A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition

Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this p...

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Published inMathematics (Basel) Vol. 12; no. 20; p. 3183
Main Authors Wu, Yan-Kuen, Guu, Sy-Ming, Chang, Ya-Chan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2024
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ISSN2227-7390
2227-7390
DOI10.3390/math12203183

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Abstract Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this paper is to generalize the above min–max programming problem with addition–overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.
AbstractList Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this paper is to generalize the above min–max programming problem with addition–overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.
Audience Academic
Author Chang, Ya-Chan
Wu, Yan-Kuen
Guu, Sy-Ming
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Cites_doi 10.1016/0165-0114(91)90171-L
10.1155/2017/2017634
10.1016/j.fss.2014.04.007
10.1109/LCSYS.2024.3439208
10.1016/j.fss.2017.04.002
10.1016/S0165-0114(97)00021-3
10.3233/IFS-151546
10.1016/j.fss.2015.02.008
10.1109/TFUZZ.2011.2173581
10.1137/S0363012902415244
10.1007/s10700-019-09305-9
10.1109/TFUZZ.2015.2428716
10.1016/j.fss.2021.12.005
10.1007/s40815-018-0530-3
10.1016/S0165-0114(97)00063-8
10.1016/S0019-9958(76)90446-0
10.1109/TFUZZ.2020.2991304
10.1016/j.na.2009.08.033
10.1016/j.fss.2023.108835
10.1016/j.fss.2006.09.012
10.1016/j.eswa.2023.122036
10.1007/978-981-97-2891-6_3
10.1016/0165-0114(91)90173-N
10.1109/TFUZZ.2016.2593496
10.1007/s10700-022-09390-3
10.1016/j.fss.2005.02.010
10.1007/978-94-017-1648-2
10.1007/s10700-021-09368-7
10.1109/FSKD.2012.6233956
10.1109/TFUZZ.2007.902018
10.1016/0165-0114(91)90170-U
10.1016/j.ins.2007.02.037
10.1016/0022-247X(85)90329-4
10.1016/j.ins.2010.06.018
10.23919/ECC64448.2024.10590973
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References Ghodousian (ref_12) 2006; 180
Wu (ref_10) 2008; 16
Guo (ref_27) 2021; 29
Wang (ref_18) 2024; 238
Guu (ref_29) 2017; 25
Guo (ref_28) 2019; 21
ref_14
ref_36
Matusiewicz (ref_37) 2022; 58
Pedrycz (ref_11) 1991; 40
Pedrycz (ref_5) 1985; 107
Zhang (ref_39) 2024; 478
Fang (ref_34) 2022; 447
Wu (ref_13) 2007; 177
Chiu (ref_33) 2019; 18
Gupta (ref_3) 1991; 40
Jenei (ref_8) 1998; 100
Zhang (ref_23) 2017; 2017
Ganguly (ref_22) 2024; 8
Xiao (ref_38) 2023; 22
Bustince (ref_16) 2007; 158
Gupta (ref_2) 1991; 40
ref_25
ref_21
Yang (ref_30) 2014; 255
Fu (ref_35) 2024; 207
Yang (ref_31) 2015; 28
ref_1
Yang (ref_26) 2018; 343
Jenei (ref_7) 1998; 99
Markovskii (ref_9) 2005; 153
Sanz (ref_17) 2010; 180
Sanchez (ref_6) 1976; 30
Dimuro (ref_15) 2016; 287
Vinter (ref_20) 2005; 44
Qiu (ref_24) 2022; 21
Bustince (ref_19) 2010; 72
Yang (ref_32) 2016; 24
Bustince (ref_4) 2012; 20
References_xml – volume: 40
  start-page: 431
  year: 1991
  ident: ref_2
  article-title: Theory of t-norms and fuzzy inference
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(91)90171-L
– volume: 2017
  start-page: 2017634
  year: 2017
  ident: ref_23
  article-title: Fuzzy control model and simulation for nonlinear supply chain system with lead times
  publication-title: Complexity
  doi: 10.1155/2017/2017634
– volume: 255
  start-page: 41
  year: 2014
  ident: ref_30
  article-title: An algorithm for minimizing a linear objective function subject to the fuzzy relation inequalities with addition-min composition
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2014.04.007
– volume: 58
  start-page: 320
  year: 2022
  ident: ref_37
  article-title: Minimizing and maximizing a linear objective function under a fuzzy max −∗ relational equation and an inequality constraint
  publication-title: Kybernetika
– volume: 180
  start-page: 411
  year: 2006
  ident: ref_12
  article-title: Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations
  publication-title: Appl. Math. Comput.
– volume: 8
  start-page: 2063
  year: 2024
  ident: ref_22
  article-title: Exact Solutions to minmax optimal control problems for constrained noisy linear systems
  publication-title: IEEE Control Syst. Lett.
  doi: 10.1109/LCSYS.2024.3439208
– volume: 343
  start-page: 126
  year: 2018
  ident: ref_26
  article-title: Addition-min fuzzy relation inequalities with application in BitTorrent-like peer-to-peer file sharing system
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2017.04.002
– volume: 99
  start-page: 179
  year: 1998
  ident: ref_7
  article-title: On Archimedean triangular norms
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(97)00021-3
– volume: 28
  start-page: 2679
  year: 2015
  ident: ref_31
  article-title: Multi-level linear programming subject to addition-min fuzzy relation inequalities with application in Peer-to-Peer file sharing system
  publication-title: J. Intell. Fuzzy Syst.
  doi: 10.3233/IFS-151546
– volume: 287
  start-page: 76
  year: 2016
  ident: ref_15
  article-title: On additive generators of overlap functions
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2015.02.008
– volume: 20
  start-page: 405
  year: 2012
  ident: ref_4
  article-title: Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2011.2173581
– volume: 44
  start-page: 939
  year: 2005
  ident: ref_20
  article-title: Minimax optimal control
  publication-title: Siam J. Control Optim.
  doi: 10.1137/S0363012902415244
– volume: 18
  start-page: 433
  year: 2019
  ident: ref_33
  article-title: A single-variable method for solving min-max programming problem with addition-min fuzzy relational inequalities
  publication-title: Fuzzy Optim. Decis. Mak.
  doi: 10.1007/s10700-019-09305-9
– volume: 24
  start-page: 111
  year: 2016
  ident: ref_32
