Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0676.06017
Nakajima, Nobuyuki
Generalized fuzzy sets.
(English)
[J] Fuzzy Sets Syst. 32, No.3, 307-314 (1989). ISSN 0165-0114

Summary: This paper is concerned with a construction of fuzzy sets not depending on a membership function. Algebraic properties of a family of fuzzy sets are investigated. In this paper, three notions are proposed: (1) a ring of generalized fuzzy sets ${\cal G}{\cal F}(X)$ of X, a complete Heyting algebra (cHa) which contains the power set ${\cal P}(X)$ of X; (2) an extension lattice $\overline{{\cal B}(L)}$, where ${\cal B}={\cal P}(X)$; and (3) the set of ${\bbfL}$-fuzzy sets, where ${\bbfL}=[L\sb x\vert$ $x\in X]$. It is shown that these three notions are equivalent. The mathematical structure of ${\cal G}{\cal F}(X)$ is studied, and a ring of generalized fuzzy sets of type 2 is introduced.
MSC 2000:
*06D20 Heyting algebras
03E99 Set theory (logic)
03E72 Fuzzy sets (logic)

Keywords: ring of generalized fuzzy sets; complete Heyting algebra; extension lattice; ${\bbfL}$-fuzzy sets

Cited in: Zbl 1092.03028

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster