Fuzzy optimization problems by parametric representation in the two-dimensional metric space

Author

Saito, Seiji ; Ishii, Hiroaki

Author_Institution

Graduate Sch. of Eng., Osaka Univ., Japan

Volume

1

fYear

2001

fDate

25-28 July 2001

Firstpage

65

Abstract

The authors present a novel representation of fuzzy numbers with bounded supports and also show that a fuzzy number means a bounded continuous curve in the two-dimensional metric space. We consider definitions of the addition, subtraction and product which are defined by the extensions principle due to Zadeh and many other theoreticians of fuzzy logic, as well as showing parametric representation of the operations between fuzzy numbers. The aim of the research is to solve fuzzy optimization problems which consist of nonlinear or linear objective functions and constraints including fuzziness. There are two important problems. One is dealing with some order relation, which is linear or not, and the other is to get a criterion for optimal solutions by considering saddle points of Lagrangian functions

Keywords

fuzzy logic; fuzzy set theory; optimisation; Lagrangian functions; Zadeh; addition; bounded continuous curve; bounded supports; extensions principle; fuzzy logic; fuzzy numbers; fuzzy optimization problems; linear objective functions; nonlinear objective functions; optimal solutions; order relation; parametric representation; product; saddle points; subtraction; two-dimensional metric space; Constraint optimization; Differential equations; Ear; Fuzzy logic; Fuzzy sets; Integral equations; Lagrangian functions; Optimization methods;

fLanguage

English

Publisher

ieee

Conference_Titel

IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th

Conference_Location

Vancouver, BC

Print_ISBN

0-7803-7078-3

Type

conf

DOI

10.1109/NAFIPS.2001.944228

Filename

944228