Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints

Samaneh Aliannezhadi; Ali Abbasi Molai; Behnaz Hedayatfar

Kybernetika (2016)

  • Volume: 52, Issue: 4, page 531-557
  • ISSN: 0023-5954

Abstract

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In this paper, the linear programming problem subject to the Bipolar Fuzzy Relation Equation (BFRE) constraints with the max-parametric hamacher composition operators is studied. The structure of its feasible domain is investigated and its feasible solution set determined. Some necessary and sufficient conditions are presented for its solution existence. Then the problem is converted to an equivalent programming problem. Some rules are proposed to reduce the dimensions of problem. Under these rules, some of the optimal variables are found without solving the problem. An algorithm is then designed to find an upper bound for its optimal objective value. With regard to this algorithm, a modified branch and bound method is extended to solve the problem. We combine the rules, the algorithm, and the modified branch and bound method in terms of an algorithm to solve the original problem.

How to cite

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Aliannezhadi, Samaneh, Abbasi Molai, Ali, and Hedayatfar, Behnaz. "Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints." Kybernetika 52.4 (2016): 531-557. <http://eudml.org/doc/286839>.

@article{Aliannezhadi2016,
abstract = {In this paper, the linear programming problem subject to the Bipolar Fuzzy Relation Equation (BFRE) constraints with the max-parametric hamacher composition operators is studied. The structure of its feasible domain is investigated and its feasible solution set determined. Some necessary and sufficient conditions are presented for its solution existence. Then the problem is converted to an equivalent programming problem. Some rules are proposed to reduce the dimensions of problem. Under these rules, some of the optimal variables are found without solving the problem. An algorithm is then designed to find an upper bound for its optimal objective value. With regard to this algorithm, a modified branch and bound method is extended to solve the problem. We combine the rules, the algorithm, and the modified branch and bound method in terms of an algorithm to solve the original problem.},
author = {Aliannezhadi, Samaneh, Abbasi Molai, Ali, Hedayatfar, Behnaz},
journal = {Kybernetika},
keywords = {bipolar fuzzy relation equations; bipolar variables; linear optimization; modified branch and bound method; max-parametric hamacher compositions; bipolar fuzzy relation equations; bipolar variables; linear optimization; modified branch and bound method; max-parametric hamacher compositions},
language = {eng},
number = {4},
pages = {531-557},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints},
url = {http://eudml.org/doc/286839},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Aliannezhadi, Samaneh
AU - Abbasi Molai, Ali
AU - Hedayatfar, Behnaz
TI - Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 4
SP - 531
EP - 557
AB - In this paper, the linear programming problem subject to the Bipolar Fuzzy Relation Equation (BFRE) constraints with the max-parametric hamacher composition operators is studied. The structure of its feasible domain is investigated and its feasible solution set determined. Some necessary and sufficient conditions are presented for its solution existence. Then the problem is converted to an equivalent programming problem. Some rules are proposed to reduce the dimensions of problem. Under these rules, some of the optimal variables are found without solving the problem. An algorithm is then designed to find an upper bound for its optimal objective value. With regard to this algorithm, a modified branch and bound method is extended to solve the problem. We combine the rules, the algorithm, and the modified branch and bound method in terms of an algorithm to solve the original problem.
LA - eng
KW - bipolar fuzzy relation equations; bipolar variables; linear optimization; modified branch and bound method; max-parametric hamacher compositions; bipolar fuzzy relation equations; bipolar variables; linear optimization; modified branch and bound method; max-parametric hamacher compositions
UR - http://eudml.org/doc/286839
ER -

References

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