Spherical Fuzzy Geometric Programming: A New Approach for System Reliability Assessment

Amirian, Sajad; Amiri, Maghsoud; Taghavifard, Mohammad Taghi

doi:10.22034/IJRRS.2023.6.1.5

Spherical Fuzzy Geometric Programming: A New Approach for System Reliability Assessment

Document Type : Original Research Article

Authors

Sajad Amirian

Maghsoud Amiri

Mohammad Taghi Taghavifard

Department of Industrial Management, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran

10.22034/IJRRS.2023.6.1.5

Abstract

The high risk of operational facilities and processes in strategic industries has made the continuous effort of operations managers to improve system reliability an undeniable necessity. The existing knowledge in fuzzy sets limits the sum of degrees of membership and non-membership of each element to more than one. However, in the real world, many ill-defined or highly complex situations require more consideration that is careful. Unlike normal fuzzy sets, the spherical fuzzy set pays attention to the degree of uncertainty of each element in decision-making situations and the degree of membership and non-membership. In addition, to help generalize the decision set, it considers the sum of squares of each membership function to be less than or equal to one. Achieving the success function is determined by maximizing the degree of membership and minimizing the degree of non-membership and uncertainty of each objective function in the spherical fuzzy set. Therefore, this paper develops a new algorithm based on the spherical fuzzy set called the spherical fuzzy geometric programming problem in system reliability. To evaluate the performance of the proposed algorithm, a descriptive example in the field of the rolling process of aluminum products is modeled in the form of a dual-objective problem, including maximization of reliability and minimization of cost.

Keywords

Reliability

Spherical fuzzy set

Geometric programming

Aluminum industry

Subjects

Case Studies Related to Reliability, Risk and Safety

Pham, "Software reliability and cost models: Perspectives, comparison, and practice," European Journal of Operational Research, vol. 149, no. 3, pp. 475-489, 2003/09/16/ 2003, doi: https://doi.org/10.1016/S0377-2217(02)00498-8.
Sourirajan, L. Ozsen, and R. Uzsoy, "A genetic algorithm for a single product network design model with lead time and safety stock considerations," European Journal of Operational Research, vol. 197, no. 2, pp. 599-608, 2009/09/01/ 2009, doi: https://doi.org/10.1016/j.ejor.2008.07.038.
T. Hazen, C. A. Boone, Y. Wang, and K. S. Khor, "Perceived quality of remanufactured products: construct and measure development," Journal of Cleaner Production, vol. 142, pp. 716-726, 2017/01/20/ 2017, doi: https://doi.org/10.1016/j.jclepro.2016.05.099.
Tang, Z. Chen, G. Hefferman, T. Wei, H. He, and Q. Yang, "A Hierarchical Distributed Fog Computing Architecture for Big Data Analysis in Smart Cities," presented at the Proceedings of the ASE BigData & SocialInformatics 2015, Kaohsiung, Taiwan, 2015. [Online]. Available: https://doi.org/10.1145/2818869.2818898.
G. Smith et al., "The reliability of skin biopsy with measurement of intraepidermal nerve fiber density," Journal of the Neurological Sciences, vol. 228, no. 1, pp. 65-69, 2005/01/15/ 2005, doi: https://doi.org/10.1016/j.jns.2004.09.032.
A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338-353, 1965/06/01/ 1965, doi: https://doi.org/10.1016/S0019-9958(65)90241-X.
J. Duffin, "Linearizing geometric programs," SIAM review, vol. 12, no. 2, pp. 211-227, 1970, doi: https://doi.org/10.1137/1012043.
E. Bellman and L. A. Zadeh, "Decision-Making in a Fuzzy Environment," Management Science, vol. 17, no. 4, pp. B-141-B-164, 1970, doi: https://doi.org/10.1287/mnsc.17.4.B141.
Atanassov, Studies in fuzziness and soft computing intuitionistic fuzzy logics. In: Fuzzy sets and systems, 1986.
Smarandache, "A unifying field in Logics: Neutrosophic Logic," in Philosophy: American Research Press, 1999, pp. 1-141. [Online]. Available at: https://core.ac.uk/download/pdf/84931.pdf
Ahmad, A. Y. Adhami, and F. Smarandache, "Single valued neutrosophic hesitant fuzzy computational algorithm for multiobjective nonlinear optimization problem," Neutrosophic sets and systems, vol. 22, pp. 76-86, 2018. [online]. Available at: https://digitalrepository.unm.edu/nss_journal/vol22/iss1/7?utm_source=digitalrepository.unm.edu%2Fnss_journal%2Fvol22%2Fiss1%2F7&utm_medium=PDF&utm_campaign=PDFCoverPages
Ahmad and A. Y. Adhami, "Neutrosophic programming approach to multiobjective nonlinear transportation problem with fuzzy parameters," International journal of management science and engineering management, vol. 14, no. 3, pp. 218-229, 2019, doi: https://doi.org/10.1080/17509653.2018.1545608.
Ahmad, A. Y. Adhami, and F. Smarandache, "Neutrosophic optimization model and computational algorithm for optimal shale gas water management under uncertainty," Symmetry, vol. 11, no. 4, p. 544, 2019, doi: https://doi.org/10.3390/sym11040544.
Ahmad, A. Y. Adhami, and F. Smarandache, "15 - Modified neutrosophic fuzzy optimization model for optimal closed-loop supply chain management under uncertainty," in Optimization Theory Based on Neutrosophic and Plithogenic Sets, F. Smarandache and M. Abdel-Basset Eds.: Academic Press, 2020, pp. 343-403. doi: https://doi.org/10.1016/B978-0-12-819670-0.00015-9
R. Yager, "Pythagorean fuzzy subsets," in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013: IEEE, pp. 57-61, doi: https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375.
Kutlu Gündoğdu and C. Kahraman, "Spherical fuzzy sets and spherical fuzzy TOPSIS method," Journal of intelligent & fuzzy systems, vol. 36, no. 1, pp. 337-352, 2019, doi: http://dx.doi.org/10.3233/JIFS-181401.
Rafiq, S. Ashraf, S. Abdullah, T. Mahmood, and S. Muhammad, "The cosine similarity measures of spherical fuzzy sets and their applications in decision making," Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6059-6073, 2019, doi: https://doi.org/10.3233/JIFS-181922.
Das, T. Roy, and M. Maiti, "Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach," Production Planning & Control, vol. 11, no. 8, pp. 781-788, 2000, doi: https://doi.org/10.1080/095372800750038382.
S. Mahapatra and T. K. Roy, "Single and multi container maintenance model: a fuzzy geometric programming approach," Journal of mathematics research, vol. 1, no. 2, p. 47, 2009, doi: https://doi.org/10.5539/jmr.v1n2p47.
Islam and T. K. Roy, "A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems," European Journal of Operational Research, vol. 173, no. 2, pp. 387-404, 2006/09/01/ 2006, doi: https://doi.org/10.1016/j.ejor.2005.01.050.