Cardinalities of Fuzzy Sets

• Main Author: Wygralak, Maciej (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Studies in Fuzziness and Soft Computing, 118
• Subjects: Discrete mathematics.; Computational complexity.; Computer science-Mathematics.; Group theory.; System theory.; Discrete Mathematics.; Complexity.; Math Applications in Computer Science.; Group Theory and Generalizations.; Systems Theory, Control.

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by...

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.