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Fuzzy linear programming problems : models and solutions

(2020) SOFT COMPUTING. 24(13). p.10043-10073
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Abstract
We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.
Keywords
Theoretical Computer Science, Software, Geometry and Topology, Fuzzy linear programming, Duality, Ranking function, Fuzzy number, Fully fuzzy system, GROUP DECISION-MAKING, TRANSPORTATION PROBLEMS, SENSITIVITY-ANALYSIS, MEHARS METHOD, MATRIX GAMES, RANKING, DUALITY, NETWORK, INTERVAL, NUMBERS

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MLA
Ghanbari, Reza, et al. “Fuzzy Linear Programming Problems : Models and Solutions.” SOFT COMPUTING, vol. 24, no. 13, 2020, pp. 10043–73, doi:10.1007/s00500-019-04519-w.
APA
Ghanbari, R., Ghorbani-Moghadam, K., Mahdavi-Amiri, N., & De Baets, B. (2020). Fuzzy linear programming problems : models and solutions. SOFT COMPUTING, 24(13), 10043–10073. https://doi.org/10.1007/s00500-019-04519-w
Chicago author-date
Ghanbari, Reza, Khatere Ghorbani-Moghadam, Nezam Mahdavi-Amiri, and Bernard De Baets. 2020. “Fuzzy Linear Programming Problems : Models and Solutions.” SOFT COMPUTING 24 (13): 10043–73. https://doi.org/10.1007/s00500-019-04519-w.
Chicago author-date (all authors)
Ghanbari, Reza, Khatere Ghorbani-Moghadam, Nezam Mahdavi-Amiri, and Bernard De Baets. 2020. “Fuzzy Linear Programming Problems : Models and Solutions.” SOFT COMPUTING 24 (13): 10043–10073. doi:10.1007/s00500-019-04519-w.
Vancouver
1.
Ghanbari R, Ghorbani-Moghadam K, Mahdavi-Amiri N, De Baets B. Fuzzy linear programming problems : models and solutions. SOFT COMPUTING. 2020;24(13):10043–73.
IEEE
[1]
R. Ghanbari, K. Ghorbani-Moghadam, N. Mahdavi-Amiri, and B. De Baets, “Fuzzy linear programming problems : models and solutions,” SOFT COMPUTING, vol. 24, no. 13, pp. 10043–10073, 2020.
@article{8663722,
  abstract     = {{We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.}},
  author       = {{Ghanbari, Reza and Ghorbani-Moghadam, Khatere and Mahdavi-Amiri, Nezam and De Baets, Bernard}},
  issn         = {{1432-7643}},
  journal      = {{SOFT COMPUTING}},
  keywords     = {{Theoretical Computer Science,Software,Geometry and Topology,Fuzzy linear programming,Duality,Ranking function,Fuzzy number,Fully fuzzy system,GROUP DECISION-MAKING,TRANSPORTATION PROBLEMS,SENSITIVITY-ANALYSIS,MEHARS METHOD,MATRIX GAMES,RANKING,DUALITY,NETWORK,INTERVAL,NUMBERS}},
  language     = {{eng}},
  number       = {{13}},
  pages        = {{10043--10073}},
  title        = {{Fuzzy linear programming problems : models and solutions}},
  url          = {{http://dx.doi.org/10.1007/s00500-019-04519-w}},
  volume       = {{24}},
  year         = {{2020}},
}

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