Latticized linear optimization on the unit interval

Authors:
Pingke Li;Shu-Cherng Fang
Affiliations:
Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC;Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC and Department of Mathematical Sciences and the Department of Industrial Engineering, ...
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2009

Citing 28
Cited 2

On matrix equations in a class of complete and completely distributive lattices

Fuzzy Sets and Systems
The fuzzy relation equation with union or intersection preserving operator

Fuzzy Sets and Systems
On solving relational equations in Brouwerian lattices

Fuzzy Sets and Systems
Processing in relational structures: fuzzy relational equations

Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view

Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy linear systems

Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications

Fuzzy sets and fuzzy logic: theory and applications
On the complexity of dualization of monotone disjunctive normal forms

Journal of Algorithms
Composite fuzzy relational equations with non-commutative conjunctions

Information Sciences—Informatics and Computer Science: An International Journal - Special issue on modeling with soft-computing
Solving fuzzy relation equations with a linear objective function

Fuzzy Sets and Systems
Optimization of fuzzy relation equations with max-product composition

Fuzzy Sets and Systems
Solving nonlinear optimization problems with fuzzy relation equation constraints

Fuzzy Sets and Systems
Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Fuzzy Sets and Systems
Fuzzy Relation Equations and Their Applications to Knowledge Engineering

Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Disjunctive optimization, max-separable problems and extremal algebras

Theoretical Computer Science
A Note on Fuzzy Relation Programming Problems with Max-Strict-t-Norm Composition

Fuzzy Optimization and Decision Making
An Algorithm for Solving Optimization Problems with One Linear Objective Function and Finitely Many Constraints of Fuzzy Relation Inequalities

Fuzzy Optimization and Decision Making
An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals and its application in joint generation

Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Optimization of fuzzy relational equations with max-av composition

Information Sciences: an International Journal
Monomial geometric programming with fuzzy relation equation constraints

Fuzzy Optimization and Decision Making
An algorithm for solving fuzzy relation equations with max-T composition operator

Information Sciences: an International Journal
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fuzzy Optimization and Decision Making
A note on systems with max--min and max-product constraints

Fuzzy Sets and Systems
Reducing the search space of a linear fractional programming problem under fuzzy relational equations with max-Archimedean t-norm composition

Fuzzy Sets and Systems
A survey on fuzzy relational equations, part I: classification and solvability

Fuzzy Optimization and Decision Making
On the relation between equations with max-product composition and the covering problem

Fuzzy Sets and Systems
An accelerated approach for solving fuzzy relation equations with a linear objective function

IEEE Transactions on Fuzzy Systems
Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints

Mathematical and Computer Modelling: An International Journal

Set covering-based surrogate approach for solving sup-$${\mathcal{T}}$$ equation constrained optimization problems

Fuzzy Optimization and Decision Making
Randomly generating test problems for fuzzy relational equations

Fuzzy Optimization and Decision Making

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper considers the latticized linear optimization (LLO) problem and its variants, which are a special class of optimization problems constrained by fuzzy relational equations or inequalities. We show that an optimal solution to such a problem can be obtained in polynomial time as long as the objective function is a max-separable function with continuous monotone components. We further show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of minimal optimal solutions. The maximum optimal solution can be constructed in polynomial time once the optimal objective value is known, while the detection of all minimal optimal solutions in an efficient manner remains as a challenging problem. The relation between LLO and max-separable optimization and related issues are also investigated.