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Fuzzy reliability assessment of urea fertiliser plant based on Petri nets method using a probabilistic picture-hesitant fuzzy set

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Abstract

A urea fertiliser plant is designed to manufacture urea, a nitrogen-based fertiliser that is widely used. Urea is an important component in modern agriculture since it provides nitrogen to plants for growth and development. This study introduces a new method for analysing fuzzy reliability of a urea fertiliser plant based on Petri nets method using a probabilistic picture-hesitant fuzzy set theory where the reliability of a system's component or unit is represented by a probabilistic picture-hesitant fuzzy element to handle uncertainties like reluctance in real-world situations. In this study, we have used the score function and accuracy function for better comparison amongst the fuzzy reliabilities of several complicated systems with series, parallel, and bridge configurations. An example of a urea fertiliser plant has been considered to be Petri nets and demonstrates the proposed technique.

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Data availability

The datasets created and/or examined for this study are not publicly accessible. However, they can be obtained from the corresponding author with appropriate demand.

References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  Google Scholar 

  • Atanassov KT, Gargov G (1987) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):1–17

    MathSciNet  Google Scholar 

  • Cai KY, Wen CY, Zhang ML (1991) Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets Syst 42(1):145–172

    MathSciNet  Google Scholar 

  • Chand, M., Kumar, A., & Sharma, M. K. (2023). A dual hesitant approach to evaluate fuzzy reliability of optical fiber communication (OFC) system. Life Cycle Reliability and Safety Engineering. 1–12.

  • Chen SM (1994) Fuzzy system reliability analysis using fuzzy number arithmetic operations. Fuzzy Sets Syst 64(1):31–38

    Article  MathSciNet  Google Scholar 

  • Chen SM (1996) New method for fuzzy system reliability analysis. Cybernet Syst 27(4):385–401

    Article  CAS  Google Scholar 

  • Cuong, B. C. (2013). Picture fuzzy sets first results, part 1. Seminar Neuro-Fuzzy Systems with Applications, Preprint 03/2013, Institute of Mathematics, Hanoi.

  • El-Ghamry E, El-Damsece M, Shokry M (2020) Reliability analysis of different systems using triangular multi-fuzzy sets estimated by statistical data. Int J Math Oper Res 16(4):499–514

    Article  MathSciNet  Google Scholar 

  • Goel, M. (2023). Availability and profit analysis of gas turbine system using new type of generalized trapezoidal fuzzy numbers. Life Cycle Reliability and Safety Engineering. 1–23.

  • Hura GS, Atwood JW (1988) The use of petri nets to analyze coherent fault trees. IEEE Trans Reliab 375:469–474

    Article  Google Scholar 

  • Jang MW, Park JH, Son MJ (2023) Probabilistic picture hesitant fuzzy sets and their application to multi-criteria decision-making. AIMS Mathematic 8(4):8522–8559

    Article  Google Scholar 

  • Jeon J, Krishnan S, Manirathinam T, Narayanamoorthy S, Nazir Ahmad M, Ferrara M, Ahmadian A (2023) An innovative probabilistic hesitant fuzzy set MCDM perspective for selecting flexible packaging bags after the prohibition on single-use plastics. Sci Rep 13(1):10206

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 12(2):327–348

  • Knezevic J, Odoom ER (2001) Reliability modelling of repairable systems using Petri Nets and fuzzy Lambda-Tau methodology. Reliab Eng Syst Saf 73(1):1–17

    Article  Google Scholar 

  • Kumar D, Singh SB, Kumar P (2022) Fuzzy reliability appraisal of a system using probabilistic dual hesitant fuzzy element emphasising score function. Int J Math Oper Res 21(1):67–82

    Article  MathSciNet  Google Scholar 

  • Kumar D, Singh SB (2014) Evaluating fuzzy reliability using rough intuitionistic fuzzy set. IN: IEEE International Conference on Computational Intelligence on Power, Energy and Controls with their Impact on Humanity. 138–142.

  • Kumar D, Singh SB (2016) Stochastic analysis of complex repairable system with deliberate failure emphasizing reboot delay. Communications in statistics—simulation and computation. 45(2):583–602.

  • Li, W., & Zhan, T. (2023). Multi-Granularity Probabilistic Rough Fuzzy Sets for Interval-Valued Fuzzy Decision Systems. International Journal of Fuzzy Systems. 1–13.

  • Liu TS, Chiou SB (1997) The application of Petri Nets to failure analysis. Reliab Eng Syst Saf 57(1):129–142

    Article  Google Scholar 

  • Liu YM, Zhu F, Jin LL (2019) Multi-attribute decision-making method based on probabilistic hesitant fuzzy entropy. Control Decis 34:861–870

    Google Scholar 

  • Naithani K, Dangwal R (2019) Fuzzy reliability of a system using trapezoidal-triangular interval-valued fuzzy numbers. Int J Stat Reliability Eng 6(2):111–119

    Google Scholar 

  • Negi S, Singh SB (2019) Fuzzy reliability evaluation of linear m-consecutive weighted-k-out-of-r-from-n: F systems. Int J Comput Sci Math 10(6):606–621

    Article  MathSciNet  Google Scholar 

  • Sharma SP, Garg H (2011) Behavioral analysis of a urea decomposition system in a fertilizer plant. Int J Ind Syst Eng 8(3):271–297

    Google Scholar 

  • Sharma RK, Kumar D, Kumar P (2008) Fuzzy modeling of system behavior for risk and reliability analysis. Int J Syst Sci 39(6):563–581

    Article  MathSciNet  Google Scholar 

  • Singer D (1990) A fuzzy set approach to fault tree and reliability analysis. Fuzzy Sets Syst 34(2):45–155

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    Google Scholar 

  • Wang R, Liu YL (2018) Picture hesitant fuzzy set and its application to multiple criteria decision-making. Symmetry 10:295

    Article  ADS  Google Scholar 

  • Xu ZS, Zhou W (2017) Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optim Decis Making 16:481–503

    Article  MathSciNet  Google Scholar 

  • Yager, R. R., (2013). Pythagoprean fuzzy subsets. In Proc. Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canad. 57–61.

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

    Article  Google Scholar 

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Funding

No financial funds from any public, private, or nonprofit organisation has been provided for this research.

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Authors and Affiliations

  1. Department of Mathematics, D.S.B Campus, Kumaun University, Nainital, Uttarakhand, 263001, India

    Sudha Rana, Deepak Kumar & Anita Kumari

Authors
  1. Sudha Rana
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  2. Deepak Kumar
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  3. Anita Kumari
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Contributions

Data curation, methodology, original draught preparation, and conceptualization were finished by SR. Writing, reviewing, and editing were finished by DK. The article was supervised by AK.

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Correspondence to Sudha Rana.

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Rana, S., Kumar, D. & Kumari, A. Fuzzy reliability assessment of urea fertiliser plant based on Petri nets method using a probabilistic picture-hesitant fuzzy set. Life Cycle Reliab Saf Eng (2024). https://doi.org/10.1007/s41872-024-00246-w

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