Data Mining Practical Machine Learning Tools and Techniques

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Introduction to linear and nonlinear programming

Theory of fuzzy integrals and its applications

Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.

Aggregation Functions: A Guide for Practitioners

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology.Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.

Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice

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.

A Practical Guide to Averaging Functions

On averaging operators for Atanassov's intuitionistic fuzzy sets

http://dro.deakin.edu.au/eserv/DU:30031468/beliakov-generalized-post-2010.pdf

Gleb Beliakov

Papers

Aggregation Functions: A Guide for Practitioners

Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice

A Practical Guide to Averaging Functions

On averaging operators for Atanassov's intuitionistic fuzzy sets

Generalized Bonferroni mean operators in multi-criteria aggregation