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Harmonic Mean

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...

Weighted Mean

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Trimmed Mean

Trimmed Mean

While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...

Normal and Tangetial Components: Problem Solving

Normal and Tangetial Components: Problem Solving

Consider a man with a mass of 70 kg seated in a chair connected to a pin support through a member BC. If the man maintains an upright position, the task is to determine the horizontal and vertical reactions of the chair on the man when the member makes a 45° angle with the horizontal. At this moment, the man has a speed of 5 m/s, increasing at a rate of 1 m/s².

Arithmetic Mean

Arithmetic Mean

The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
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Harmonic Nanoparticles for Regenerative Research

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Generalized ordered weighted harmonic averaging operator with trapezoidal neutrosophic numbers for solving MADM

S Paulraj¹, G Tamilarasi¹

¹Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu 600025 India.

Journal of Ambient Intelligence and Humanized Computing

|October 18, 2021

Summary

This study introduces new aggregation operators for neutrosophic environments, enhancing flexibility in multi-attribute decision-making (MADM) problems. The developed Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging (SVTNGOWHA) operator improves upon existing methods.

Keywords:

Harmonic averaging operator Multi-attribute decision making Single valued trapezoidal neutrosophic numbers

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Area of Science:

Mathematics
Decision Sciences

Background:

Harmonic mean offers flexibility in algebraic calculations and aggregating negative indicators.
Neutrosophic environments require robust aggregation operators for complex decision-making.

Purpose of the Study:

To develop novel aggregation operators within a neutrosophic framework.
To extend existing operators, specifically introducing the Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging (SVTNGOWHA) operator.
To apply these operators to multi-attribute decision-making (MADM) problems.

Main Methods:

Development of new aggregation operators under a neutrosophic environment.
Extension of the single valued trapezoidal neutrosophic ordered weighted harmonic averaging (SVTNOWHA) operator to the generalized SVTNGOWHA operator.
Application and testing of the proposed operators using illustrative examples in MADM.

Main Results:

Successful development of the SVTNGOWHA operator, an extension of the SVTNOWHA operator.
Demonstration of the operators' applicability and effectiveness in solving MADM problems.
Validation of the proposed methods through numerical examples.

Conclusions:

The new aggregation operators, particularly the SVTNGOWHA operator, offer enhanced flexibility and utility in neutrosophic MADM.
The developed methods provide a valuable tool for decision-making in complex, uncertain environments.
Further research can explore additional applications and variations of these neutrosophic aggregation operators.