Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations

In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties fo...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 53; no. 1; pp. 55 - 62
Main Authors: Zhou, XueGang, Ahat, Rashida
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 2011
Elsevier
Subjects:
Calculus of variations and optimal control
Convex and discrete geometry
equations
Exact sciences and technology
Fuzzy optimization
Fuzzy relational equations
Geometric programming
Geometry
Mathematical analysis
Mathematics
Max-product composition
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Sciences and techniques of general use
system optimization
Fuzzy relational equations
Fuzzy optimization
Max-product composition
Geometric programming
Convex set
Optimization method
Numerical analysis
Applied mathematics
Optimal solution
Variational calculus
Mathematical model
Computer aided analysis
Mathematical programming
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties for the optimization problem under the assumptions of both negative and nonnegative exponents in the objective function. Second, an efficient procedure is developed to find an optimal solution without looking for all the potential minimal solutions and without using the value matrix. An example is provided to illustrate the procedure.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.07.018