A novel defuzzification method of SV-trapezoidal neutrosophic numbers and multi-attribute decision making: a comparative analysis

  • İrfan DeliEmail author
Methodologies and Application


The aim of this paper is to investigate the multiple attribute decision-making (MADM) problems where both the attribute value and attribute weight of alternatives are single-valued trapezoidal neutrosophic numbers (SVTN-numbers). Ranking of SVTN-numbers are always a necessary step in solving the MADM problems under SVTN environment, and the literature review reckoned the existence of six to seven ranking methods. After all the existing ranking methods of SVTN-numbers are examined, we firstly define the concept of centroid point and examine several useful properties of the developed concept. Then, we develop hamming ranking value and Euclidean ranking value of SVTN-numbers to compare the SVTN-numbers. Furthermore, based on the proposed ranking values, we develop a novel defuzzification method to MADM with linguistic information and give a real example deal with manufacturing company to illustrate the feasibility and effectiveness of the developed approach. Finally, we present some examples to compare the proposed method with the existing ranking results and the results verified through comparative analysis.


Neutrosophic sets Trapezoidal neutrosophic numbers Defuzzification Centroid point Hamming ranking value Euclidean ranking value Decision making 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

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


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Kilis 7 Aralık UniversityKilisTurkey

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