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

Khaled M. Elbassioni

doi:10.1016/j.fss.2008.02.020

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

Khaled M. Elbassioni

Electrical Engineering

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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 language	British English
Pages (from-to)	2272-2277
Number of pages	6
Journal	Fuzzy Sets and Systems
Volume	159
Issue number	17
DOIs	https://doi.org/10.1016/j.fss.2008.02.020
State	Published - 1 Sep 2008

Keywords

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

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AB - 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.

KW - Enumeration algorithms

KW - Finding all minimal solutions

KW - Minimal hitting sets

KW - Systems with fuzzy relation equation constraints

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ER -

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

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