Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections

TL;DR

This paper introduces and studies fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands, and fuzzy band projections within fuzzy ordered linear spaces, extending classical Riesz space theory into the fuzzy context.

Contribution

It defines fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands, and fuzzy band projections, and establishes their fundamental properties, advancing the theory of fuzzy Riesz spaces.

Findings

Defined fuzzy Riesz subspaces, ideals, bands, and band projections.

Established fundamental properties of these fuzzy structures.

Extended classical Riesz space concepts into fuzzy ordered spaces.

Abstract

Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties.