# Fuzzy mappings

Mathematica Applicanda (1983)

- Volume: 11, Issue: 22
- ISSN: 1730-2668

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topStanisław Heilpern. "Fuzzy mappings." Mathematica Applicanda 11.22 (1983): null. <http://eudml.org/doc/293176>.

@article{StanisławHeilpern1983,

abstract = {Let X be the class of all fuzzy subsets of a metric space X. A fuzzy subset A is called an approximate value if A is a closed and convex fuzzy subset with supA(x)=1; the class of all such elements is denoted by W(X), and it is a metric space with the distance D(A,B)=sup dist(Aα,Bα), where Aα and Bα denote the α-level of A and B, respectively, and dist( , ) denotes the generalized Hausdorff distance [see, e.g., M. P. Chen and M. H. Shin , J. Math. Anal. Appl. 71 (1979), no. 2, 516–524; MR0548780]. The author is especially concerned with W(R). Algebraic operations in W(R) are defined and basic rules for arithmetic operations on approximate values are proved. Moreover, functions with values in W(R) are also investigated. Finally, a fixed point theorem for fuzzy mappings is stated and an example is given [for the proof see the author, ibid. 83 (1981), no. 2, 566–569; MR0641351].},

author = {Stanisław Heilpern},

journal = {Mathematica Applicanda},

keywords = {Fuzzy topology; Fuzzy set theory; Fixed-point and coincidence theorems},

language = {eng},

number = {22},

pages = {null},

title = {Fuzzy mappings},

url = {http://eudml.org/doc/293176},

volume = {11},

year = {1983},

}

TY - JOUR

AU - Stanisław Heilpern

TI - Fuzzy mappings

JO - Mathematica Applicanda

PY - 1983

VL - 11

IS - 22

SP - null

AB - Let X be the class of all fuzzy subsets of a metric space X. A fuzzy subset A is called an approximate value if A is a closed and convex fuzzy subset with supA(x)=1; the class of all such elements is denoted by W(X), and it is a metric space with the distance D(A,B)=sup dist(Aα,Bα), where Aα and Bα denote the α-level of A and B, respectively, and dist( , ) denotes the generalized Hausdorff distance [see, e.g., M. P. Chen and M. H. Shin , J. Math. Anal. Appl. 71 (1979), no. 2, 516–524; MR0548780]. The author is especially concerned with W(R). Algebraic operations in W(R) are defined and basic rules for arithmetic operations on approximate values are proved. Moreover, functions with values in W(R) are also investigated. Finally, a fixed point theorem for fuzzy mappings is stated and an example is given [for the proof see the author, ibid. 83 (1981), no. 2, 566–569; MR0641351].

LA - eng

KW - Fuzzy topology; Fuzzy set theory; Fixed-point and coincidence theorems

UR - http://eudml.org/doc/293176

ER -

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