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Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment

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Abstract

Interval neutrosophic sets (INSs) capturing the uncertainties by characterizing into the intervals of the truth, the indeterminacy, and the falsity membership degrees, is a more flexible way to explore the decision-making applications. In this paper, we develop a nonlinear programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve decision-making problems in which criterion values and their importance are given in the form of interval neutrosophic numbers (INNs). Based on the concept of closeness coefficient, we firstly construct a pair of the nonlinear fractional programming model and then transform it into the linear programming model. Furthermore, to determine the ranking of considered alternatives, likelihood-based comparison relations are constructed. Finally, an illustrative example demonstrates the applicability of the proposed method for dealing with decision making problems with incomplete knowledge.

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Acknowledgments

The author would like to thank the Editor-in-Chief and referees for providing very helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, Thapar University Patiala, Patiala, 147004, Punjab, India

    Harish Garg &  Nancy

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  1. Harish Garg
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  2. Nancy
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Correspondence to Harish Garg.

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Garg, H., Nancy Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Appl Intell 48, 2199–2213 (2018). https://doi.org/10.1007/s10489-017-1070-5

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