Saddle point optimality conditions in fuzzy optimization problems

Zeng-tai Gong

Hong-xia Li

pp. 7-14

in: Bing-yuan Cao, Cheng-yi Zhang, Tai-fu Li (eds), Fuzzy information and Engineering I, Berlin, Springer, 2009

Abstract

The fuzzy-valued Lagrangian function of constrained fuzzy programming as well as its duality are proposed via a new concept of fuzzy ordering, and the duality theorems are given. At the same time, the sufficient condition for the optimal solution of the fuzzy optimization problem is obtained by virtue of the saddle point of fuzzyvalued Lagrangian function, and the necessary condition for the optimal solution of the convex fuzzy optimization problem is also presented.