Min(Max) – Min(Max) – Max(Min) (∗): Compositions of Neutrosophic Fuzzy Matrices and its Application in Medical Diagnosis

Abstract

 In this article, we introduce two types of compositions in Neutrosophic Fuzzy Matrices 
(NFM): max(min) - max(min) - min(max) (◦) and min(max) – min(max) – max(min) ( ∗) compositions. 
Using these compositions, we derive several significant results. Additionally, we demonstrate how 
to construct idempotent NFM from any given NFM through the min(max) – min(max) – max(min) ( 
∗)  
composition. To demonstrate the application of these theoretical findings, a numerical example 
is provided. Furthermore, we present an algorithm designed to solve decision-making (DM) 
problems using the min(max) – min(max) – max(min) ( ∗) composition. A practical example is 
included to highlight the success of the proposed method. Additionally, a practical problem from 
our local environment was identified and successfully resolved. A thorough comparative analysis of 
the solutions for existing problems was conducted to evaluate their effectiveness in detail. We have 
adopted the same example as presented in the composition method used in Mamoni Dhar [50] is 
max(min)-min(max)-min(max) (∗). In our analysis, we replaced the score function used in that paper with various alternative score functions in Sahin [44], Nancy, Garg [45]. Upon comparing the results, 
we observed variations when different score functions were applied. Furthermore, when the 
min(max) – min(max) – max(min) ( ∗) composition method (proposed method) was applied, the 
results remained consistent. Finally, our proposed composition method, min(max) – min(max) – 
max(min) (∗)  is better than Mamoni Dhar [50] composition method, max(min)-min(max)-min(max) 
(∗). 

DOI: 10.5281/zenodo.15467983