Michel Grabisch – författare
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5 produkter
5 produkter
Del 127 - Encyclopedia of Mathematics and its Applications
Aggregation Functions
Inbunden, Engelska, 2009
1 932 kr
Skickas inom 7-10 vardagar
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.
1 646 kr
Skickas inom 10-15 vardagar
This decade has witnessed increasing interest in fuzzy technology both from academia and industry. It is often said that fuzzy theory is easy and simple so that engineers can progress quickly to real applications. However, the lack of knowledge of design methodologies and the theoretical results of fuzzy theory have often caused problems for design engineers. The aim of this book is to provide a rigorous background for uncertainty calculi, with an emphasis on fuzziness. "Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference" is primarily about the type of knowledge expressed in a natural language, that is, in linguistic terms. The approach to modelling such knowledge is based upon the mathematical theory of uncertainty related to the fuzzy measures and integrals and their applications. The book consists of two parts: Chapters 2-6 comprise the theory, and applications are offered in Chapters 7-10. In the theory section the exposition is mathematical in nature and gives a complete background on uncertainty measures and integrals, especially in a fuzzy setting.Applications concern recent ones of fuzzy measures and integrals to problems such as pattern recognition, decision making and subjective multicriteria evaluations.
1 492 kr
Skickas inom 10-15 vardagar
The book provides a thorough treatment of set functions, games and capacities as well as integrals with respect to capacities and games, in a mathematical rigorous presentation and in view of application to decision making. After a short chapter introducing some required basic knowledge (linear programming, polyhedra, ordered sets) and notation, the first part of the book consists of three long chapters developing the mathematical aspects. This part is not related to a particular application field and, by its neutral mathematical style, is useful to the widest audience. It gathers many results and notions which are scattered in the literature of various domains (game theory, decision, combinatorial optimization and operations research). The second part consists of three chapters, applying the previous notions in decision making and modelling: decision under uncertainty, decision with multiple criteria, possibility theory and Dempster-Shafer theory.
1 492 kr
Skickas inom 10-15 vardagar
The book provides a thorough treatment of set functions, games and capacities as well as integrals with respect to capacities and games, in a mathematical rigorous presentation and in view of application to decision making.
1 598 kr
Skickas inom 10-15 vardagar
This decade has witnessed increasing interest in fuzzy technology both from academia and industry. It is often said that fuzzy theory is easy and simple so that engineers can progress quickly to real applications. However, the lack of knowledge of design methodologies and the theoretical results of fuzzy theory have often caused problems for design engineers. The aim of this book is to provide a rigorous background for uncertainty calculi, with an emphasis on fuzziness. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference is primarily about the type of knowledge expressed in a natural language, that is, in linguistic terms. The approach to modeling such knowledge is based upon the mathematical theory of uncertainty related to the fuzzy measures and integrals and their applications. The book consists of two parts: Chapters 2--6 comprise the theory, and applications are offered in Chapters 7--10. In the theory section the exposition is mathematical in nature and gives a complete background on uncertainty measures and integrals, especially in a fuzzy setting.Applications concern recent ones of fuzzy measures and integrals to problems such as pattern recognition, decision making and subjective multicriteria evaluations.