Soft Computing

, Volume 22, Issue 15, pp 5007–5020 | Cite as

Pythagorean fuzzy engineering economic analysis of solar power plants

  • Veysel ÇobanEmail author
  • Sezi Çevik Onar


The total world energy consumption is rising, and the alternative energy sources are sought to meet this demand. Renewable energy sources have distinctive features that make these sources environmental friendly and increase their share in total energy supply. Renewable energies, which are inexhaustible and renew themselves, are predicted to be the primary energy source for the future. The sun, which is the most important renewable energy source and the source of other energies, is also used for direct and indirect energy generation. In order to realize investments in solar energy systems that require high initial investment, their economic suitability must be assessed appropriately. Life cycle cost (LCC) and levelized cost of energy (LCOE) methods are widely used in economic evaluation and comparison of the large-scale solar energy system. Yet, solar energy investment decisions involve uncertainty and imprecision due to the vagueness in production levels and energy prices. An ample economic analysis should be able to evaluate the uncertainty and consider the dynamic costs and benefits. Pythagorean fuzzy sets are excellent tools for dealing with uncertainty and imprecision inherent in a system. In this study, the Pythagorean fuzzy set theory is applied so that the uncertainties and the opinions of the decision makers are more realistically incorporated into the economic analysis. The proposed Pythagorean LCC and LCOE methods enable dealing with the solar energy investments with fuzzy parameters. Alternative energy systems with different technological features and economic conditions can be more accurately compared using the proposed method.


