Abstract
The new extension of the uncertain set is presented by Kutlu Gündogdu and Kahraman (J Intell Fuzzy Syst (Preprint):1–16, 2019) and named as a spherical fuzzy set (SFS). The SFS is the superset of fuzzy, intuitionistic fuzzy, and Pythagorean fuzzy sets, respectively (Yager in Pythagorean fuzzy subsets, vol 2. IEEE, pp 57–61, 2013). The SFS inherently involves three membership functions, namely; positive, neutral, and negative membership degrees of the element into the SFS. In this chapter, we present the spherical fuzzy linear programming problem (SFLPP) in which the different parameters are represented by spherical fuzzy numbers (SFNs). The crisp version of the SFLPP is obtained with the aid of positive, neutral, and negative membership degrees. Furthermore, the spherical fuzzy optimization model is presented to solve the SFLPP. A numerical example and case study are presented to show the working efficiency of the proposed research. At last, the conclusion and future research scope are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmad F, Adhami AY (2019) Neutrosophic programming approach to multiobjective nonlinear transportation problem with fuzzy parameters. Int J Manag Sci Eng Manag 14(3):218–229
Ahmad F, Adhami AY, Smarandache F (2018) Single valued neutrosophic hesitant fuzzy computational algorithm for multiobjective nonlinear optimization problem. Neutrosophic Sets Syst 22:76–86
Ahmad F, Adhami AY, Smarandache F (2019) Neutrosophic optimization model and computational algorithm for optimal shale gas water management under uncertainty. Symmetry 11(4):544
Ahmad F, Adhami AY, Smarandache F (2020) Modified neutrosophic fuzzy optimization model for optimal closed-loop supply chain management under uncertainty. In: Optimization theory based on neutrosophic and plithogenic sets. Academic Press, pp 343–403
Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86(3):299–306
Atanassov KT (2017) Intuitionistic fuzzy logics. Springer International Publishing
Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manage Sci 17(4):140–164
Czyzyk J, Mesnier MP, Moré JJ (1998) The NEOS server. IEEE J Comput Sci Eng 5(3):68–75
Kutlu Gündoğdu F, Kahraman C (2019) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst (Preprint):1–16
Rafiq M, Ashraf S, Abdullah S, Mahmood T, Muhammad S (2019) The cosine similarity measures of spherical fuzzy sets and their applications in decision making. J Intell Fuzzy Syst (Preprint):1–15
Rizk-Allah RM, Hassanien AE, Elhoseny M (2018) A multi-objective transportation model under neutrosophic environment. Comput Electr Eng 69:705–719
Smarandache F (1999) A unifying field in logics: neutrosophic logic. Philosophy. American Press
Yager RR (2013) Pythagorean fuzzy subsets, vol 2. IEEE, pp 57–61
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ahmad, F., Adhami, A.Y. (2021). Spherical Fuzzy Linear Programming Problem. In: Kahraman, C., Kutlu Gündoğdu, F. (eds) Decision Making with Spherical Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 392. Springer, Cham. https://doi.org/10.1007/978-3-030-45461-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-030-45461-6_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-45460-9
Online ISBN: 978-3-030-45461-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)