Overview

This is the first book presenting cardinality theory of fuzzy sets with triangular norms, including its scalar and ""fuzzy"" streams. This theory constitutes not only a powerful basis but also a useful tool for modelling and processing vague and imprecise quantitative information. The multiple application areas of the theory encompass computer science, soft computing, computing with words, and decision-making. Starting with a presentation of the fundamentals of triangular norms and fuzzy set theory, the book offers a self-contained, concise and systematic exposition of cardinalities of fuzzy sets that includes many examples.

Full Product Details

Author:   Maciej Wygralak ,  Adam Mickiewicz
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2003 ed.
Volume:   118
Dimensions:   Width: 15.60cm , Height: 1.40cm , Length: 23.40cm
Weight:   1.060kg
ISBN:  

9783540003373

ISBN 10:   3540003371
Pages:   195
Publication Date:   11 March 2003
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

1. Triangular Operations and Negations (Allegro).- 1.1. Triangular Norms and Conorms.- 1.2. Negations.- 1.3. Associated Triangular Operations.- 1.4. Archimedean Triangular Operations.- 1.5. Induced Negations and Complementary Triangular Operations.- 1.6. Implications Induced by Triangular Norms.- 2. Fuzzy Sets (Andante spianato).- 2.1. The Concept of a Fuzzy Set.- 2.2. Operations on Fuzzy Sets.- 2.3. Generalized Operations.- 2.4. Other Elements of the Language of Fuzzy Sets.- 2.5. Towards Cardinalities of Fuzzy Sets.- 3. Scalar Cardinalities of Fuzzy Sets (Scherzo).- 3.1. An Axiomatic Viewpoint.- 3.2. Cardinality Patterns.- 3.3. Valuation Property and Subadditivity.- 3.4. Cartesian Product Rule and Complementarity.- 3.5. On the Fulfilment of a Group of the Properties.- 4. Generalized Cardinals with Triangular Norms (Rondeau à la polonaise).- 4.1. Generalized FGCounts.- 4.2. Generalized FLCounts.- 4.3. Generalized FECounts.- List of Symbols.

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