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96CrossRefzbMATHGoogle Scholar
  2. Atanassov K (1989) Geometrical interpretation of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia. Reprinted: Int. J. Bioautomation, 2016, 20(S1):27–42Google Scholar
  3. Atanassov KT (1999) Intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets, pp 1–137. SpringerGoogle Scholar
  4. Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, HeidelbergCrossRefzbMATHGoogle Scholar
  5. Atanassov KT, Riecan B (2006) On two operations over intuitionistic fuzzy sets. J Appl Math Stat Inform (JAMSI) 2(2):145–148Google Scholar
  6. Bolinger M, Seel J, LaCommare KH (2017) Utility-scale solar 2016: an empirical analysis of project cost, performance, and pricing trends in the United States. Lawrence Berkeley National Lab.(LBNL), Berkeley, CA, United StatesGoogle Scholar
  7. Buckley JJ, Eslami E, Feuring T (2013) Fuzzy mathematics in economics and engineering, vol 91. Physica, HeidelbergzbMATHGoogle Scholar
  8. Campbell M et al (2009) Minimizing utility-scale PV power plant LCOE through the use of high capacity factor configurations. In: 2009 34th IEEE photovoltaic specialists conference (PVSC). IEEEGoogle Scholar
  9. Çoban V, Onar SÇ (2017) Modelling solar energy usage with fuzzy cognitive maps. In: Intelligence systems in environmental management: theory and applications, pp 159–187. SpringerGoogle Scholar
  10. Conkling RL (2011) Energy pricing: economics and principles. Springer, BerlinCrossRefGoogle Scholar
  11. Crawley GM (2016) Solar energy. World Scientific Publishing Co. Pte. Ltd, HackensackCrossRefGoogle Scholar
  12. Dahl C (2015) International energy markets: understanding pricing, policies, and profits. PennWell Books, TulsaGoogle Scholar
  13. Darling SB et al (2011) Assumptions and the levelized cost of energy for photovoltaics. Energy Environ Sci 4(9):3133–3139CrossRefGoogle Scholar
  14. De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):477–484MathSciNetCrossRefzbMATHGoogle Scholar
  15. Duffie JA, Beckman WA (2013) Solar engineering of thermal processes. Wiley, HobokenCrossRefGoogle Scholar
  16. E.a.N.R.M. (ENRM) (2017a) Solar energy and technologies. Accessed 05 Dec 2017
  17. E.a.N.R.M (ENRM) (2017b) Renewable energy resources support mechanism (YEKDEM). Accessed 20 Nov 2017
  18. Energy HOMER (2017) Glossary. Accessed 12 Dec 2017
  19. Finance BNE (2015) New energy outlook 2015. Accessed 10 Dec 2017
  20. Insure S (2017) Top 5 largest solar power plants of the world. Accessed 10 Nov 2017
  21. International Energy Agency (IEA) (2017) World energy outlook 2017. Accessed 28 Feb 2018
  22. Kahraman C (2008) Fuzzy engineering economics with applications, vol 233. Springer, BerlinzbMATHGoogle Scholar
  23. Kahraman C, Çevik Onar S, Öztayşi B (2015) Engineering economic analyses using intuitionistic and hesitant fuzzy sets. J Intell Fuzzy Syst 29(3):1151–1168MathSciNetCrossRefzbMATHGoogle Scholar
  24. Kahraman C, Onar SC, Oztaysi B (2017) Present worth analysis using pythagorean fuzzy sets. In: Advances in fuzzy logic and technology 2017, pp 336–342. SpringerGoogle Scholar
  25. Kalogirou SA (2013) Solar energy engineering: processes and systems. Academic Press, OxfordGoogle Scholar
  26. Mendel JM, John RB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  27. Mendel J, Wu D (2010) Perceptual computing: aiding people in making subjective judgments, vol 13. Wiley, HobokenCrossRefGoogle Scholar
  28. Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11(4):3368–3372CrossRefGoogle Scholar
  29. N.R.E.L. (NREL) (2017) Distributed generation energy technology capital costs. Accessed 10 Nov 2017
  30. P.D.o.E.a.M.E. (PDEME) (2017) Project decision metrics: levelized cost of energy (LCOE). Accessed 10 Nov 2017
  31. Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160CrossRefGoogle Scholar
  32. Peng X, Yuan H, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32:991–1029CrossRefGoogle Scholar
  33. Roubens M (1990) Inequality constraints between fuzzy numbers and their use in mathematical programming. In: Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, pp 321–330. SpringerGoogle Scholar
  34. Short W, Packey DJ, Holt T (1995) A manual for the economic evaluation of energy efficiency and renewable energy technologies. National Renewable Energy Lab., Golden, CO, United StatesGoogle Scholar
  35. Sullivan WG, Wicks EM, Luxhoj JT (2009) Engineering economy. Pearson Prentice Hall, Upper Saddle RiverGoogle Scholar
  36. Talavera D et al (2013) Sensitivity analysis on some profitability indices for photovoltaic grid-connected systems on buildings: the case of two top photovoltaic European areas. J Sol Energy Eng 135(1):011003CrossRefGoogle Scholar
  37. Timilsina GR, Kurdgelashvili L, Narbel PA (2012) Solar energy: markets, economics and policies. Renew Sustain Energy Rev 16(1):449–465CrossRefGoogle Scholar
  38. U.N. (UN) (2017) World Population Prospects 2017. Accessed 20 Nov 2017
  39. U.S. Department of Energy (USDE), Office of Indian Energy (2015). Levelized Cost of Energy (LCOE). Accessed 25 Jan 2018
  40. U.S.E.I.A. (USEIA) (2017a) Levelized costs and levelized avoided cost of new generation resources in the annual energy outlook 2017. Accessed 20 Nov 2017
  41. U.S.E.I.A. (USEIA) (2017b) Renewable and alternative fuels. Accessed 20 Nov 2017
  42. Vergura S, Lameira VJ (2011) Technical-financial comparison between a PV plant and a CSP plant. Sistem Gestao 6(2):210–220CrossRefGoogle Scholar
  43. World Energy Council (WEC) (2016) World energy resources 2016. Accessed 10 Dec 2017
  44. Yager RR (2013) Pythagorean fuzzy subsets. In: IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013 joint. IEEEGoogle Scholar
  45. Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRefGoogle Scholar
  46. Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452CrossRefGoogle Scholar
  47. Zatzman GM (2012) Sustainable energy pricing: nature, sustainable engineering, and the science of energy pricing. Wiley, HobokenCrossRefGoogle Scholar
  48. Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Industrial Engineering DepartmentIstanbul Technical UniversityMaçka, IstanbulTurkey

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