  article-title: Min-max programming problem subject to addition-min fuzzy relation inequalities
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2015.2428716
– volume: 447
  start-page: 1
  year: 2022
  ident: ref_34
  article-title: Minimizing a linear objective function under a max-overlap function fuzzy relational equation constraint
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2021.12.005
– ident: ref_1
– volume: 21
  start-page: 281
  year: 2019
  ident: ref_28
  article-title: A smoothing approach for minimizing a linear function subject to fuzzy relation inequalities with addition-min composition
  publication-title: Int. J. Fuzzy Syst.
  doi: 10.1007/s40815-018-0530-3
– volume: 100
  start-page: 273
  year: 1998
  ident: ref_8
  article-title: On continuous triangular norms
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(97)00063-8
– volume: 30
  start-page: 38
  year: 1976
  ident: ref_6
  article-title: Resolution of composite fuzzy relation equations
  publication-title: Inf. Control
  doi: 10.1016/S0019-9958(76)90446-0
– volume: 29
  start-page: 2444
  year: 2021
  ident: ref_27
  article-title: A novel smoothing approach for linear objective optimizations subject to fuzzy relation inequalities with addition-min composition
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2020.2991304
– volume: 72
  start-page: 1488
  year: 2010
  ident: ref_19
  article-title: Overlap functions
  publication-title: Nonlinear Anal. Theory Methods Appl.
  doi: 10.1016/j.na.2009.08.033
– volume: 478
  start-page: 108835
  year: 2024
  ident: ref_39
  article-title: Optimal symmetric interval solution of fuzzy relation inequality considering the stability in P2P educational information resources sharing system
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2023.108835
– volume: 158
  start-page: 496
  year: 2007
  ident: ref_16
  article-title: Image thresholding using restricted equivalent functions and maximizing the measures of similarity
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2006.09.012
– volume: 238
  start-page: 122036
  year: 2024
  ident: ref_18
  article-title: An overlap function-based three-way intelligent decision model under interval-valued fuzzy information systems
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2023.122036
– volume: 207
  start-page: 37
  year: 2024
  ident: ref_35
  article-title: Linear programming subject to max-product fuzzy relation inequalities with discrete variables
  publication-title: Lect. Notes Data Eng. Commun. Technol.
  doi: 10.1007/978-981-97-2891-6_3
– volume: 40
  start-page: 473
  year: 1991
  ident: ref_3
  article-title: Design of fuzzy logic controllers based on generalized T-operators
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(91)90173-N
– volume: 25
  start-page: 985
  year: 2017
  ident: ref_29
  article-title: A linear programming approach for minimizing a linear function subject to fuzzy relational inequalities with addition-min composition
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2016.2593496
– volume: 22
  start-page: 213
  year: 2023
  ident: ref_38
  article-title: Evaluation and its derived classification in a server-to-client architecture based on the fuzzy relation inequality
  publication-title: Fuzzy Optim. Decis. Mak.
  doi: 10.1007/s10700-022-09390-3
– volume: 153
  start-page: 261
  year: 2005
  ident: ref_9
  article-title: On the relation between equations with max-product composition and the covering problem
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2005.02.010
– ident: ref_14
  doi: 10.1007/978-94-017-1648-2
– volume: 21
  start-page: 291
  year: 2022
  ident: ref_24
  article-title: Min-max programming problem with constraints of addition-min-product fuzzy relation inequalities
  publication-title: Fuzzy Optim. Decis. Mak.
  doi: 10.1007/s10700-021-09368-7
– ident: ref_25
  doi: 10.1109/FSKD.2012.6233956
– ident: ref_36
– volume: 16
  start-page: 73
  year: 2008
  ident: ref_10
  article-title: An efficient procedure for solving a fuzzy relational equation with max-Archimedean t-norm composition
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2007.902018
– volume: 40
  start-page: 415
  year: 1991
  ident: ref_11
  article-title: Sanchez, Fuzzy relation equations theory as a basis of fuzzy modelling: An overview
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(91)90170-U
– volume: 177
  start-page: 4216
  year: 2007
  ident: ref_13
  article-title: Optimization of fuzzy relational equations with max-av composition
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2007.02.037
– volume: 107
  start-page: 520
  year: 1985
  ident: ref_5
  article-title: On generalized fuzzy relational equations and their applications
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(85)90329-4
– volume: 180
  start-page: 3674
  year: 2010
  ident: ref_17
  article-title: Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2010.06.018
– ident: ref_21
  doi: 10.23919/ECC64448.2024.10590973
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Snippet Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer...
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StartPage 3183
SubjectTerms addition–overlap function composition
Computer programming
Constraints
Data transfer (computers)
File sharing
Iterative methods
Linear programming
Maxima and minima
min–max programming problem
Norms
Operators (mathematics)
Optimization
Peer to peer computing
Polynomials
Preferences
Programming
single-variable method
Tests, problems and exercises
Variables
Variables (Mathematics)
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Title A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition
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https://doi.org/10.3390/math12203183
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