عنوان

Cardinalities of Fuzzy Sets

شابک

3540363823

شابک

9783540363828

شماره

b565778

عنوان اصلي

Cardinalities of Fuzzy Sets

نام عام مواد

[Book]

نام نخستين پديدآور

by Maciej Wygralak.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

2003

نام خاص و کميت اثر

1 ressource en ligne (XIV, 195 pages)

عنوان فروست

Studies in Fuzziness and Soft Computing, 118.

متن يادداشت

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.

متن يادداشت

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 the same type of num­ bers: the natural numbers. That these complementary aspects of the counting pro­ cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc­ tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.

موضوع مستند نشده

Computer science -- Mathematics.

موضوع مستند نشده

Group theory.

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Maciej Wygralak.

مستند نام اشخاص تاييد نشده

Maciej Wygralak

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y