IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v17y2018i2d10.1007_s10700-017-9269-9.html
   My bibliography  Save this article

Different optimum notions for fuzzy functions and optimality conditions associated

Author

Listed:
  • R. Osuna-Gómez

    (Universidad de Sevilla)

  • B. Hernández-Jiménez

    (Universidad Pablo de Olavide)

  • Y. Chalco-Cano

    (Universidad de Tarapacá)

  • G. Ruiz-Garzón

    (Universidad de Cádiz)

Abstract

Fuzzy numbers have been applied on decision and optimization problems in uncertain or imprecise environments. In these problems, the necessity to define optimal notions for decision-maker’s preferences as well as to prove necessary and sufficient optimality conditions for these optima are essential steps in the resolution process of the problem. The theoretical developments are illustrated and motivated with several numerical examples.

Suggested Citation

  • R. Osuna-Gómez & B. Hernández-Jiménez & Y. Chalco-Cano & G. Ruiz-Garzón, 2018. "Different optimum notions for fuzzy functions and optimality conditions associated," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 177-193, June.
  • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9269-9
    DOI: 10.1007/s10700-017-9269-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-017-9269-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10700-017-9269-9?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Panigrahi, Motilal & Panda, Geetanjali & Nanda, Sudarsan, 2008. "Convex fuzzy mapping with differentiability and its application in fuzzy optimization," European Journal of Operational Research, Elsevier, vol. 185(1), pages 47-62, February.
    3. Luciano Stefanini & Barnabas Bede, 2008. "Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations," Working Papers 0803, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
    4. Wu, Hsien-Chung, 2007. "The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function," European Journal of Operational Research, Elsevier, vol. 176(1), pages 46-59, January.
    5. Hsien-Chung Wu, 2007. "The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 203-224, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Beatriz Hernández-Jiménez & Gabriel Ruiz-Garzón & Antonio Beato-Moreno & Rafaela Osuna-Gómez, 2021. "A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets," Mathematics, MDPI, vol. 9(9), pages 1-14, April.

    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. Md Sadikur Rahman & Ali Akbar Shaikh & Irfan Ali & Asoke Kumar Bhunia & Armin Fügenschuh, 2021. "A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations," Mathematics, MDPI, vol. 9(8), pages 1-22, April.
    2. Fabiola Roxana Villanueva & Valeriano Antunes Oliveira, 2022. "Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 896-923, September.
    3. Rekha R. Jaichander & Izhar Ahmad & Krishna Kummari & Suliman Al-Homidan, 2022. "Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    4. Yating Guo & Guoju Ye & Wei Liu & Dafang Zhao & Savin Treanţǎ, 2021. "Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    5. Luhandjula, M.K. & Rangoaga, M.J., 2014. "An approach for solving a fuzzy multiobjective programming problem," European Journal of Operational Research, Elsevier, vol. 232(2), pages 249-255.
    6. Tadeusz Antczak, 2023. "Optimality conditions for invex nonsmooth optimization problems with fuzzy objective functions," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 1-21, March.
    7. 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.
    8. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. 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.
    10. A. Rufián-Lizana & Y. Chalco-Cano & G. Ruiz-Garzón & H. Román-Flores, 2014. "On some characterizations of preinvex fuzzy mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 771-783, July.
    11. Shi, Fangfang & Ye, Guoju & Liu, Wei & Zhao, Dafang, 2023. "A class of nonconvex fuzzy optimization problems under granular differentiability concept," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 430-444.
    12. Zhang, Chuang-liang & Huang, Nan-jing & O’Regan, Donal, 2023. "On variational methods for interval-valued functions with some applications," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    13. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    14. Shaojie Zhang & Mahdi Hasanipanah & Biao He & Ahmad Safuan A. Rashid & Dmitrii Vladimirovich Ulrikh & Qiancheng Fang, 2022. "An Optimized Clustering Approach to Investigate the Main Features in Predicting the Punching Shear Capacity of Steel Fiber-Reinforced Concrete," Sustainability, MDPI, vol. 14(19), pages 1-21, October.
    15. Agarwal, Deepika & Singh, Pitam & El Sayed, M.A., 2023. "The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 861-877.
    16. Nanxiang Yu & Dong Qiu, 2017. "The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers," Complexity, Hindawi, vol. 2017, pages 1-8, August.
    17. U. M. Pirzada & V. D. Pathak, 2013. "Newton Method for Solving the Multi-Variable Fuzzy Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 867-881, March.
    18. Kin Keung Lai & Shashi Kant Mishra & Sanjeev Kumar Singh & Mohd Hassan, 2022. "Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    19. Jiang, C. & Zhang, Z.G. & Zhang, Q.F. & Han, X. & Xie, H.C. & Liu, J., 2014. "A new nonlinear interval programming method for uncertain problems with dependent interval variables," European Journal of Operational Research, Elsevier, vol. 238(1), pages 245-253.
    20. Savin Treanţă & Tareq Saeed, 2023. "On Weak Variational Control Inequalities via Interval Analysis," Mathematics, MDPI, vol. 11(9), pages 1-11, May.

    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:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9269-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.