Skip to main content
SpringerLink
Log in

Random Fuzzy Multiobjective Linear Programming with Variance Covariance Matrices

  • Conference paper
  • First Online:
Transactions on Engineering Technologies

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 275))

  • 873 Accesses

Abstract

In this paper, we propose an interactive decision making method for random fuzzy multiobjective linear programming problems with variance covariance matrices (RFMOLP-VC). In the proposed method, it is assumed that the decision maker has fuzzy goals for not only permissible objective levels of a probability maximization model for RFMOLP-VC but also the corresponding distribution function values. Using the fuzzy decision, such two kinds of membership functions are integrated. In the integrated membership space, a satisfactory solution is obtained from among a Pareto optimal solution set through the interaction with the decision maker.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
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. Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer

    Google Scholar 

  2. Charnes A, Cooper WW (1959) Chance constrained programming. Manage Sci 6:73–79

    Article  MathSciNet  MATH  Google Scholar 

  3. Danzig GB (1955) Linear programming under uncertainty. Manage Sci 1:197–206

    Article  Google Scholar 

  4. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press

    Google Scholar 

  5. Glen JJ (1987) Mathematical models in farm planning : a survey. Oper Res 35:641–666

    Article  Google Scholar 

  6. Hasuike T, Katagiri K, Ishii H (2009) Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets Syst 160:2579–2596

    Article  MathSciNet  MATH  Google Scholar 

  7. Hayashi K (2000) Multicriteria analysis for agricultural resource management : a critical survey and future perspectives. Eur J Oper Res 122:486–500

    Article  MATH  Google Scholar 

  8. Huang X (2007) Optimal Project Selection with Random Fuzzy Parameters. Int J Prod Econ 106:513–522

    Article  Google Scholar 

  9. Itoh T, Ishii H, Nanseki T (2003) A model of crop planning under uncertainty in agricultural management. Int J Prod Econ 81–82:555–558

    Article  Google Scholar 

  10. Kall P, Mayer J (2005) Stochastic linear programming models, theory, and computation. Springer, Berlin

    MATH  Google Scholar 

  11. Katagiri H, Hasuike T, Ishii H (2008) A random fuzzy programming models based on possibilistic programming. In: Proceedings of 2008 IEEE international conference on systems, man and, cybernetics (SMC2008), pp 1788–1793

    Google Scholar 

  12. Katagiri H, Sakawa M, Matsui T (2011) Interactive multiobjective random fuzzy programming problems through the possibility-based fractile model. In: Proceedings of 2011 IEEE international conference on systems, man and, cybernetics (SMC2011), pp 3144–3148

    Google Scholar 

  13. Katagiri H, Sakawa M, Matsui T (2011) An interactive satisficing method for multiobjective random fuzzy programming problems through the possibility-based probability model. In: Proceedings of 2011 IEEE international conference on fuzzy systems, pp 1778–1782

    Google Scholar 

  14. Katagiri H, Uno T, Kato K, Tsuda H, Tsubaki H (2012) Interactive multiobjective random fuzzy programming: necessity-based value at risk model. In: Proceedings of 2012 IEEE international conference on systems, man and, cybernetics (SMC2012), pp 727–732

    Google Scholar 

  15. Katagiri H, Uno T, Kato K, Tsuda H, Tsubaki H (2013) Random fuzzy multi-objective linear programming: optimization of possibilistic value at risk (PVaR). Expert Syst Appl 40:563–574

    Article  Google Scholar 

  16. Lai YJ, Hwang CL (1992) Fuzzy mathematical programming. Springer, Berlin

    Book  MATH  Google Scholar 

  17. Liu B (2002) Random fuzzy dependent-chance programming and its hybrid intelligent algorithm. Inf Sci 141:259–271

    Article  MATH  Google Scholar 

  18. Liu B (2004) Uncertainty theory. Springer, Berlin

    Book  MATH  Google Scholar 

  19. Sakalli US, Baykoc OF (2010) An application of investment decision with random fuzzy outcomes. Expert Syst Appl 37:3405–3414

    Article  Google Scholar 

  20. Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press, New York

    Book  MATH  Google Scholar 

  21. Toyonaga T, Itoh T, Ishii H (2005) A crop planning with fuzzy random profit coefficients. Fuzzy Optim Decis Making 4:51–69

    Article  MathSciNet  MATH  Google Scholar 

  22. Xu J, Yao L, Zhao X (2011) A multi-objective chance-constrained network optimal model with random fuzzy coefficients and its application to logistics distribution center location problem. Fuzzy Optim Decis Making 10:255–285

    Article  MathSciNet  MATH  Google Scholar 

  23. Yano H (2012) Interactive decision making for fuzzy random multiobjective linear programming problems with variance-covariance matrices through probability maximization. In: Proceedings of the 6th international conference on soft computing and intelligent systems and 13th international symposium on advanced intelligent systems, SCIS-ISIS 2012, 20–24 Nov 2012, Kobe, pp 965–970

    Google Scholar 

  24. Yano H, Matsui M (2013) Random fuzzy multiobjective linear programming through probability maximization. In: Proceedings of the international multi conference of engineers and computer scientists 2013, IMECS 2013, lecture notes in engineering and computer Science, 13–15 Mar 2013, Hong Kong, pp 1135–1140

    Google Scholar 

  25. Yano H, Matsui M (2013) Random fuzzy multiobjective linear programming through probability maximization and its application to farm planning. IAENG Int J Appl Math 43(2):87–93

    MathSciNet  Google Scholar 

  26. Yano H, Sakawa M (2012) Interactive multiobjective fuzzy random linear programming through fractile criteria. Advances in fuzzy systems, vol 2012. Hindawi Publishing Corp., Article ID:521080

    Google Scholar 

  27. Yano H, Sakawa M (2013) Interactive fuzzy programming for multiobjective fuzzy random linear programming problems through possibility-based probability maximization. Int J Oper Res. doi:10.1007/s12351-013-0135-4

  28. Zimmermann H-J (1987) Fuzzy sets, decision-making and expert systems. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Humanities and Social Sciences, Nagoya City University, Nagoya, 467-8501, Japan

    Hitoshi Yano

  2. Graduate School of Information Science, Nagoya University, Nagoya, 4464-8601, Japan

    Kota Matsui

Authors
  1. Hitoshi Yano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kota Matsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hitoshi Yano .

Editor information

Editors and Affiliations

  1. Department of Multimedia Engineering College of Engineering, Mokpo National University, Chonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Faculty of Information Sciences and Engineering, University of Canberra, Canberra, Aust Capital Terr, Australia

    Xu Huang

  4. Computer Sci. in the Graduate Division, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Yano, H., Matsui, K. (2014). Random Fuzzy Multiobjective Linear Programming with Variance Covariance Matrices. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7684-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-7684-5_27

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7683-8

  • Online ISBN: 978-94-007-7684-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation