Convergence analysis of solution sets for fuzzy optimization problems

Nguyen Van Hung; Vo Minh Tam; Nguyen Huy Tuan; Donal O'Regan

doi:10.1016/j.cam.2019.112615

Convergence analysis of solution sets for fuzzy optimization problems

Nguyen Van Hung
, Vo Minh Tam
, Nguyen Huy Tuan
, Donal O'Regan

Mathematics

Ton Duc Thang University
Dong Thap University
Duy Tan University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

34 Citations (Scopus)

Abstract

In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)_n). Then we establish the concept of D-convergence of a sequence of fuzzy mappings and its characterizations. Finally, the Painlevé–Kuratowski lower convergence and the Painlevé–Kuratowski convergence of approximate solution sets for these problems are proposed using D-convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.

Original language	English
Article number	112615
Number of pages	0
Journal	Journal of Computational and Applied Mathematics
Volume	369
DOIs	https://doi.org/10.1016/j.cam.2019.112615
Publication status	Published - 1 May 2020

Keywords

Approximate solution
Fuzzy mappings
Fuzzy optimization problems
The D-convergence
The Painlevé–kuratowski convergence

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10.1016/j.cam.2019.112615

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title = "Convergence analysis of solution sets for fuzzy optimization problems",

abstract = "In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)n). Then we establish the concept of D-convergence of a sequence of fuzzy mappings and its characterizations. Finally, the Painlev{\'e}{\textendash}Kuratowski lower convergence and the Painlev{\'e}{\textendash}Kuratowski convergence of approximate solution sets for these problems are proposed using D-convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.",

keywords = "Approximate solution, Fuzzy mappings, Fuzzy optimization problems, The D-convergence, The Painlev{\'e}{\textendash}kuratowski convergence",

author = "Hung, \{Nguyen Van\} and Tam, \{Vo Minh\} and Tuan, \{Nguyen Huy\} and Donal O'Regan",

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T1 - Convergence analysis of solution sets for fuzzy optimization problems

AU - Hung, Nguyen Van

AU - Tam, Vo Minh

AU - Tuan, Nguyen Huy

AU - O'Regan, Donal

PY - 2020/5/1

Y1 - 2020/5/1

N2 - In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)n). Then we establish the concept of D-convergence of a sequence of fuzzy mappings and its characterizations. Finally, the Painlevé–Kuratowski lower convergence and the Painlevé–Kuratowski convergence of approximate solution sets for these problems are proposed using D-convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.

AB - In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)n). Then we establish the concept of D-convergence of a sequence of fuzzy mappings and its characterizations. Finally, the Painlevé–Kuratowski lower convergence and the Painlevé–Kuratowski convergence of approximate solution sets for these problems are proposed using D-convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.

KW - Approximate solution

KW - Fuzzy mappings

KW - Fuzzy optimization problems

KW - The D-convergence

KW - The Painlevé–kuratowski convergence

UR - https://www.scopus.com/pages/publications/85075766103

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DO - 10.1016/j.cam.2019.112615

M3 - Article

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VL - 369

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 112615

ER -

Convergence analysis of solution sets for fuzzy optimization problems

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Keywords

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