zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Fixed points in intuitionistic fuzzy metric spaces. (English) Zbl 1142.54362
Summary: The purpose of this paper, using the idea of intuitionistic fuzzy set due to {\it K. Atanassov} [Fuzzy Sets Syst. 20, 87--96 (1986; Zbl 0631.03040)], we define the notion of intuitionistic fuzzy metric spaces due to {\it O. Kramosil} and {\it J. Michalek} [Fuzzy metric and statistical metric spaces. Kybernetika11, 326--334 (1975)]. Further the well-known fixed point theorems of Banach and Edelstein are extended to intuitionistic fuzzy metric spaces with the help of {\it M. Grabiec} [Fuzzy Sets Syst. 27, No. 3, 385--389 (1988; Zbl 0664.54032)].

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
03E72Fuzzy set theory
WorldCat.org
Full Text: DOI
References:
[1] Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy sets syst 20, 87-96 (1986) · Zbl 0631.03040
[2] Atanassov, K.: New operations defined over the intuitionistic fuzzy sets. Fuzzy sets syst 61, 137-142 (1994) · Zbl 0824.04004
[3] Çoker, D.: An introduction to intuitionistic fuzzy topological spaces. Fuzzy sets syst 88, 81-89 (1997) · Zbl 0923.54004
[4] Deng, Z. -K.: Fuzzy pseudo-metric spaces. J math anal appl 86, 74-95 (1982) · Zbl 0501.54003
[5] Dubois, D.; Prade, H.: Fuzzy sets: theory and applications to policy analysis and information systems. (1980) · Zbl 0444.94049
[6] Edelstein, M.: On fixed and periodic points under contractive mappings. J London math soc 37, 74-79 (1962) · Zbl 0113.16503
[7] Erceg, M. A.: Metric spaces in fuzzy set theory. J math anal appl 69, 205-230 (1979) · Zbl 0409.54007
[8] George, A.; Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy sets syst 64, 395-399 (1994) · Zbl 0843.54014
[9] George, A.; Veeramani, P.: On some results of analysis for fuzzy metric spaces. Fuzzy sets syst 90, 365-368 (1997) · Zbl 0917.54010
[10] Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy sets syst 27, 385-389 (1988) · Zbl 0664.54032
[11] Gregori, V.; Ramaguera, S.: Some properties of fuzzy metric spaces. Fuzzy sets syst 115, 485-489 (2000) · Zbl 0985.54007
[12] Gregori, V.; Sapena, A.: On fixed point theorems in fuzzy metric spaces. Fuzzy sets syst 125, 245-253 (2002) · Zbl 0995.54046
[13] Hadzic, O.; Pap, E.: Fixed point theory in PM-spaces. (2001)
[14] Kaleva, O.; Seikkala, S.: On fuzzy metric spaces. Fuzzy sets syst 12, 225-229 (1984) · Zbl 0558.54003
[15] Klement, E. P.: Operations on fuzzy sets: an axiomatic approach. Inform sci 27, 221-232 (1984) · Zbl 0515.03036
[16] Klement, E. P.; Mesiar, R.; Pap, E.: A characterization of the ordering of continuous t-norms. Fuzzy sets syst 86, 189-195 (1997) · Zbl 0914.04006
[17] Klement, E. P.; Mesiar, R.; Pap, E.: Triangular norms. Trends in logic 8. (2000) · Zbl 0972.03002
[18] Kramosil, O.; Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326-334 (1975) · Zbl 0319.54002
[19] Lowen, R.: Fuzzy set theory. (1996) · Zbl 0854.04006
[20] Menger, K.: Statistical metrics. Proc natl acad sci 28, 535-537 (1942) · Zbl 0063.03886
[21] Park, J. H.: Intuitionistic fuzzy metric spaces. Chaos, solitons & fractals 22, 1039-1046 (2004) · Zbl 1060.54010
[22] Radu V. On the t-norms with the fixed point property. In: Seminarul de Teoria Probabilitatilar şi Aplicatii. Uni. din Timiş oara, No. 184. 1984, p. 72. · Zbl 0567.60009
[23] Schweizer, B.; Sklar, A.: Statistical metric spaces. Pac J math 10, 314-334 (1960) · Zbl 0091.29801
[24] Zadeh, L. A.: Fuzy sets. Inform control 8, 338-353 (1965) · Zbl 0139.24606