Using the Support Functions to Embed the Families of Fuzzy Sets into Banach Spaces

Abstract

With the help of support functions of fuzzy sets, we are able to embed some interesting families of fuzzy sets into Banach spaces. It is better to make the embedded Banach spaces as small as possible, which can be achieved by considering the weak* topology. In this case, the weak* continuity of support functions should be studied. The concept of a maximal embedding behavior is also presented in this paper, which shows the maximal subset satisfying the completeness.

Keywords

• Banach space
• closed unit ball
• norm topology
• unit sphere
• weak* topology