Fuzzy optimization for portfolio selection based on embedding theorem in fuzzy normed linear spaces

Abstract

In this paper, we propose a novel approach Embedding Theoremabout Menger probabilistic normed Spaces. The main idea behind ourapproach consists of taking advantage of interplays between Mengerprobabilistic normed spaces and normed spaces in a way to get anequivalent stochastic program. This helps avoiding pitfalls due to severe over simplification of the reality. The embedding theorem showsthat the set of all fuzzy numbers can be embedded into a Mengerprobabilistic Banach space. Inspired by this embedding theorem, wepropose a solution concept of fuzzy optimization problem which isobtained by applying the embedding function to the original fuzzyoptimization problem.