Intelligent Counting Under Information Imprecision: Applications to Intelligent Systems and Decision Support

✍ Scribed by Maciej Wygralak (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 294
• Series: Studies in Fuzziness and Soft Computing 292
• Edition: 1
• Category: Library

✦ Synopsis

Counting belongs to the most elementary and frequent mental activities of human beings. Its results are a basis for coming to a decision in a lot of situations and dimensions of our life. This book presents a novel approach to the advanced and sophisticated case, called intelligent counting, in which the objects of counting are imprecisely, fuzzily specified.

Formally, this collapses to counting in fuzzy sets, interval-valued fuzzy sets or I-fuzzy sets (Atanassov's intuitionistic fuzzy sets).

The monograph is the first one showing and emphasizing that the presented methods of intelligent counting are human-consistent: are reflections and formalizations of real, human counting procedures performed under imprecision and, possibly, incompleteness of information. Other applications of intelligent counting in various areas of intelligent systems and decision support will be discussed, too.

The whole presentation is self-contained, systematic, and equipped with many examples, figures and tables. Computer and information scientists, researchers, engineers and practitioners, applied mathematicians, and postgraduate students interested in information imprecision are the target readers.

✦ Table of Contents

Front Matter....Pages 1-10
Introduction....Pages 1-16
Front Matter....Pages 17-17
Basic Notions of the Language of Fuzzy Sets....Pages 19-70
Further Aspects of Triangular Norms - A Study Inspired by Flexible Querying....Pages 71-91
Aggregation of Information and Aggregation Operators....Pages 93-109
Fuzzy Relations, Approximate Reasoning, Fuzzy Rule-Based Systems....Pages 111-137
Modeling Incompletely Known Fuzzy Sets....Pages 139-160
Front Matter....Pages 161-161
General Remarks and Motivations....Pages 163-165
Scalar Approach....Pages 167-186
Fuzzy Approach....Pages 187-229
Selected Applications....Pages 231-260
Cardinalities of Infinite Fuzzy Sets....Pages 261-270
Back Matter....Pages 271-290

✦ Subjects

Computational Intelligence; Operation Research/Decision Theory; Artificial Intelligence (incl. Robotics)