Preinvexity Of N-dimensional Fuzzy Number-valued Functions And Convex Optimization Problem

As is known to all,convex optimization is a special class of mathematical opti-mization problems.Meanwhile,in the process of mathematical modeling of specific optimization problems.We note that there is often uncertainty of parameters or dates.In order to describe these uncertain parameters or dates more intuitive and easy to obtain and calculate in the mathematical modeling,we consider whether it can be represented as fuzzy number in some sense.Therefore,fuzzy convex analysis theory and its corresponding fuzzy optimizat.ion problems have been st.udied by many researchers.However,most of the above works are discussed for 1-dimensional preinvexity fuzzy number-valued functions.preinvexity of high-dimensional fuzzy mapping have not been discussed.Thus,In this paper,by means of the partial order relation in n-dimensional fuzzy number space,combining the characteristics of n-dimensional fuzzy mapping.the problems of the preinvex and convex optimization of n-dimensional fuzzy mappings are investigated and discussed in detail.We summarized the main result.s of the paper as follows:First of all,by means of the partial order relation in n-dimensional fuzzy number space,some preinvexity of n-dimensional fuzzy number-valued functions are defined,including preinvexity.weakly preinvexity,strictly preinvexity,weakly strictly preinvexity,prequasiinvexity,weakly prequasiinvexity strictly prequasiinvexity,weakly strictly prequasiinvexity and so on.In addition,their interrelation of the preinvexi-ty of n-dimensional fuzzy numbeir-valued functions are discussed,and some examples are given to illustra.te the interrelation of the preinvexity.Then,we present criteria for n-dimensional preinvex fuzzy number-valued func-tions under upper or lower semicontinuity condition,respectively.And related properties of n-dimensional preinvexity fuzzy number-valued functions are given.Finally,the two-parameter optimization problem and fuzzy mathematical programming problem related to n-dimensional preinvex fuzzy number-valued functions are researched.