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Fuzzy Unconstrained Geometric Programming Problem

  • Sahidul Islam
  • Wasim Akram Mandal
Chapter
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Abstract

Since 1960s, geometric programming (GP) is utilized in different fields (like operations management, engineering science, and so on). Geometric programming (GP) is one of the powerful techniques to solve a specific type of nonlinear programming problem (NLP). The theory of geometric programming (GP) is first introduced in 1961 by Duffin and Zener. The first publication on geometric programming (GP) was published by Duffin and Zener in 1967. There are numerous references to applications and strategies for GP in the survey paper by Ecker. In the standard geometric model, all coefficients are considered as fixed. In real circumstances, it will have some little fluctuations.

References

  1. R.E. Bellman, L.A. Zadeh, Decision-making in a fuzzy environment. Manage. Sci. 17, B141–B164 (1970)MathSciNetCrossRefGoogle Scholar
  2. B.Y. Cao, in Solution and Theory of Question for a Kind of Fuzzy Positive Geometric Program. Proceedings of the 2nd IFSA Congress, Tokyo, Japan 1 (1987), pp. 205–208Google Scholar
  3. B.Y. Cao, Fuzzy geometric programming (I). Fuzzy Sets Syst. 53(2), 135–154 (1993)MathSciNetCrossRefGoogle Scholar
  4. S. Islam, T.K. Roy, A fuzzy EPQ model with flexibility and reliability consideration and demand dependent unit production cost under a space constraint: a fuzzy geometric programming approach. Appl. Math. Comput. 176(2), 531–544 (2006)MathSciNetzbMATHGoogle Scholar
  5. N.K. Mandal, T.K. Roy, A displayed inventory model with L-R fuzzy number. Fuzzy Optim. Decis. Mak. 5(3), 227–243 (2006)Google Scholar
  6. L.F. Mendoça, J.M. Sousa, J.M.G. Sá da Costa, Optimization problems in multivariable fuzzy predictive control. Int. J. Approximate Reasoning 36, 199–221 (2004)MathSciNetCrossRefGoogle Scholar
  7. LINGO: The Modeling Language and Optimizer (1999). Lindo system Inc., Chicago, IL 60622, USA Google Scholar
  8. L. Liu, G.H. Huang, Y. Liu, G.A. Fuller, G.M. Zeng, A fuzzy-stochastic robust programming model for regional air quality management under uncertainty. Eng. Optim. 35, 177–199 (2003)MathSciNetCrossRefGoogle Scholar
  9. E. Shivanian, E. Khorram, Monomial geometric programming with fuzzy relation inequality constraints with max-product composition. Comput. Ind. Eng. 56(4), 1386–1392 (2009)CrossRefGoogle Scholar
  10. J.-H. Yang, B.-Y. Cao, in Geometric Programming with Fuzzy Relation Equation Constraints. FUZZ-IEEE (2005), pp. 557–560Google Scholar
  11. S. Yousef, N. Badra, T.G. Yazied Abu-El, Geometric programming problems with fuzzy parameters and its application to crane load sway. World Appl. Sci. J. 7(1), 94–101 (2009)Google Scholar
  12. L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar
  13. M.P. Biswal, Fuzzy programming technique to solve multi-objective geometric programming problems. Fuzzy Sets Syst. 51(1), 67–71 (1992)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Sahidul Islam
    • 1
  • Wasim Akram Mandal
    • 2
  1. 1.Department of MathematicsUniversity of KalyaniKalyani, NadiaIndia
  2. 2.Beldanga D.H. Senior MadrasahBeldanga, MurshidabadIndia

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