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Trapezoidal neutrosophic set and its application to multiple attribute decision-making

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Abstract

Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers. Then, a trapezoidal neutrosophic number weighted arithmetic averaging (TNNWAA) operator and a trapezoidal neutrosophic number weighted geometric averaging (TNNWGA) operator are proposed to aggregate the trapezoidal neutrosophic information, and their properties are investigated. Furthermore, a multiple attribute decision-making method based on the TNNWAA and TNNWGA operators and the score and accuracy functions of a trapezoidal neutrosophic number is established to deal with the multiple attribute decision-making problems in which the evaluation values of alternatives on the attributes are represented by the form of trapezoidal neutrosophic numbers. Finally, an illustrative example about software selection is given to demonstrate the application and effectiveness of the developed method.

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Acknowledgments

This paper was supported by the National Natural Science Foundation of China (No. 71471172).

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Authors and Affiliations

  1. Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000, Zhejiang Province, People’s Republic of China

    Jun Ye

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  1. Jun Ye
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Correspondence to Jun Ye.

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Ye, J. Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural Comput & Applic 26, 1157–1166 (2015). https://doi.org/10.1007/s00521-014-1787-6

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  • DOI: https://doi.org/10.1007/s00521-014-1787-6

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