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Minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm

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Abstract

This paper shows that the problem of minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1 linear fractional optimization problem in polynomial time. Consequently, parametrization techniques, e.g., Dinkelbach’s algorithm, can be applied by solving a classical set covering problem in each iteration. Similar reduction can also be performed on the sup-T equation constrained optimization problems with an objective function being monotone in each variable separately. This method could be extended as well to the case in which the triangular norm is non-Archimedean.

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Authors and Affiliations

  1. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695-7906, USA

    Pingke Li & Shu-Cherng Fang

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Shu-Cherng Fang

  3. College of Management, Dalian University of Technology, Dalian, 116024, China

    Shu-Cherng Fang

Authors
  1. Pingke Li
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  2. Shu-Cherng Fang
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Correspondence to Pingke Li.

Additional information

The work is supported by the National Science Foundation of the United States under Grant No. #DMI-0553310.

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Li, P., Fang, SC. Minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm. J Syst Sci Complex 22, 49–62 (2009). https://doi.org/10.1007/s11424-009-9146-x

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  • DOI: https://doi.org/10.1007/s11424-009-9146-x

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