Orthodox and non-orthodox sets : some philosophical remarks

• Autorzy: Pawlak, Z.
• Języki publikacji: EN

Abstrakty

EN

We outline the relationship between classical (orthodox) sets from one side, and fuzzy and rough (non-orthodox) sets from another side. The classical concept of a set used in mathematics leads to antinomies, i.e., it is contradictory. This deficiency has, however, rather philosophical than practical meaning. Antinomies are associated with very "artificial'1 sets constructed in logic but not found in sets used in mathematics. That is why one can use mathematics safely. Fuzzy set and rough set theory are two different approaches to vagueness and are not remedy for classical set theory difficulties. Fuzzy set theory addresses graduainess of knowledge, expressed by the fuzzy membership, whereas rough set theory addresses granularity of knowledge, expressed by the indiscernibility relation. From practical point of view both theories are not competing but are rather complementary.

Słowa kluczowe

EN

classical sets; fuzzy sets; rough sets

• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2005
• Tom: Vol. 30, No. 2
• Strony: 133-140
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Pawlak, Z.

• Institute of Computer Sciences, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland and Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Baltycka 5, 44-000 Gliwice, Poland,

Bibliografia

• [1] Cantor G., Grundlagen einer allgemeinen Mannigfaltigkeitlehre, Leipzig , 1883.
• [2] Frege G., Grundlagen der Arithmetik 2,Verlag von Herman Phole, Jena, 1893.
• [3] Pawlak Z., Rough sets, Int. J. of Information and Computer Sciences, 11, 5, 1982, 341-356.
• [4] Read S., Thinking about logic, an introduction to the philosophy of logic, Oxford University Press, Oxford, New York, 1995.
• [5] Russell В., Principles of Mathematics, London, 1903.
• [6] Zadeh L., Fuzzy sets, Information and Control, 8, 1965, 338-353.