An Introduction to Data Analysis using Aggregation Functions in R

1. Front Matter

   Pages i-x

   PDF

2. Aggregating Data with Averaging Functions

   • Simon James

   Pages 1-35

3. Transforming Data

   • Simon James

   Pages 37-73

4. Weighted Averaging

   • Simon James

   Pages 75-95

5. Averaging with Interaction

   • Simon James

   Pages 97-127

6. Fitting Aggregation Functions to Empirical Data

   • Simon James

   Pages 129-162

7. Solutions

   • Simon James

   Pages 163-196

8. Back Matter

   Pages 197-199

   PDF

This textbook helps future data analysts comprehend aggregation function theory and methods in an accessible way, focusing on a fundamental understanding of the data and summarization tools. Offering a broad overview of recent trends in aggregation research, it complements any study in statistical or machine learning techniques. Readers will learn how to program key functions in R without obtaining an extensive programming background.


Sections of the textbook cover background information and context, aggregating data with averaging functions, power means, and weighted averages including the Borda count. It explains how to transform data using normalization or scaling and standardization, as well as log, polynomial, and rank transforms. The section on averaging with interaction introduces OWS functions and the Choquet integral, simple functions that allow the handling of non-independent inputs. The final chapters examine software analysis with an emphasison parameter identification rather than technical aspects.


This textbook is designed for students studying computer science or business who are interested in tools for summarizing and interpreting data, without requiring a strong mathematical background. It is also suitable for those working on sophisticated data science techniques who seek a better conception of fundamental data aggregation. Solutions to the practice questions are included in the textbook.

• Aggregation functions
• Programming in R
• Data analysis
• Weighted arithmetic mean
• Weighted geometric mean
• Weighted power means
• OWA function
• Choquet integral
• Weight learning
• Linear programming

“The monograph is devoted to the problem of data aggregation in its various aspects from general concepts of adequate representation of numerous data in a concise form to practical calculations illustrated by applying abilities of R language. … the students and researchers familiar with R can find the book to be a very friendly introduction to statistical approaches to the aggregation with interactions between variables.” (Stan Lipovetsky, Technometrics, Vol. 59 (3), November, 2017)

• School of Information Technology, Deakin University, Burwood, Australia

  Simon James

Simon James completed his PhD on The use of aggregation functions in decision making under the supervision of Dr. Gleb Beliakov at Deakin University in 2010. Since then he has held a Lecturing position in the School of Information Technology. Before undertaking his PhD, he had completed a double degree in education and arts, providing a solid grounding in reflective teaching practice. He currently teaches mathematics to students across a range of undergraduate and post-graduate courses, including education, science, IT and data analytics. His research interests to date have included aggregation functions, fuzzy sets, group decision making and consensus, and the application of indices in ecology. He has authored over 40 journal and conference papers and has been an associate editor for IEEE Transactions on Fuzzy Systems since 2015.

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