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

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.