A note on systems with max-min and max-product constraints

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We consider a system A {ring operator} x ≥ b, where A ∈ R+m × n is a non-negative matrix and b ∈ R+m is a non-negative vector over the n-dimensional variable l ≤ x ≤ u, where l, u ∈ R+n are lower and upper bounds, respectively, and {ring operator} is either a max-min or a max-product composition. It is shown that the set of minimal solutions of such systems can be computed in incremental quasi-polynomial time.

Original languageBritish English
Pages (from-to)2272-2277
Number of pages6
JournalFuzzy Sets and Systems
Issue number17
StatePublished - 1 Sep 2008


  • Enumeration algorithms
  • Finding all minimal solutions
  • Minimal hitting sets
  • Systems with fuzzy relation equation constraints


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