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Linear optimization with bipolar fuzzy relational equation constraints using the Łukasiewicz triangular norm

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Abstract

This paper discusses the linear optimization problem constrained by a system of bipolar fuzzy relational equations with max-\(T\) composition, where the involved triangular norm is the Łukasiewicz t-norm. Although it is in general NP-hard, such an optimization problem can be reformulated in polynomial time into a 0-1 integer linear optimization problem and then solved taking advantage of well developed techniques in integer optimization.

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Author information

Author notes

  1. Yuhan Liu

    Present address: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221, USA

Authors and Affiliations

  1. Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China

    Pingke Li & Yuhan Liu

Authors
  1. Pingke Li
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  2. Yuhan Liu
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Corresponding author

Correspondence to Pingke Li.

Additional information

Communicated by T. Allahviranloo.

This work was supported by the National Natural Science Foundation of China under Grants 61203131, 11171177, and 71301084.

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Li, P., Liu, Y. Linear optimization with bipolar fuzzy relational equation constraints using the Łukasiewicz triangular norm. Soft Comput 18, 1399–1404 (2014). https://doi.org/10.1007/s00500-013-1152-1

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  • DOI: https://doi.org/10.1007/s00500-013-1152-1

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