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A Practical Guide to Averaging Functions

2015-10-15 Technology & Engineering
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Release : 2015-10-15
Genre : Technology & Engineering
Kind : eBook
Book Rating : 530/5 ( reviews)

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Book Synopsis A Practical Guide to Averaging Functions by : Gleb Beliakov

Download or read book A Practical Guide to Averaging Functions written by Gleb Beliakov. This book was released on 2015-10-15. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an easy-to-use and practice-oriented reference guide to mathematical averages. It presents different ways of aggregating input values given on a numerical scale, and of choosing and/or constructing aggregating functions for specific applications. Building on a previous monograph by Beliakov et al. published by Springer in 2007, it outlines new aggregation methods developed in the interim, with a special focus on the topic of averaging aggregation functions. It examines recent advances in the field, such as aggregation on lattices, penalty-based aggregation and weakly monotone averaging, and extends many of the already existing methods, such as: ordered weighted averaging (OWA), fuzzy integrals and mixture functions. A substantial mathematical background is not called for, as all the relevant mathematical notions are explained here and reported on together with a wealth of graphical illustrations of distinct families of aggregation functions. The authors mainly focus on practical applications and give central importance to the conciseness of exposition, as well as the relevance and applicability of the reported methods, offering a valuable resource for computer scientists, IT specialists, mathematicians, system architects, knowledge engineers and programmers, as well as for anyone facing the issue of how to combine various inputs into a single output value.

An Introduction to Data Analysis using Aggregation Functions in R

2016-11-07 Computers
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Release : 2016-11-07
Genre : Computers
Kind : eBook
Book Rating : 62X/5 ( reviews)

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Book Synopsis An Introduction to Data Analysis using Aggregation Functions in R by : Simon James

Download or read book An Introduction to Data Analysis using Aggregation Functions in R written by Simon James. This book was released on 2016-11-07. Available in PDF, EPUB and Kindle. Book excerpt: 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 emphasis on 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 in Theory and in Practice

2017-05-17 Technology & Engineering
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Release : 2017-05-17
Genre : Technology & Engineering
Kind : eBook
Book Rating : 064/5 ( reviews)

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Book Synopsis Aggregation Functions in Theory and in Practice by : Vicenç Torra

Download or read book Aggregation Functions in Theory and in Practice written by Vicenç Torra. This book was released on 2017-05-17. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the abstracts of the contributions presented at AGOP 2017, the 9th International Summer School on Aggregation Operators. The conference took place in Skövde (Sweden) in June 2017. Contributions include works from theory and fundamentals of aggregation functions to their use in applications. Aggregation functions are usually defined as those functions that are monotonic and that satisfy the unanimity condition. In particular settings these conditions are relaxed. Aggregation functions are used for data fusion and decision making. Examples of these functions include means, t-norms and t-conorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals).

Uncertainty Data in Interval-Valued Fuzzy Set Theory

2018-06-27 Technology & Engineering
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Release : 2018-06-27
Genre : Technology & Engineering
Kind : eBook
Book Rating : 106/5 ( reviews)

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Book Synopsis Uncertainty Data in Interval-Valued Fuzzy Set Theory by : Barbara Pękala

Download or read book Uncertainty Data in Interval-Valued Fuzzy Set Theory written by Barbara Pękala. This book was released on 2018-06-27. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to fuzzy sets theory and their operations, with a special focus on aggregation and negation functions. Particular attention is given to interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets and their use in uncertainty models involving imperfect or unknown information. The theory and application of interval-values fuzzy sets to various decision making problems represent the central core of this book, which describes in detail aggregation operators and their use with imprecise data represented as intervals. Interval-valued fuzzy relations, compatibility measures of interval and the transitivity property are thoroughly covered. With its good balance between theoretical considerations and applications of originally developed algorithms to real-world problem, the book offers a timely, inspiring guide to mathematicians and engineers developing new decision making models or implementing/applying existing ones to a wide range of applications involving imprecise or incomplete data.

Discrete Fuzzy Measures

2019-03-19 Technology & Engineering
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Release : 2019-03-19
Genre : Technology & Engineering
Kind : eBook
Book Rating : 053/5 ( reviews)

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Book Synopsis Discrete Fuzzy Measures by : Gleb Beliakov

Download or read book Discrete Fuzzy Measures written by Gleb Beliakov. This book was released on 2019-03-19. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as capacities, allow one to combine degrees of preferences, support or fuzzy memberships into one representative value, taking into account interactions between the inputs. The notions of mutual reinforcement or redundancy are modeled explicitly through coefficients of fuzzy measures, and fuzzy integrals, such as the Choquet and Sugeno integrals combine the inputs. Building on previous monographs published by the authors and dealing with different aspects of aggregation, this book especially focuses on the Choquet and Sugeno integrals. It presents a number of new findings concerning computation of fuzzy measures, learning them from data and modeling interactions. The book does not require substantial mathematical background, as all the relevant notions are explained. It is intended as concise, timely and self-contained guide to the use of fuzzy measures in the field of multicriteria decision making.

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