Numerical solutions for systems of `qualitative' nonlinear algebraic equations by fuzzy logic

This paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations F ( x ) = 0 in which the function F ( · ) is not explicitly defined and may be underdetermined. Such systems arise frequently in many engineering design problems where design...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 150; no. 3; pp. 599 - 609
Main Authors: Selekwa, Majura F., Collins, Emmanuel G.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.03.2005
Elsevier
Subjects:
Analysis
Applied sciences
Calculus of variations and optimal control
Design
Exact sciences and technology
Fuzzy mathematical programming
General logic
Logic and foundations
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Design
Fuzzy mathematical programming
Analysis
Non linear equation
Fuzzy logic
Experimental design
Algebraic equation
Algebraic logic
Fuzzy programming
Newton method
Explicit equation
Mathematical programming
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:This paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations F ( x ) = 0 in which the function F ( · ) is not explicitly defined and may be underdetermined. Such systems arise frequently in many engineering design problems where design parameters must be chosen using qualitative information by the designer to meet a set of desired performance constraints. The proposed method also can be used for a consistent system of nonlinear equations in which F ( · ) is explicitly defined and may have fewer independent equations than the number of unknowns. However, this method is very computationally demanding; hence, it is not advisable to apply it to problems involving explicit functions that can be solved using other existing numerical methods. It is seen that this method works quite well and numerical solutions for such problems can be obtained, although it is much slower than Newton's method when employed to consistent, explicit nonlinear equations.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2004.06.008