Convex interval and fuzzy (valued) functions with functionals

Bing-yuan Cao

pp. 233-244

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

Abstract

The writer in this paper, on the foundation of interval and fuzzy (value) function, interval and fuzzy (value) functional variation, puts forward a concept on convex interval and convex fuzzy (value) function with functional, gives the definition of a convex function and convex functional about an interval, a common function at fuzzy points, a fuzzy-valued function at common points and a fuzzy-valued function at fuzzy points, and judges their convexity condition. This lays a foundation on the application of fuzzy optimal theories and fuzzy variation methods at physical and approximate calculation.