Fuzzy strong $\phi$-b-normed linear space for fuzzy bounded linear operators

TL;DR

This paper introduces fuzzy bounded linear operators within fuzzy strong φ-b-normed linear spaces, exploring their properties, operator fuzzy norms, and establishing the completeness of the space of such operators.

Contribution

It develops the concepts of fuzzy continuous and bounded linear operators in fuzzy strong φ-b-normed spaces and proves the completeness of the space of bounded operators.

Findings

Defined fuzzy continuous and bounded linear operators in the new space

Developed the concept of operator fuzzy norm

Proved the completeness of BF(X,Y)

Abstract

In this paper, concept of fuzzy continuous operator, fuzzy bounded linear operator are introduced in fuzzy strong $\phi$-b-normed linear spaces and their relations are studied. Idea of operator fuzzy norm is developed and completeness of BF(X,Y) is established.