IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp861-877.html
   My bibliography  Save this article

The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems

Author

Listed:
  • Agarwal, Deepika
  • Singh, Pitam
  • El Sayed, M.A.

Abstract

The Karush–Kuhn–Tucker (KKT) optimality conditions have a crucial role in finding the efficient solution of any optimization problem. Many researchers have been focussing on the establishment of KKT optimality conditions for deterministic fractional optimization problems (FOP). Also, solution algorithms for fuzzy-valued fractional optimization problem have been proposed by the researchers. However as far as authors are aware, there is no study available for the establishment of optimality conditions for the fuzzy-valued fractional optimization problem (FVFOP). In this paper, KKT optimality conditions are derived for FVFOP. Differentiation of fuzzy-valued functions is obtained using Hausdorff metric which find the distance of two fuzzy numbers and Hukuhara difference which is used to determine the difference between two fuzzy-valued functions. Considered FVFOP is transformed into non-fractional objective using the modified objective approach. The solution concept is developed using Lagrange multipliers, α-cuts and Dinkelbach algorithm. The proposed optimality conditions are verified by the numerical problems and the results are shown graphically for different values of α.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:861-877
    DOI: 10.1016/j.matcom.2022.10.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004396
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.10.024?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. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. R. Jagannathan, 1966. "On Some Properties of Programming Problems in Parametric form Pertaining to Fractional Programming," Management Science, INFORMS, vol. 12(7), pages 609-615, March.
    3. R. Osuna-Gómez & A. Rufián-Lizana & P. Ruíz-Canales, 2000. "Multiobjective fractional programming with generalized convexity," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 97-110, June.
    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.
    6. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
    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. Lin, Xueshan & Huang, Tao & Bompard, Ettore & Wang, Beibei & Zheng, Yaxian, 2023. "Ex-ante market power evaluation and mitigation in day-ahead electricity market considering market maturity levels," Energy, Elsevier, vol. 278(C).

    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. 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.
    2. 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.
    3. 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.
    4. 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).
    5. Meijia Yang & Yong Xia & Jiulin Wang & Jiming Peng, 2018. "Efficiently solving total least squares with Tikhonov identical regularization," Computational Optimization and Applications, Springer, vol. 70(2), pages 571-592, June.
    6. 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.
    7. 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.
    8. Savin Treanţă & Tareq Saeed, 2023. "On Weak Variational Control Inequalities via Interval Analysis," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    9. Neha Gupta, 2019. "Optimization of fuzzy bi-objective fractional assignment problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 1091-1102, September.
    10. 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.
    11. Meena K. Bector & I. Husain & S. Chandra & C. R. Bector, 1988. "A duality model for a generalized minmax program," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 493-501, October.
    12. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    13. 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.
    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. 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.
    16. Suvasis Nayak & Akshay Kumar Ojha, 2019. "Solution approach to multi-objective linear fractional programming problem using parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 174-190, March.
    17. 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.
    18. Garrido, Rodrigo A. & Bronfman, Andrés C., 2017. "Equity and social acceptability in multiple hazardous materials routing through urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 102(C), pages 244-260.
    19. 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.
    20. 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.

    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:eee:matcom:v:205:y:2023:i:c:p:861-877. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.