Main Article Content

Abstract

This article proposes a new version of the technique of order preference by similarity to an ideal solution (TOPSIS) to solve fuzzy multi-attribute group decision making (MAGDM) problems using trapezoidal interval type-2 fuzzy sets (IT2FSs). The traditional TOPSIS ranks the alternatives according to their relative degree of closeness to the ideal solutions. On the other hand, TOPSIS based on similarity measure ranks the alternatives according to their total degree of similarity to the ideal solutions. This study extends TOPSIS using similarity measure using map distance to IT2FSs. First, the similarity measure based on map distance for interval-valued fuzzy sets (IVFSs) is extended to encompass IT2FSs due to the deficiency in IT2FSs similarity measures. Then, TOPSIS using similarity measure is applied. Hence, fuzzy MAGDM problems can be handled in a more flexible intelligent manner and avoiding defuzzification with its drawbacks. An illustrative example is given to explain the approach. Then, a practical problem in assessing thermal energy storage technologies in solar power systems is solved, where the weights of the attributes and the performance of the qualitative attributes are linguistic variables modeled by IT2FSs. The reliability of two normalization techniques is examined and the impact of the theoretical and empirical reference points on the solution is investigated.

Keywords

Fuzzy multi-criteria decision making TOPSIS Similarity measures Interval type-2 fuzzy sets Solar power systems

Article Details

How to Cite
Sharaf, I. M. (2021). An interval type-2 fuzzy TOPSIS for MAGDM applied to solar power systems. Pakistan Journal of Statistics and Operation Research, 17(3), 559-575. https://doi.org/10.18187/pjsor.v17i3.2798

