Skip to main content
SpringerLink
Log in

Fuzzy Number Linear Programming

  • Chapter
  • First Online:
Fuzzy Linear Programming: Solution Techniques and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 379))

  • 394 Accesses

Abstract

The aim of this chapter is to study linear programming problem with fuzzy coefficients as one of the convenient model of fuzzy linear programs. In this way, we first introduce a general form of Fuzzy Number Linear programming (FNLP) problems and then give the fundamental concepts which are useful in throughout of the chapter.

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. Bas, E.: A robust optimization approach to diet problem with overall glycemic load as objective function. Appl. Math. Model. 38, 4926–4940 (2014)

    Article  MathSciNet  Google Scholar 

  2. Bazaraa, M.S., Jarvis, J.J., Sherali, H.D.: Linear Programming and Network Flows. Wiley-Interscience, Hoboken (2005)

    MATH  Google Scholar 

  3. Cadenas, J.M., Pelta, D.A., Pelta, H.R., Verdegay, J.L.: Application of fuzzy optimization to diet problems in argentienan farms. Eur. J. Oper. Res. 158, 218–228 (2004)

    Article  Google Scholar 

  4. Castrodeza, C., Lara, P., Pena, T.: Multi-criteria fractional model for feed formulation: economic, nutritional and environmental criteria. Agric. Syst. 86, 76–96 (2005)

    Article  Google Scholar 

  5. Darvishi SalooKolaei, D., Teimouri Yansari, A., Nasseri, S.H.: Application of fuzzy optimization in diet formulation. J. Math. Comput. Sci. 2, 459–468 (2011)

    Article  Google Scholar 

  6. Darvishi Salookolaei, D., Liu, S., Nasseri, S.H.: A new approach in animal diet using grey system theory. Grey Syst. Theory Appl. 8(2), 167–180 (2018)

    Article  Google Scholar 

  7. Ebrahimnejad, A.: Sensitivity analysis in fuzzy number linear programming problems. Mathe. Comput. Model. 53(9-10), 1878–1888 (2011)

    Article  MathSciNet  Google Scholar 

  8. Ebrahimnejad, A.: Cost efficiency measures with trapezoidal fuzzy numbers in data envelopment analysis based on ranking functions: application in insurance organization and hospital. Int. J. Fuzzy Syst. Appl. 2(3), 51–68 (2012)

    Article  Google Scholar 

  9. Ebrahimnejad, A., Nasseri, S.H.: Using complementary slackness property to solve linear programming with fuzzy parameters. Fuzzy Inf. Eng. 1(3), 233–245 (2009)

    Article  Google Scholar 

  10. Ebrahimnejad, A., Nasseri, S.H.: A dual simplex method for bounded linear programmes with fuzzy numbers. Int. J. Math. Oper. Res. 2(6), 762–779 (2010)

    Article  MathSciNet  Google Scholar 

  11. Ebrahimnejad, A., Nasseri, S.H., Mansourzadeh, S.M.: Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients. Int. J. Oper. Res. Inf. Syst. 2(1), 96–120 (2011)

    Article  Google Scholar 

  12. Eghbali, H., Eghbali, M.A., Vahidian Kamyad, A.: Optimizing human diet problem based on price and taste using multi-objective fuzzy linear programming approach. Int. J. Optimiz. Control Theories Appl. 2(2), 139–151 (2012)

    Article  Google Scholar 

  13. Gupta, R., Chandan, M.: Use of controlled random search technique for global optimization in animal diet problem. Int. J. Emerg. Technol. Adv. Eng. 3(2), 284–284 (2013)

    Google Scholar 

  14. Hsu, K.C., Wang, F.S.: Fuzzy optimization for detecting enzyme targets of human uric acid metabolism. Bioinformatics. 29(24), 3191–3198 (2013)

    Article  Google Scholar 

  15. Mahdavi-Amiri, N., Nasseri, S.H.: Duality in fuzzy number linear programming by use of a certain linear ranking function. Appl. Math. Comput. 180(1), 206–216 (2006)

    MathSciNet  MATH  Google Scholar 

  16. Mahdavi-Amiri, N., Nasseri, S.H.: Duality results and a dual simplex method for linear programming with trapezoidal fuzzy variables. Fuzzy Sets Syst. 158, 1961–1978 (2007)

    Google Scholar 

  17. Mahdavi-Amiri, N., Nasseri, S.H., Yazdani, A.: Fuzzy primal simplex algorithms for solving fuzzy linear programming problems. Iran. J. Oper. Res. 1, 68–84 (2009)

