Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Georgescu, George | Popescu, Andrei
Affiliations: Institute of Mathematics, Calea Grivitei Nr. 21, P.O. Box 1-767, Bucharest, Romania | Fundamentals of Computer Science, Faculty of Mathematics University of Bucharest, Romania
Abstract: A classical (crisp) concept is given by its extent (a set of objects) and its intent (a set of properties). In commutative fuzzy logic, the generalization comes naturally, considering fuzzy sets of objects and properties. In both cases (the first being actually a particular case of the second), the situation is perfectly symmetrical: a concept is given by a pair (A,B), where A is the largest set of objects sharing the attributes from B and B is the largest set of attributes shared by the objects from A (with the necessary nuance when fuzziness is concerned). Because of this symmetry, working with objects is the same as working with properties, so there is no need to make any choice. In this paper, we define concepts in a "non-commutative fuzzy world", where conjunction of sentences is not necessarily commutative, which leads to the following non-symmetrical situation: a concept has one extent (because, at the end of the day, concepts are meant to embrace, using certain descriptions, diverse sets of objects), but two intents, given by the two residua (implications) of the non-commutative conjunction.
Journal: Fundamenta Informaticae, vol. 53, no. 1, pp. 23-54, 2002
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
[email protected]
For editorial issues, like the status of your submitted paper or proposals, write to [email protected]
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
[email protected]
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office [email protected]
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
[email protected]
For editorial issues, like the status of your submitted paper or proposals, write to [email protected]
如果您在出版方面需要帮助或有任何建, 件至: [email protected]