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Quadratic Interpolation Technique to Minimize Univariable Fuzzy Functions

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Abstract

In this paper, a quadratic interpolation technique is proposed to minimize a univariable fuzzy-number-valued function. The fuzzy max-ordering relation of fuzzy numbers is used for optimal solution concept. The Hausdorff distance and Hukuhara difference between two fuzzy numbers, and the Hukuhara differentiability of fuzzy functions, are employed in order to derive the quadratic interpolation method. Convergence rates of the proposed two points and three points quadratic interpolation techniques are also analyzed. A numerical example is included to illustrate the proposed techniques.

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Acknowledgments

We are really grateful to the anonymous reviewers and the editors for their constructive comments and valuable suggestions. The first author gratefully acknowledges financial support from the Outstanding Potential for Excellence in Research and Academics Award and from the Research Initiation Grant (BITS/GAU/RIG/53), BITS Pilani, Hyderabad Campus, India. The second author acknowledges the financial support given by the Department of Science and Technology, Government of India (SR/S4/M: 497/07).

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Authors and Affiliations

  1. Birla Institute of Science and Technology, Pilani, Hyderabad Campus, Secunderabad, 500078, Telengana, India

    Debdas Ghosh

  2. Indian Institute of Technology Kharagpur, Kharagpur, 721302, West Bengal, India

    Debjani Chakraborty

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  1. Debdas Ghosh
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  2. Debjani Chakraborty
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Correspondence to Debdas Ghosh.

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Ghosh, D., Chakraborty, D. Quadratic Interpolation Technique to Minimize Univariable Fuzzy Functions. Int. J. Appl. Comput. Math 3, 527–547 (2017). https://doi.org/10.1007/s40819-015-0123-x

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  • DOI: https://doi.org/10.1007/s40819-015-0123-x

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