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

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., Dink...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 22; no. 1; pp. 49 - 62
Main Authors Li, Pingke, Fang, Shu-Cherng
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2009
Subjects
Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
Fractional optimization
fuzzy relational equations
triangular norms
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ISSN1009-6124
1559-7067
DOI10.1007/s11424-009-9146-x

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Summary: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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-009-9146-x