Skip to main content
SpringerLink
Log in

Complex Spherical Fuzzy Sets and an Application to Catering Services in Aviation 4.0

  • Chapter
  • First Online:
Intelligent and Fuzzy Techniques in Aviation 4.0

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 372))

Abstract

In this research, the recent development of three dimensional fuzzy sets namely, spherical fuzzy sets is extended to complex spherical fuzzy sets (CSFSs) and the novelty of CSFSs with their operations and properties are investigated. The range of CSFSs membership functions lie in complex plane, not limited to [0, 1]. So, the CSFSs describe complex membership functions in a set in terms of complex numbers which leads to a new mathematical framework and comprehensive study of their properties. Some of the aggregation operators and distance measures are established with their mathematical proof. Further an intelligent system based on EDAS (Evaluation based on Distance from Average Solution) method has been developed using the proposed complex spherical fuzzy aggregation operators. An application is proposed for aviation industry 4.0 in order to assess the performance of catering services. Finally a numerical illustration has been demonstrated for the proposed innovative method.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  2. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  Google Scholar 

  3. Yager, R.R.: Pythagorean fuzzy subsets. In: Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada (2013)

    Google Scholar 

  4. Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers, and decision making. Int. J. Intell. Syst. 28(5), 436–452 (2013)

    Article  Google Scholar 

  5. Smarandache, F.: A Unifying Field in Logics, Neutrosophic Logic, Neutrosophy, Neutrosophic Set and Neutrosophic Probabilty, 4th edn. American Research Press, Rehoboth (1999)

    MATH  Google Scholar 

  6. Kutlu Gundogdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36(1), 337–352 (2019)

    Article  Google Scholar 

  7. Kutlu Gundogdu, F., Kahraman, C.: A novel spherical fuzzy QFD method and its application to the linear delta robot technology development. Eng. Appl. Artif. Intell. 87, (2020). https://doi.org/10.1016/j.engappai.2019.103348

  8. Aydin, S., Kutlu Gundogdu, F.: Interval-valued spherical fuzzy MULTIMOORA method and its application to Industry 4.0. In: Kahraman, C., Kutlu Gündodu, F. (eds.) Decision Making with Spherical Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol. 392. Springer, Cham (2021) . https://doi.org/10.1007/978-3-030-45461-6-13

  9. Ashraf, S., Abdullah, S., Mahmood, T.: GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems. Math. Sci. 12(4), 263–275 (2018)

    Google Scholar 

  10. Ashraf, S., Abdullah, S., Mahmood, T., Ghani, F., Mahmood, T.: Spherical fuzzy sets and their applications in multi-attribute decision making problems. J. Intell. Fuzzy Syst. 36, 2829–2844 (2019)

    Article  Google Scholar 

  11. Ashraf, S., Abdullah, S.: Spherical aggregation operators and their application in multi-attribute group decision-making. Int. J. Intell. Syst. 34(3), 493–523 (2019)

    Article  Google Scholar 

  12. Jin, H., Ashraf, S., Abdullah, S.: Spherical fuzzy logarithmic aggregation operators based on entropy and their application in decision support systems. Entropy 21(7), 628 (2019)

    Article  MathSciNet  Google Scholar 

  13. Jin, H., Ashraf, S., Abdullah, S., Qiyas, M., Bano, M., Zeng, S.: Linguistic spherical fuzzy aggregation operators and their applications in multi-attribute decision making problems. Mathematics 7(5), 413 (2019)

    Article  Google Scholar 

  14. Raq, M., Ashraf, S., Abdullah, S., Mahmood, T., Muhammad, S.: The cosine similarity measures of spherical fuzzy sets and their applications in decision making. J. Intell. Fuzzy Syst. 36, 6059–6073 (2019)

    Article  Google Scholar 

  15. Ashraf, S., Abdullah, S., Mahmood, T.: Spherical fuzzy Dombi aggregation operators and their application in group decision making problems. J. Ambient Intell. Human. Comput. 1–19 (Preprint) (2019)

    Google Scholar 

  16. Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10, 2 (2002). https://doi.org/10.1109/91.995119

    Article  Google Scholar 

  17. Bi, L., Dai, S., Hu, B.: Complex fuzzy geometric aggregation operators. Symmetry 10(7), 251 (2018)

    Article  Google Scholar 

  18. Bi, L., Dai, S., Hu, B.: Complex fuzzy arithmetic aggregation operators. J. Intell. Fuzzy Syst. 36(3), 2765–2771 (2019)

    Article  Google Scholar 

  19. Hu, B., Bi, L., Dai, S.: Complex fuzzy power aggregation operators. Math. Prob. Eng. (2019). https://doi.org/10.1155/2019/9064385

    Article  MathSciNet  MATH  Google Scholar 

  20. Alkouri, A.S., Salleh, A.R.: Complex intuitionistic fuzzy sets. AIP Conf. Proc. 1482, 464 (2012). https://doi.org/10.1063/1.4757515

    Article  Google Scholar 

  21. Ullah, K., Mahmood, T., Ali, Z.: On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. 6(1) (2020)

    Google Scholar 

  22. Ali, M., Smarandache, F.: Complex neutrosophic set. Neural Comput. Appl. 28, 1817–1834 (2017). https://doi.org/10.1007/s00521-015-2154-y

    Article  Google Scholar 

  23. Ali, Z., Mahmood, T., Yang, M.S.: Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry 12, 1311 (2020). https://doi.org/10.3390/sym10060193

    Article  Google Scholar 

  24. Mahmood, T., Ullah, K., Khan, Q.: An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput. Appl. 31, 7041–7053 (2019). https://doi.org/10.1007/s00521-018-3521-2

    Article  Google Scholar 

  25. Kutlu Gundodu, F., Kahraman, C., Karaan, A.: Spherical fuzzy VIKOR method and its application to waste management. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A., Sari, I. (eds.) Intelligent and Fuzzy Techniques in Big Data Analytics and Decision Making. INFUS 2019. Advances in Intelligent Systems and Computing, vol. 1029. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23756-1-118

  26. Keshavarz Ghorabaee, M., Zavadskas, E.K., Olfat, L., Turskis, Z.: Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 26, 435–451 (2015)

    Article  Google Scholar 

  27. Keshavarz Ghorabaee, M., Zavadskas, E.K., Amiri, M., Turskis, Z.: Extended EDAS method for fuzzy multi-criteria decision-making: an application to supplier selection. Int. J. Comput. Commun. Control 11, 358–371 (2016). https://doi.org/10.15837/ijccc.2016.3.2557

  28. Kahraman, C., Keshavarz Ghorabaee, M., Zavadskas, E.K., Onar, S.C., Yazdani, M., Oztaysi, B.: Intuitionistic fuzzy EDAS method: an application to solid waste disposal site selection. J. Environ. Eng. Landscape Manage. 25, 1–12 (2017). https://doi.org/10.3846/16486897.2017.1281139

    Article  Google Scholar 

  29. Buyukozkan, G., Feyzioglu, O., Havle, C.A.: Analysis of success factors in aviation 4.0 using integrated intuitionistic fuzzy MCDM methods. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A., Sari, I. (eds.) Intelligent and Fuzzy Techniques in Big Data Analytics and Decision Making. INFUS 2019. Advances in Intelligent Systems and Computing, vol. 1029. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23756-1-73

  30. Oztemel, E., Gursev, S.: Literature review of Industry 4.0 and related technologies. J. Intell. Manuf. 31, 127–182 (2020). https://doi.org/10.1007/s10845-018-1433-8

  31. Barbosa, G.F., Aroca, R.V.: Advances of Industry 4.0 concepts on aircraft construction: an overview of trends. J. Steel Struct. Constr. 3, 125 (2017). https://doi.org/10.4172/2472-0437.1000125

Download references

Author information

Authors and Affiliations

  1. Sacred Heart College (Autonomous), Tirupattur District, Tamilnadu, 635601, India

    D. Ajay & J. Aldring

Authors
  1. D. Ajay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Aldring
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Air Force Academy, National Defence University, Istanbul, Turkey

    Serhat Aydın

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ajay, D., Aldring, J. (2022). Complex Spherical Fuzzy Sets and an Application to Catering Services in Aviation 4.0. In: Kahraman, C., Aydın, S. (eds) Intelligent and Fuzzy Techniques in Aviation 4.0. Studies in Systems, Decision and Control, vol 372. Springer, Cham. https://doi.org/10.1007/978-3-030-75067-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation