Skip to main content
SpringerLink
Log in

Multi-objective Fuzzy Geometric Programming Problem Using Fuzzy Geometry

  • Chapter
  • First Online:
Book cover Trends in Mathematics and Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 796))

  • 386 Accesses

Abstract

This paper proposes a methodology to obtain fuzzy Pareto optimal frontier of multi-objective fuzzy geometric programming problem. The method that we derive here does not depend on the degree-of-difficulty of the problem under consideration. A study on the fuzzy convexity of the posynomials involved is also given here. Fuzzy geometric and algebraic approaches have been considered for the said optimization problem and is supported with a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Beightler, C.S., Phillips, D.T.: Applied Geometric Programming. Wiley, New York (1976)

    Google Scholar 

  2. Cao, B.Y.: Fuzzy Geometric Programming. Applied Optimization, Springer (2002)

    Google Scholar 

  3. Choi, J., Bricker, D.: Effectiveness of geometric programming algorithm for optimization of machining economics models. Comput. Oper. Res. 10, 957–961 (1996)

    Article  Google Scholar 

  4. Chakraborty, D., Ghosh, D.: Analytical fuzzy plane geometry II. Fuzzy Sets Syst. 243, 84–109 (2014)

    Article  MathSciNet  Google Scholar 

  5. Dufflin, R.J., Peterson, E.L., Zener, C.: Geometric Programming: Theory and Applications. Willey, New York (1967)

    Google Scholar 

  6. Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry I. Fuzzy Sets Syst. 209, 66–83 (2012)

    Article  MathSciNet  Google Scholar 

  7. Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry III. Fuzzy Sets Syst. 283, 83–107 (2016)

    Article  MathSciNet  Google Scholar 

  8. Ghosh, D., Chakraborty, D.: On Fuzzy Ideal Cone Method to Capture Entire Fuzzy Non dominated Set of Fuzzy Multi-criteria Optimization Problems with Fuzzy Parameters. Facets of Uncertainties and Applications, pp. 249–260. Springer, India (2015)

    Google Scholar 

  9. Jung, H., Klein, C.: Optimal inventory policies under decreasing cost functions via geometric programming. Eur. J. Oper. Res. 132, 628–642 (2001)

    Article  Google Scholar 

  10. Kim, D., Lee, W.: Optimal join pricing and lot sizing with fixed and variable capacity. Eur. J. Oper. Res. 109, 212–227 (1998)

    Article  Google Scholar 

  11. Kortanek, K., Xu, X., Ye, Y.: An infeasible interior-point algorithm for solving primal and dual geometric programs. Math. Programm. 76, 155–181 (1997)

    MathSciNet  MATH  Google Scholar 

  12. Liu, S.T.: Geometric programming with fuzzy parameters in engineering optimization. Internat. J. Approx. Reason. 46(3), 484–498 (2007)

    Article  Google Scholar 

  13. Lui, S.: Posynomial geometric programming with interval exponents and coefficients. Eur. J. Oper. Res. 186, 17–27 (2008)

    Article  MathSciNet  Google Scholar 

  14. Qu, S., Zhang, K., Wang, F.: A global optimization using linear relaxation for generalized geometric programming. Eur. J. Oper. Res. 190, 345–356 (2008)

    Article  MathSciNet  Google Scholar 

  15. Peterson, E.: The fundamental relations between geometric programming duality, parametric programming duality and ordinary Lagrangian duality. Ann. Oper. Res. 105, 109–153 (2001)

    Article  MathSciNet  Google Scholar 

  16. Rajgopal, J., Bricker, D.: Solving posynomial geometric programming problems via generalized linear programming. Computat. Optim. Appl. 21, 95–109 (2002). World Appl. Sci. J. 7(1): 94–101 (2009)

    Google Scholar 

  17. Shivanian, E., Khorram, E.: Monomial geometric programming with fuzzy relation in equality constraints with max-product composition. Comput. Ind. Eng. 56, 1386–1392 (2009)

    Article  Google Scholar 

  18. Yang, H., Bricker, D.: Investigation of path-following algorithms for signomial geometric programming problems. Eur. J. Oper. Res. 103, 230–241 (1997)

    Article  Google Scholar 

  19. Zhou, X.G., Yang, X.P., Cao, B.Y.: Posynomial geometric programming problem subject to max-min fuzzy relation equations. Inf. Sci. 328, 15–25 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

First two authors gratefully acknowledge the financial support provided by Department of Science & Technology, India (SR/S4/MS:858/13).

Author information

Authors and Affiliations

  1. Indian Institute of Technology, Kharagpur, 721302, India

    Debjani Chakraborty, Abhijit Chatterjee &  Aishwaryaprajna

Authors
  1. Debjani Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhijit Chatterjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aishwaryaprajna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Debjani Chakraborty .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, University of Cádiz, Puerto Real, Cádiz, Spain

    María Eugenia Cornejo

  2. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T. Kóczy

  3. Department of Mathematics, Science Faculty, University of Cádiz, Puerto Real, Cádiz, Spain

    Jesús Medina

  4. Faculty of Science and Technology, University of Algarve, Faro, Portugal

    Antonio Eduardo De Barros Ruano

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chakraborty, D., Chatterjee, A., Aishwaryaprajna (2019). Multi-objective Fuzzy Geometric Programming Problem Using Fuzzy Geometry. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_14

Download citation

Publish with us

Policies and ethics

Search

Navigation