Vaguely Defined Objects: Representations, Fuzzy Sets and Nonclassical Cardinality theory: 33 (Theory and Decision Library B, 33) - Hardcover

Wygralak, M.

Hardcover

ISBN 10: 0792338502 ISBN 13: 9780792338505

Publisher: Kluwer Academic Publishers, 1995

Synopsis

Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their (too) categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

About this title

Review

`The book is highly original, rigorous, and well written. It is a valuable contribution to the growing literature dealing with the many faces of uncertainty.'
International Journal of General Systems, 26:4 (1997)

Synopsis

This monograph explores the cardinal, or quantitative, aspects of objects in the presence of vagueness, called "vaguely defined objects". In the first part of the book such topics as fuzzy sets and derivative ideas, twofold fuzzy sets, and flow sets are concisely reviewed as typical mathematical representations of vaguely defined objects. Also, a unifying, approximative representation is presented. The second part uses this representation, together with Lukasiewicz logic as a basis for constructing a complete, general and easily applicable nonclassical cardinality theory for vaguely defined objects. Applications to computer and information science are discussed. This volume should be of interest to mathematicians, computer and information scientists, whose work involves mathematical aspects of vagueness, fuzzy sets and their methods, applied many-valued logics, expert systems and data bases.

Edition details

• Publisher: Kluwer Academic Publishers
• Publication date: 1995
• Language: English
• ISBN 10: 0792338502
• ISBN 13: 9780792338505
• Binding: Hardcover
• Number of pages: 283