Decreasing rearrangement and a fuzzy variational problem

B. Emamizadeh

doi:10.1016/j.aml.2004.06.021

Decreasing rearrangement and a fuzzy variational problem

B. Emamizadeh

Research output: Journal Publication › Article › peer-review

6 Citations (Scopus)

Abstract

In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be transformed into a one dimensional setting.

Original language	English
Pages (from-to)	171-178
Number of pages	8
Journal	Applied Mathematics Letters
Volume	18
Issue number	2
DOIs	https://doi.org/10.1016/j.aml.2004.06.021
Publication status	Published - Feb 2005
Externally published	Yes

Keywords

Cuts
Fuzzy sets
Good partition
Rearrangements of functions
Separating power
Variational problem

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aml.2004.06.021

Cite this

@article{350af2dd770644849ea967638803f9ca,

title = "Decreasing rearrangement and a fuzzy variational problem",

abstract = "In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be transformed into a one dimensional setting.",

keywords = "Cuts, Fuzzy sets, Good partition, Rearrangements of functions, Separating power, Variational problem",

author = "B. Emamizadeh",

note = "Funding Information: The author thanks Dr. C. Dujet for making valuable comments on the primary version of the paper. He also thanks the Institute for Studies in Theoretical Physics and Mathematics for partial financial support.",

year = "2005",

month = feb,

doi = "10.1016/j.aml.2004.06.021",

language = "English",

volume = "18",

pages = "171--178",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Ltd.",

number = "2",

}

TY - JOUR

T1 - Decreasing rearrangement and a fuzzy variational problem

AU - Emamizadeh, B.

N1 - Funding Information: The author thanks Dr. C. Dujet for making valuable comments on the primary version of the paper. He also thanks the Institute for Studies in Theoretical Physics and Mathematics for partial financial support.

PY - 2005/2

Y1 - 2005/2

N2 - In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be transformed into a one dimensional setting.

AB - In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be transformed into a one dimensional setting.

KW - Cuts

KW - Fuzzy sets

KW - Good partition

KW - Rearrangements of functions

KW - Separating power

KW - Variational problem

UR - http://www.scopus.com/inward/record.url?scp=13844276011&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2004.06.021

DO - 10.1016/j.aml.2004.06.021

M3 - Article

AN - SCOPUS:13844276011

SN - 0893-9659

VL - 18

SP - 171

EP - 178

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 2

ER -

Decreasing rearrangement and a fuzzy variational problem

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this