Minimizing a nonlinear function under a fuzzy max-t-norm relational equation constraint

Authors:
Jun-Lin Lin;Yan-Kuen Wu;Pei-Chann Chang
Affiliations:
Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li 320, Taiwan;Department of Industrial Management, Vanung University, Chung-Li 320, Taiwan;Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li 320, Taiwan
Venue:
Expert Systems with Applications: An International Journal
Year:
2009

Citing 17
Cited 1

Solution algorithms for fuzzy relational equations with max-product composition

Fuzzy Sets and Systems
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
Fuzzy relation equations for coding/decoding processes of images and videos

Information Sciences—Informatics and Computer Science: An International Journal
Solutions of fuzzy relation equations based on continuous t-norms

Information Sciences: an International Journal
On the relation between fuzzy max-Archimedean t-norm relational equations and the covering problem

Fuzzy Sets and Systems
GA-TSKfnn: Parameters tuning of fuzzy neural network using genetic algorithms

Expert Systems with Applications: An International Journal
On the relation between equations with max-product composition and the covering problem

Fuzzy Sets and Systems
On various eigen fuzzy sets and their application to image reconstruction

Information Sciences: an International Journal
Fuzzy relational compression

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An efficient solution procedure for fuzzy relation equations with max-product composition

IEEE Transactions on Fuzzy Systems
Fast solving method of fuzzy relational equation and its application to lossy image compression/reconstruction

IEEE Transactions on Fuzzy Systems
An accelerated approach for solving fuzzy relation equations with a linear objective function

IEEE Transactions on Fuzzy Systems
An Efficient Procedure for Solving a Fuzzy Relational Equation With Max–Archimedean t-Norm Composition

IEEE Transactions on Fuzzy Systems

The quadratic programming problem with fuzzy relation inequality constraints

Computers and Industrial Engineering

Quantified Score

Hi-index	12.05

Visualization

Abstract

This work studies a nonlinear optimization problem subject to fuzzy relational equations with max-t-norm composition. Since the feasible domain of fuzzy relational equations with more than one minimal solution is non-convex, traditional nonlinear programming methods usually cannot solve them efficiently. This work proposes a genetic algorithm to solve this problem. This algorithm first locates the feasible domain through the maximum solution and the minimal solutions of the fuzzy relational equations, to significantly reduce the search space. The algorithm then executes all genetic operations inside this feasible domain, and thus avoids the need to check the feasibility of each solution generated. Moreover, it uses a local search operation to fine-tune each mutated solution. Experimental results indicate that the proposed algorithm can accelerate the searching speed and find the optimal solution.