An Integrated CODAS Method and Novel Surface-based  Weighted Distance Measures under Neutrosophic Environment

Madineh Farnam; Gholam Hassan Shirdel; Majid Darehmiraki

Authors

Madineh Farnam Department of Mathematic, Faculty of Basic Sciences, University of Qom, Qom, Iran;
Gholam Hassan Shirdel Department of Mathematic, Faculty of Basic Sciences, University of Qom, Qom, Iran;
Majid Darehmiraki Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khouzestan, Iran;

Keywords:

Neutrosophic Set; Neutrosophic Trapezoidal Fuzzy Number; Distance Measure; Multi Criteria Decision Making

Abstract

Information theory provides suitable tools for solving practical problems, particularly
multi-criteria decision-making (MCDM) problems under neutrosophic environments. Generally, a
wide range of MCDM solution methods are constructed based on distance measures category. The
defined distance measures for continuous neutrosophic numbers, especially its trapezoidal type, is
very limited rather than discrete type. The main goals of this study is to come up with a way to add
two new types of weighted distance measures based on meaningful surfaces: Euclidean and
Hamming. To define these measures, all three components of the neutrosophic trapezoidal fuzzy
number (truth, indeterminacy, and falsity membership functions) have been used simultaneously.
The proof of some theorems and properties for the weighted distance measures demonstrates their
validity. The CODAS algorithm is known as one of the distance-based methods for solving MCDM
problems. The following represents the CODAS algorithm based on two novel distance measures. In
addition, an explanatory example from the research literature is given to check the performance of
the proposed hybrid algorithm. The results of this study indicate that the algorithm based on the
proposed measures obtains a reasonable and appropriate ranking order between the options.
Furthermore, the sensitivity parameter analysis and comparative analysis show the flexibility and
accuracy of the suggested measures in the combined algorithm. The acceptable efficiency of proposed
distance measures formed on the surfaces can shed light on research related to distance measures in
the methodology and implicated aspects.