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Duality for a class of fuzzy nonlinear optimization problem under generalized convexity

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Abstract

In this paper, a Mond-Weir type dual program for a nonlinear primal problem under fuzzy environment is formulated. The solution concept of primal-dual problems is inspired by the nondominated solution. We have considered ordering among fuzzy numbers as a partial ordering and using the concept of Hukuhara difference between two fuzzy numbers and \(H\)-differentiability, appropriate duality theorems are established under pseudo/quasi-convexity assumptions. We have also illustrated a numerical example which satisfies the duality relations discussed in the paper.

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Acknowledgments

The authors are thankful to the anonymous referee for his/her valuable suggestions and critical comments, which have substantially improved the presentation of the paper. Also, the second author is thankful to Ministry of Human Resource development, New Delhi (India) for financial support.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    S. K. Gupta

  2. Department of Mathematics, Marwadi Education Foundation Group of Institutions, Rajkot, 360 005, India

    D. Dangar

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  1. S. K. Gupta
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  2. D. Dangar
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Correspondence to D. Dangar.

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Gupta, S.K., Dangar, D. Duality for a class of fuzzy nonlinear optimization problem under generalized convexity. Fuzzy Optim Decis Making 13, 131–150 (2014). https://doi.org/10.1007/s10700-013-9176-7

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