    Google Scholar 

  18. Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variable. Fuzzy Sets Syst. 109, 21–33 (2000)

    Article  MathSciNet  Google Scholar 

  19. Maleki, H.R.: Ranking functions and their applications to fuzzy linear programming. Far East J. Math. Sci. 4, 283–301 (2002)

    Google Scholar 

  20. Mamat, M., Deraman, S.K., Noor, N.M.M., Mohd, I.: Diet problem and nutrient requirement using fuzzy linear programming approaches. Asian J. Appl. Sci. 5(1), 52–59 (2012)

    Article  Google Scholar 

  21. Mamat, M., Rokhayati, Y., Mohamad, N.N., Mohd, I.: Optimizing human diet problem with fuzzy price using fuzzy linear approach. Pak. J. Nutr. 10(6), 594–598 (2011)

    Article  Google Scholar 

  22. Moraes, L.E., Wilen, J.E., Robinson, P.H., Fadel, J.G.: A linear programming model to optimize diets in environmental policy scenario. J. Dairy Sci. 95, 1267–1282 (2012)

    Article  Google Scholar 

  23. Nasseri, S.H., Darvishi, D.: Animal diet formulation with floating price. Iran. J. Optim. 8(2), 101–110 (2016)

    Google Scholar 

  24. Nasseri, S.H., Darvishi, D.: Planning livestock diet with fuzzy requirements. J. Inf. Optim. Sci. 4, 1–19 (2018)

    MathSciNet  Google Scholar 

  25. Nasseri, S.H., Ebrahimnejad, A.: A fuzzy dual simplex method for fuzzy number linear programming problem. Adv. Fuzzy Sets Syst. 5(1), 81–95 (2010)

    Google Scholar 

  26. National Research Council (NRC): Nutrient Requirements of Dairy Cattle. The National Academic Press, Washington, DC (2001)

    Google Scholar 

  27. Niemi, J.K., Sevon-Aimonen, M., Pietola, K., Stalder, K.J.: The value of precision feeding technologies for grow-finish swine. Livest. Sci. 129, 13–23 (2010)

    Article  Google Scholar 

  28. Piyaratne, M.K.D.K., Dias, N.G.J., Attapattu, N.S.B.M.: Linear model based software approach with ideal amino acid profiles for least-cost poultry ration formulation. Inf. Technol. J. 11(7), 788–793 (2012)

    Article  Google Scholar 

  29. Pomar, C., Dubeau, F., Letourneau-Montminy, M.P., Boucher, C., Julien, P.O.: Reducing phosphorus concentration in pig diets by adding an environmental objective to the traditional feed formulation algorithm. Livest. Sci. 111, 16–27 (2007)

    Article  Google Scholar 

  30. Saxena, P., Khanna, N.: Animal feed formulation: mathematical programming techniques. Perspect. Agric. Vet. Sci. Nutr. Nat. Resour. 9(35), 1–12 (2014)

    Google Scholar 

  31. Saxena, P.: Comparison of linear and nonlinear programming techniques for animal diet. Appl. Math. 1(2), 106–108 (2011)

    Article  Google Scholar 

  32. Saxena, P., Kumar, V., kumar, R.: Optimization for animal diet formulation: programming technique. In: 3rd International Conference on Computing for Sustainable Global Development, 16–18 March 2016

    Google Scholar 

  33. Tozer, P.R.: Least cost ration formulations for Holstein dairy heifers by using linear and stochastic programming. Dairy Sci. 83, 443–451 (2000)

    Article  Google Scholar 

  34. Wang, F.S., Wu, W.H., Hsu, K.C.: Fuzzy optimization in metabolic systems. Int. J. Biol. Food Vet. Agric. Eng. 8(7), 661–665 (2014)

    Google Scholar 

  35. Waugh, F.V.: The minimum cost dairy feed. J. Farm Econ. 33, 299–310 (1951)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    Seyed Hadi Nasseri

  2. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

  3. Foshan University, Foshan, Guangdong, China

    Bing-Yuan Cao

Authors
  1. Seyed Hadi Nasseri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Ebrahimnejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing-Yuan Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyed Hadi Nasseri .

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

Nasseri, S.H., Ebrahimnejad, A., Cao, BY. (2019). Fuzzy Number Linear Programming. In: Fuzzy Linear Programming: Solution Techniques and Applications. Studies in Fuzziness and Soft Computing, vol 379. Springer, Cham. https://doi.org/10.1007/978-3-030-17421-7_3

Download citation

Publish with us

Policies and ethics

Search

Navigation