Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making

Abstract

As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal 
numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets 
on subset of real numbers. Harmonic mean is a conservative average, which is widely used to 
aggregate central tendency data. In the existing literature, the harmonic mean is generally considered 
as a fusion technique of numerical data information. In this paper, we investigate a method for the 
situations in which the input data are expressed in neutrosophic values. Therefore, we propose two 
aggregations are called harmonic aggregation operators and weighted harmonic mean operators on 
N-valued neutrosophic trapezoidal numbers. We also proved some desired properties such as 
idempotency, monotoniticy, commutativity and boundedness of the developed operators. Moreover, 
we developed an algorithm by defining a score function under N-valued neutrosophic trapezoidal 
numbers to compare the N-valued neutrosophic trapezoidal numbers.  Finally, we gave an 
illustrative example, using the proposed aggregation operators to rank the alternatives with N
valued neutrosophic trapezoidal numbers. 

DOI: 10.5281/zenodo.14538076