IDEAS home Printed from https://ideas.repec.org/a/hin/complx/8179763.html
   My bibliography  Save this article

Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter

Author

Listed:
  • Xiaobin Yang
  • Haitao Lin
  • Gang Xiao
  • Huanbin Xue
  • Xiaopeng Yang

Abstract

Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum ( ) and infimum ( ) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max- fuzzy relation equations system.

Suggested Citation

  • Xiaobin Yang & Haitao Lin & Gang Xiao & Huanbin Xue & Xiaopeng Yang, 2019. "Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    • Handle: RePEc:hin:complx:8179763
    DOI: 10.1155/2019/8179763
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/8179763.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/8179763.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/8179763?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ishibuchi, Hisao & Tanaka, Hideo, 1990. "Multiobjective programming in optimization of the interval objective function," European Journal of Operational Research, Elsevier, vol. 48(2), pages 219-225, September.
    2. Jiang, C. & Han, X. & Liu, G.R. & Liu, G.P., 2008. "A nonlinear interval number programming method for uncertain optimization problems," European Journal of Operational Research, Elsevier, vol. 188(1), pages 1-13, July.
    3. K. Ganesan & P. Veeramani, 2006. "Fuzzy linear programs with trapezoidal fuzzy numbers," Annals of Operations Research, Springer, vol. 143(1), pages 305-315, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abhijit Baidya & Uttam Kumar Bera & Manoranjan Maiti, 2016. "The grey linear programming approach and its application to multi-objective multi-stage solid transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 500-522, September.
    2. Debdas Ghosh, 2016. "A Newton method for capturing efficient solutions of interval optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 648-665, September.
    3. Liu, Yong-Jun & Zhang, Wei-Guo & Zhang, Pu, 2013. "A multi-period portfolio selection optimization model by using interval analysis," Economic Modelling, Elsevier, vol. 33(C), pages 113-119.
    4. Jianjian Wang & Feng He & Xin Shi, 2019. "Numerical solution of a general interval quadratic programming model for portfolio selection," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-16, March.
    5. Chakrabortty, Susovan & Pal, Madhumangal & Nayak, Prasun Kumar, 2013. "Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages," European Journal of Operational Research, Elsevier, vol. 228(2), pages 381-387.
    6. Yong-Jun Liu & Wei-Guo Zhang & Jun-Bo Wang, 2016. "Multi-period cardinality constrained portfolio selection models with interval coefficients," Annals of Operations Research, Springer, vol. 244(2), pages 545-569, September.
    7. Qi Wang & Peipei Qi & Shipei Li, 2021. "A Concurrence Optimization Model for Low-Carbon Product Family Design and the Procurement Plan of Components under Uncertainty," Sustainability, MDPI, vol. 13(19), pages 1-22, September.
    8. T. Antczak, 2018. "Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 205-224, January.
    9. Mrinal Jana & Geetanjali Panda, 2018. "$$\chi$$ χ -Optimal solution of single objective nonlinear optimization problem with uncertain parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 165-186, March.
    10. P. Kumar & G. Panda, 2017. "Solving nonlinear interval optimization problem using stochastic programming technique," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 752-765, December.
    11. Tong Xin & Guolai Yang & Liqun Wang & Quanzhao Sun, 2020. "Numerical Calculation and Uncertain Optimization of Energy Conversion in Interior Ballistics Stage," Energies, MDPI, vol. 13(21), pages 1-21, November.
    12. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
    13. Lifeng Li, 2023. "Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 247-265, June.
    14. Wang, Ying-Ming & Elhag, Taha M.S., 2007. "A goal programming method for obtaining interval weights from an interval comparison matrix," European Journal of Operational Research, Elsevier, vol. 177(1), pages 458-471, February.
    15. Majumdar, J. & Bhunia, A.K., 2007. "Elitist genetic algorithm for assignment problem with imprecise goal," European Journal of Operational Research, Elsevier, vol. 177(2), pages 684-692, March.
    16. Mashadi & Yuliana Safitri & Sukono & Igif Gimin Prihanto & Muhamad Deni Johansyah & Moch Panji Agung Saputra, 2024. "The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    17. Mahdi Zarghami & Nasim Safari & Ferenc Szidarovszky & Shafiqul Islam, 2015. "Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4285-4303, September.
    18. Wei Wang & Yaofeng Xu & Liguo Hou, 2019. "Optimal allocation of test times for reliability growth testing with interval-valued model parameters," Journal of Risk and Reliability, , vol. 233(5), pages 791-802, October.
    19. Manuel Arana-Jiménez & Carmen Sánchez-Gil, 2020. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers," Journal of Global Optimization, Springer, vol. 77(1), pages 27-52, May.
    20. Rong, M. & Mahapatra, N.K. & Maiti, M., 2008. "A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time," European Journal of Operational Research, Elsevier, vol. 189(1), pages 59-75, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:8179763. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.