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A novel method of ranking intuitionistic fuzzy numbers using value and \(\theta \) multiple of ambiguity at flexibility parameters

  • Fuzzy systems and their mathematics
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Abstract

In this paper, a novel method of ordering intuitionistic fuzzy numbers, combining the ‘value’ and the ‘ambiguity’ of an intuitionistic fuzzy number, is developed. The value and the ambiguity are calculated at \((\alpha , \beta )\)-levels, rather than calculating for the whole range of integration. These levels are termed as flexibility parameters, which allows a decision-maker to take a decision at levels of decision-making. In many studies, the reasonable properties of ranking intuitionistic fuzzy numbers were never tested. However, in this study, every effort is made to investigate the reasonable properties thoroughly. Furthermore, ordering of intuitionistic fuzzy numbers by existing methods relies heavily on intuition and the geometry of intuitionistic fuzzy numbers. The proposed method fully complies with the reasonable properties of ranking intuitionistic fuzzy numbers, as well as the coherent intuition and geometry of the intuitionistic fuzzy numbers. In addition, newer properties are being developed in this study. This demonstrates the novelty of the proposed method. A few numerical examples are also discussed demonstrating the proposed method. Lastly, the proposed method has been successfully applied to a risk analysis problem.

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Acknowledgements

I appreciatively acknowledge the time and expertize devoted to reviewing papers by the Associate Editor, the members of the editorial board, and the anonymous referees, which helped in improving the paper.

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  1. Department of Mathematics, Cotton University, Guwahati, Assam, 781001, India

    Rituparna Chutia

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Chutia, R. A novel method of ranking intuitionistic fuzzy numbers using value and \(\theta \) multiple of ambiguity at flexibility parameters. Soft Comput 25, 13297–13314 (2021). https://doi.org/10.1007/s00500-021-06102-8

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