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The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers

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  • Nanxiang Yu
  • Dong Qiu

Abstract

We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT) optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:1242841
    DOI: 10.1155/2017/1242841
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    References listed on IDEAS

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    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. 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. Geetanjali Panda & Motilal Panigrahi & Sudarsan Nanda, 2006. "Equivalence class in the set of fuzzy numbers and its application in decision-making problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-19, August.
    4. 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.
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