Fuzzy $\alpha$-cut and related structures

TL;DR

This paper introduces fuzzy α-cuts and localic frames, exploring their properties and algebraic structures, demonstrating that fuzzy α-cuts form a localic frame with potential applications.

Contribution

It presents a novel concept of fuzzy α-cuts, investigates their algebraic structures, and establishes their relation to localic frames, expanding theoretical understanding.

Findings

Fuzzy α-cuts form a localic frame.

Algebraic structures from fuzzy α-cuts are characterized.

Potential applications of fuzzy α-cuts are discussed.

Abstract

This paper deals with a new notion called fuzzy $\alpha$-cut and its properties. A notion called localic frame is also introduced. Algebraic structures arising out of the family of fuzzy $\alpha$-cuts have been investigated. It will be seen that this family forms a localic frame. Some significance and usefulness of fuzzy $\alpha$-cuts are discussed.