zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized fuzzy sets. (English) Zbl 1092.03028
Summary: Our aim is to generalize Lemma 2 and Lemma 3 of {\it N. Nakajima}’s article “Generalized fyzzy sets” [Fuzzy Sets Syst. 32, 307--314 (1989; Zbl 0676.06017)]. In this article, a construction of fuzzy sets without depending on a membership function, algebraic properties of a family of fuzzy sets, a ring of generalized fuzzy sets $\text{GF}(X)$ of $X$, a complete Heyting algebra (cHa) which contains the power set $P(X)$ of $X$, an extension lattice $\overline {B(L)}$ where $B=P(X)$, and the set of ${\bold L}$-fuzzy sets where ${\bold L}=\{Lx\mid x\in X\}$ were proposed and shown that they are equivalent depending on Lemma 2 and Lemma 3. In his article Lemma 2, Lemma 3 were not shown in their generalized version. In our article we show that these lemmas can be generalized.

03E72Fuzzy set theory
06D20Heyting algebras