Abstract
The 3D extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS) aim to describe experts’ judgments more informatively and explicitly. Introduction of generalized three dimensional spherical fuzzy sets (SFS) including some essential differences from the other fuzzy sets is presented in the literature with their arithmetic, aggregation, and defuzzification operations [1]. This study summarizes the previously introduced spherical fuzzy sets and as an application spherical fuzzy TOPSIS method will be applied to the site selection of photovoltaic power station.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Kutlu Gündoğdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. Prepr. 36(1), 337–352 (2019)
Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Atanassov, K.T.: Geometrical interpretation of the elements of the intuitionistic fuzzy objects Preprint IM-MFAIS (1989) 1–89, Sofia. Reprinted: Int. J. Bioautomation 20(S1), 27–42 (2016)
Garibaldi, J.M., Ozen, T.: Uncertain fuzzy reasoning: a case study in modelling expert decision making. IEEE Trans. Fuzzy Syst. 15(1), 16–30 (2007)
Grattan-Guinness, I.: Fuzzy membership mapped onto interval and many-valued quantities. Zeitschrift fur mathematische Logik und Grundladen der Mathematik 22(1), 149–160 (1976)
Jahn, K.U.: Intervall-wertige Mengen. Math. Nachr. 68(1), 115–132 (1975)
Sambuc, R.: Function Φ-Flous, Application a l’aide au Diagnostic en Pathologie Thyroidienne. Ph. D. thesis, University of Marseille (1975)
Smarandache, F.: Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis. American Research Press, Rehoboth (1998)
Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)
Yager, R.R.: Pythagorean fuzzy subsets. In: Joint IFSA World Congress and NAFIPS Annual Meeting, pp. 57–61. Edmonton, Canada (2013)
Yager, R.: On the theory of bags. Int. J. Gen. Syst. 13(1), 23–37 (1986)
Xu, Z., Zhang, X.: Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl. Based Syst. 52, 53–64 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gündoğdu, F.K. (2020). Principals of Spherical Fuzzy Sets. 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. https://doi.org/10.1007/978-3-030-23756-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-23756-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23755-4
Online ISBN: 978-3-030-23756-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)