Nguyen VT, Ho TP (2021) A spherical fuzzy analytic hierarchy process (SF-AHP) and combined compromise solution (CoCoSo) algorithm in distribution center location selection: a case study in agricultural supply chain. Axioms 10(2):53

    Article  Google Scholar 

  17. Deveci M, Pamucar D, Gokasar I (2021) Fuzzy power Heronian function based CoCoSo method for the advantage prioritization of autonomous vehicles in real-time traffic management. Sustain Cities Soc 69:102846

    Article  Google Scholar 

  18. Peng X, Dai J (2018) Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Comput Appl 29(10):939–954

    Article  Google Scholar 

  19. Diakoulaki D, Mavrotas G, Papayannakis L (1995) Determining objective weights in multiple criteria problems: the critic method. Comput Oper Res 22(7):763–770

    Article  MATH  Google Scholar 

  20. Mishra AR, Rani P, Pandey K (2021) Fermatean fuzzy CRITIC-EDAS approach for the selection of sustainable third-party reverse logistics providers using improved generalized score function. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-021-02902-w

    Article  Google Scholar 

  21. Lai H, Liao H (2021) A multi-criteria decision making method based on DNMA and CRITIC with linguistic D numbers for blockchain platform evaluation. Eng Appl Artif Intell 101:104200

    Article  Google Scholar 

  22. Chen Y, Zhang Z, Gao C, Deng W, Chen W, Ao T (2021) Quantitative analysis of soil sustainability after applying stabilizing amendments in long-term Cd-contaminated paddy soils. Environ Pollut 286:117205

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Alcantud JCR, Santos-Garcia G, Peng X, Zhan J (2019) Dual extended hesitant fuzzy sets. Symmetry 11(5):714

    Article  MATH  Google Scholar 

  25. Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  26. Peng X, Yang Y, Song JP, Jiang Y (2015) Pythagorean fuzzy soft set and its application. Comput Eng 41(7):224–229

    Google Scholar 

  27. Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160

    Article  MathSciNet  Google Scholar 

  28. Yager RR (2013) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

  29. Wang L, Garg H (2021) Algorithm for multiple attribute decision-making with interactive Archimedean norm operations under Pythagorean fuzzy uncertainty. Int J Comput Intell Syst 14:503–527

    Article  Google Scholar 

  30. Han Q, Li W, Song Y, Zhang T, Wang R (2019) A new method for MAGDM Based on improved TOPSIS and a novel Pythagorean fuzzy soft entropy. Symmetry 11(7):905

    Article  Google Scholar 

  31. Guleria A, Bajaj RK (2019) On Pythagorean fuzzy soft matrices, operations and their applications in decision making and medical diagnosis. Soft Comput 23(17):7889–7900

    Article  MATH  Google Scholar 

  32. Athira TM, John SJ, Garg H (2019) Entropy and distance measures of Pythagorean fuzzy soft sets and their applications. J Intell Fuzzy Syst 37(3):4071–4084

    Article  Google Scholar 

  33. Jia-hua D, Zhang H, He Y (2019) Possibility Pythagorean fuzzy soft set and its application. J Intell Fuzzy Syst 36(1):413–421

    Article  Google Scholar 

  34. Shahzadi G, Akram M, Davvaz B (2020) Pythagorean fuzzy soft graphs with applications. J Intell Fuzzy Syst 38(4):4977–4991

    Article  Google Scholar 

  35. Zulqarnain R, Xin X, Garg H, Khan W (2021) Aggregation operators of Pythagorean fuzzy soft sets with their application for green supplier chain management. J Intell Fuzzy Syst 40(3):5545–5563

    Article  Google Scholar 

  36. Riaz M, Naeem K, Afzal D (2020) A similarity measure under Pythagorean fuzzy soft environment with applications. Comput Appl Math 39(4):1–17

    Article  MathSciNet  MATH  Google Scholar 

  37. Riaz M, Naeem K, Aslam M, Afzal D, Almahdi FAA, Jamal SS (2020) Multi-criteria group decision making with Pythagorean fuzzy soft topology. J Intell Fuzzy Syst 39(5):6703–6720

    Article  Google Scholar 

  38. Zulqarnain RM, Xin XL, Garg H, Ali R (2021) Interaction aggregation operators to solve multi criteria decision making problem under Pythagorean fuzzy soft environment. J Intell Fuzzy Syst 41(1):1151–1171

    Article  Google Scholar 

  39. Ma Z, Xu Z (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219

    Article  Google Scholar 

  40. Wu S, Wei G (2017) Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21(3):189–201

    Google Scholar 

  41. Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    Article  Google Scholar 

  42. Peng X, Dai J (2017) Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32(11):1187–1214

    Article  Google Scholar 

  43. Peng X (2019) Algorithm for Pythagorean fuzzy multi-criteria decision making based on WDBA with new score function. Fundam Inform 165(2):99–137

    Article  MathSciNet  MATH  Google Scholar 

  44. Lin M, Chen Z, Xu Z, Gou X, Herrera F (2021) Score function based on concentration degree for probabilistic linguistic term sets: an application to TOPSIS and VIKOR. Inf Sci 551:270–290

    Article  MathSciNet  Google Scholar 

  45. Jiang H, Zhan J, Chen D (2021) PROMETHEE II method based on variable precision fuzzy rough sets with fuzzy neighborhoods. Artif Intell Rev 54(2):1281–1319

    Article  Google Scholar 

  46. Zhan J, Alcantud JCR (2019) A novel type of soft rough covering and its application to multicriteria group decision making. Artif Intell Rev 52(4):2381–2410

    Article  Google Scholar 

  47. Zhan J, Alcantud JCR (2019) A survey of parameter reduction of soft sets and corresponding algorithms. Artif Intell Rev 52(3):1839–1872

    Article  Google Scholar 

  48. Zhang L, Zhan J (2019) Fuzzy soft \(\beta\)-covering based fuzzy rough sets and corresponding decision-making applications. Int J Mach Learn Cybern 10(6):1487–1502

    Article  Google Scholar 

  49. Zhan J, Ye J, Ding W, Liu P (2021) A novel three-way decision model based on utility theory in incomplete fuzzy decision systems. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2021.3078012

    Article  Google Scholar 

  50. Zhang K, Zhan J, Wu WZ (2021) On multi-criteria decision-making method based on a fuzzy rough set model with fuzzy \(\alpha\)-neighborhoods. IEEE Trans Fuzzy Syst 29:2491–2505

    Article  Google Scholar 

  51. Yu GF, Li DF, Liang DC, Li GX (2021) An intuitionistic fuzzy multi-objective goal programming approach to portfolio selection. Int J Inf Technol Decis Mak 20:1477–1497

    Article  Google Scholar 

Download references

Acknowledgements

Our work is sponsored by the National Natural Science Foundation of China (no. 62006155).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dongting Sun.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, X., Sun, D. & Luo, Z. Pythagorean fuzzy soft decision-making method for cache replacement policy selection in fog computing. Int. J. Mach. Learn. & Cyber. 13, 3663–3690 (2022). https://doi.org/10.1007/s13042-022-01619-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-022-01619-2

Keywords

Navigation