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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generali...
Aggregation Functions
Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers.
Soft Methodology and Random Information Systems
The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.
Modeling Decisions for Artificial Intelligence
This book constitutes the proceedings of the 7th InternationalConference on Modeling Decisions for Artificial Intelligence, MDAI 2010,held in Perpignan, France, in October 2010. The 25 papers presented were carefully reviewed and selected from 43submissions. The volume also contains extended abstracts of the threeinvited papers. The topics covered are aggregation operators anddecision making; clustering and similarity; computational intelligence;and data privacy.
Information Processing and Management of Uncertainty
These three volumes (CCIS 442, 443, 444) constitute the proceedings of the 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2014, held in Montpellier, France, July 15-19, 2014. The 180 revised full papers presented together with five invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on uncertainty and imprecision on the web of data; decision support and uncertainty management in agri-environment; fuzzy implications; clustering; fuzzy measures and integrals; non-classical logics; data analysis; real-world applications; aggregation; probabilistic networ...
Fuzzy Logic and Soft Computing
Soft computing is a new, emerging discipline rooted in a group of technologies that aim to exploit the tolerance for imprecision and uncertainty in achieving solutions to complex problems. The principal components of soft computing are fuzzy logic, neurocomputing, genetic algorithms and probabilistic reasoning. This volume is a collection of up-to-date articles giving a snapshot of the current state of the field. It covers the whole expanse, from theoretical foundations to applications. The contributors are among the world leaders in the field. Contents:Fuzzy Logic and Genetic AlgorithmsLearningFuzzy and Hybrid SystemsDecision and Aggregation TechniquesFuzzy Logic in DatabasesFoundations of Fuzzy LogicApplications of Fuzzy Sets Readership: Researchers and computer scientists. keywords:
Advances in Computational Intelligence, Part IV
These four volumes (CCIS 297, 298, 299, 300) constitute the proceedings of the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, held in Catania, Italy, in July 2012. The 258 revised full papers presented together with six invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy machine learning and on-line modeling; computing with words and decision making; soft computing in computer vision; rough sets and complex data analysis: theory and applications; intelligent databases and information system; information fusion systems; philosophical and...
Aggregation Functions in Theory and in Practice
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).
Modelling, Computation and Optimization in Information Systems and Management Sciences
Constitutes the refereed proceedings of the Second International Conference MCO 2008, Metz, France, September 2008. This title organizes the papers in topical sections on optimization and decision making; data mining theory, systems and applications; computer vision and image processing; and computer communications and networks.
Preferences and Decisions under Incomplete Knowledge
Nowadays, decision problems are pervaded with incomplete knowledge, i.e., imprecision and/or uncertain information, both in the problem description and in the preferential information. In this volume leading scientists in the field address various theoretical and practical aspects related to the handling of this incompleteness. The problems discussed are taken from multi-objective linear programming, rationality considerations in preference modelling, non-probabilistic utility theory, data fusion, group decision making and multicriteria decision aid. The book is oriented towards researchers, graduate and postgraduate students in decision analysis, fuzzy sets and fuzzy logic, and operations research/management science.