References

  1. Alva, G., Lin, Y., Fang, G. (2018) An overview of thermal energy storage systems. Energy 144, 341-378 DOI: https://doi.org/10.1016/j.energy.2017.12.037
  2. Ashtiani, B., Haghighirad, F., Makui, A., Montazer, G.A. (2009) Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Appl Soft comput, 9, 457-461. DOI: https://doi.org/10.1016/j.asoc.2008.05.005
  3. Beg, I., Rashid, T. (2017) A fuzzy similarity measure based on equivalence relation with application in cluster analysis. International Journal of Computers and Applications, 39(3), 148-154. DOI: https://doi.org/10.1080/1206212X.2017.1309220
  4. Brauers WKM, Zavadskas EK (2006) The MOORA method and its application to privatization in a transition economy. Control and Cybernetics 35 (2):445-496.
  5. Cavallaro, F. (2010) Fuzzy TOPSIS approach for assessing thermal-energy storage in concentrated solar power (CSP) systems. Applied Energy 87:496-503. DOI: https://doi.org/10.1016/j.apenergy.2009.07.009
  6. Cavallaro, F., Zavadskas, E.K., Streimikienec, D., Mardani, A. (2019) Assessment of concentrated solar power (CSP) technologies based on a modified intuitionistic fuzzy topsis and trigonometric entropy weights. Technological Forecasting and Social Change 140: 258-270. DOI: https://doi.org/10.1016/j.techfore.2018.12.009
  7. Chen, C.-T. (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Sys, 114, 1-9. DOI: https://doi.org/10.1016/S0165-0114(97)00377-1
  8. Chen, S.-J. (2011) Measure of similarity between interval-valued fuzzy numbers for fuzzy recommendation process based on quadratic mean operator. Expert Syst Appl, 38, 2386-2394. DOI: https://doi.org/10.1016/j.eswa.2010.08.027
  9. Chen, S.-J., Chen, S.-M. (2008) Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers. Computers and Mathematics with Applications, 55, 1670-1685. DOI: https://doi.org/10.1016/j.camwa.2007.06.022
  10. Chen, S.-J., Kao, H.-W. (2010) Measure of similarity between interval-valued fuzzy numbers based on standard deviation operator. International Conference of Electronics and information Engineering (ICEEIE 2010), 2, 376-380, Kyoto, Japan. DOI: https://doi.org/10.1109/ICEIE.2010.5559801
  11. Chen, S.-J., Wang, Z.-Y., Li, W.-R. (2013) Calculating the degree of similarity between interval–valued fuzzy numbers based on map distance. Proceedings of the International Multi Conference of Engineers and Computer Scientists (IMECS 2013), Hong Kong.
  12. Chen, S.-M., Chen, J.-H. (2009) Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number operator. Expert Syst Appl, 36, 6309-6317. DOI: https://doi.org/10.1016/j.eswa.2008.08.017
  13. Chen, S.-M., Lee, L.-W. (2010) Fuzzy multiple attributes group-decision making based on the interval type-2 TOPSIS method. Expert Syst Appl, 37, 2790-2798. DOI: https://doi.org/10.1016/j.eswa.2009.09.012
  14. Cheng, S.-H., Chen, S.-M., Huang, Z.-C. (2016) Autocratic decision making using group recommendations based on ranking interval type-2 fuzzy sets. Inf Sci, 361-362, 135-161. DOI: https://doi.org/10.1016/j.ins.2016.04.035
  15. Dymova, L., Sevastjanov, P., Tikhonenko, A. (2015) An interval type-2 fuzzy extension of the TOPSIS methods using alpha cuts. KNOWL-BASED SYST, 83, 116-127. DOI: https://doi.org/10.1016/j.knosys.2015.03.014
  16. Hagras, H. (2004) A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans. Fuzzy Syst. 12(4), 524-539. DOI: https://doi.org/10.1109/TFUZZ.2004.832538
  17. Hwang, C.L., Yoon, K. (1981) Multiple attributes decision making methods and applications. Springer, Berlin Heidelberg DOI: https://doi.org/10.1007/978-3-642-48318-9_3
  18. Ilieva, G. (2016) TOPSIS modification with interval type-2 fuzzy numbers. Cybernetics and Information Technologies, 16(2), 60-68. DOI: https://doi.org/10.1515/cait-2016-0020
  19. Kahraman, C., Öztayşi, B., Sari, I. U., Turanoglu, E, (2014) Fuzzy analytic process with interval type-2 fuzzy sets. KNOWL-BASED SYST, 59, 48-57. DOI: https://doi.org/10.1016/j.knosys.2014.02.001
  20. Kearney, D., Kelly, B., Herrmann, U., Cable, R., Pacheco, J., Mahoney, R., et al. (2004) Engineering aspects of a molten salt heat transfer fluid in a trough solar field. Energy (29), 861–70. DOI: https://doi.org/10.1016/S0360-5442(03)00191-9
  21. Kuravi, S., Traha, J., Goswami, D.Y., Rahman, M.M., Stefanakos, E.K. (2013) Thermal energy storage technologies and systems for concentrating solar power plants. Progress in Energy and Combustion Science, 39, 285-319. DOI: https://doi.org/10.1016/j.pecs.2013.02.001
  22. Mohamadghasemi, A. (2020) A Note On “An Interval Type-2 Fuzzy Extension Of The TOPSIS Method Using Alpha Cuts” . Journal of Optimization in Industrial Engineering 13( 2), 227- 238.
  23. Pelay, U., Luo, L., Fan, Y., Stitou, D., Rood, M. (2017) Thermal energy storage systems for concentrated solar power plants. Renewable and Sustainable Energy Reviews 79, 82–100 DOI: https://doi.org/10.1016/j.rser.2017.03.139
  24. Rashid, T., Beg, I. and Husnine, S.M. (2014) Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS. Appl Soft comput, 21, 462-468. DOI: https://doi.org/10.1016/j.asoc.2014.04.002
  25. Sepúlveda, R., Castello, O., Melin, P., Rodriguez-Diaz, A., Montiel, O. (2007) Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic. Information Sciences, 177(10), 2023-2048. DOI: https://doi.org/10.1016/j.ins.2006.10.004
  26. Sharaf, I.M. (2018) TOPSIS with similarity measure for MADM applied to network selection. Comp. Appl. Math. 37, 4104–4121. DOI: https://doi.org/10.1007/s40314-017-0556-4
  27. Van Delft, A., Nijkamp, P. (1977) Multi-Criteria Analysis and Regional Decision-Making. Studies in Applied Regional Science 8, Springer –Verlag US.
  28. Wei, S.-H., Chen S.-M. (2009) A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst Appl, 36, 589-598. DOI: https://doi.org/10.1016/j.eswa.2007.09.033
  29. Wu, D., Mendel, J.M. (2008) A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets. Inf Sci, 178, 381-402. DOI: https://doi.org/10.1016/j.ins.2007.04.014
  30. Wu, T., Liu, X., Liu, F. (2018) An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information. Information Sciences 432, 392–410 DOI: https://doi.org/10.1016/j.ins.2017.12.006
  31. Zheng, G., Wang, J., Zhou, W., Zhang, Y. (2010) A Similarity Measure between Interval Type-2 Fuzzy Sets. Proceedings of the 2010 IEEE International Conference on Mechatronics and Automation , Xi'an, China. DOI: https://doi.org/10.1109/ICMA.2010.5589072