Title :
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
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;
Conference_Titel :
IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th
Conference_Location :
Vancouver, BC
Print_ISBN :
0-7803-7078-3
DOI :
10.1109/NAFIPS.2001.944228
