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Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions

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Abstract

Zadeh introduced fuzzy set theory in the year 1965 to overcome the enigma and obscurity in the real world problems. The underlying power of fuzzy sets is that linguistic / qualitative variables can be used along with quantitative variables to represent continuous imprecise concepts. The continuous anagram concepts need to be modeled by continuous fuzzy numbers instead of intervals and real numbers. So, many researchers developed various fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers, hexagonal fuzzy numbers, octagonal fuzzy numbers and decagonal fuzzy numbers based on shapes in literature. While offering these fuzzy numbers, there are some inadvertences in the existing definition of hexagonal, octagonal and decagonal fuzzy numbers. In this study, some flaws in the concept of hexagonal fuzzy numbers in literature are rectified and a new definition of hexagonal fuzzy numbers in the general form is proposed. Moreover, a complete ranking of hexagonal fuzzy numbers using score functions has also been proposed and is validated through fuzzy Multi Attribute Decision Making (MADM) problem and fuzzy linear system. Further, an algorithm for solving fully fuzzy generalized hexagonal fuzzy linear system of equations as an application of proposed ranking principle is given and is numerically illustrated.

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Acknowledgements

The authors thank the anonymous referees and editors for their valuable suggestions and queries which improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, India

    V. Lakshmana Gomathi Nayagam, Jagadeeswari Murugan & K. Suriyapriya

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  1. V. Lakshmana Gomathi Nayagam
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  2. Jagadeeswari Murugan
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  3. K. Suriyapriya
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Correspondence to Jagadeeswari Murugan.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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The authors ensure that they have written entirely original works based on their own research, and if the authors have used the work and/or words of others, that this has been appropriately cited or quoted with the the best of their knowledge. This study was funded by Rajiv Gandhi National Fellowship-UGC, India (Grant no. RGNF-2014-15-SC-TAM-74350).

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Communicated by Marcos Eduardo Valle.

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Nayagam, V.L.G., Murugan, J. & Suriyapriya, K. Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions. Comp. Appl. Math. 39, 323 (2020). https://doi.org/10.1007/s40314-020-01292-7

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  • DOI: https://doi.org/10.1007/s40314-020-01292-7

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