Abstract
Geometric programming (GP) optimization techniques are an important and interesting topic since the 1970s. The significant development can be realized by having enormous researches in this field, such as fuzzy geometric optimization technique, multiobjective goal geometric programming, different goal geometric programming techniques, etc. Thus this chapter investigates a new algorithm based on the spherical fuzzy set (SFS) named as spherical fuzzy geometric programming problem (SFGPP) under the spherical fuzzy environment. The SFGPP inevitably involves the degree of neutrality along with truth and a falsity membership degree of the element into the feasible decision set. It also generalizes the decision set by imposing the restriction that the sum of squares of each membership function must be less than or equal to one. The attainment of achievement function is determined by maximizing the truth and minimizing the neutral and negative membership degree of each objective function under the spherical fuzzy decision set. At last, numerical examples and conclusions are presented to reveal the applicability and future research scope in the SF domain.
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 and systems 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
Atanassov KT (1986) Studies in fuzziness and soft computing intuitionistic fuzzy logics. In: Fuzzy sets and systems
Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley
Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):B-141
Beightler CS, Phillips DT (1976) Applied geometric programming. Wiley
Das K, Roy TK, Maiti M (2000) Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach. Prod Plan Control 11(8):781–788
Dolan BED, Fourer R, Moré JJ, Munson TS (2002) Optimization on the NEOS Server. SIAM News 35(6):1–5
Duffin RJ (1970) Linearizing geometric programs. SIAM review 12(2):211–227
Floudas CA (2013) Deterministic global optimization: theory, methods and applications, vol 37. Springer Science and Business Media
Islam S, Roy TK (2006) Continuous optimization a new fuzzy multi-objective programming: entropy based geometric programming and its application of transportation problems 173:387–404
Kundu T, Islam S (2018) Neutrosophic goal geometric programming problem and its application to multi-objective reliability optimization model. Int J Fuzzy Syst 20(6):1986–1994
Kutlu Gündoğdu F, Kahraman C (2019) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst (Preprint), 1–16
Mahapatra GS, Roy TK (2009) Single and multi-container maintenance model: a fuzzy geometric programming approach. J Math Res 1(2):47
Peterson EL (2001) The origins of geometric programming. Ann Oper Res 105(1):15
Rafiq M, Ashraf S, Abdullah S, Mahmood T (2019) The cosine similarity measures of spherical fuzzy sets and their applications in decision making, (Preprint) 1–15
Smarandache F (1999) A unifying field in logics: neutrosophic logic. Philosophy. https://doi.org/10.5281/zenodo.49174
Yager RR (2013) Pythagorean fuzzy subsets. IEEE 2:57–61
Zener C (1971) Engineering design by geometric programming. Wiley
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 Geometric 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_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-45461-6_22
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)