A comparative study of ideals in fuzzy orders

摘要

This paper presents a comparative study of three kinds of ideals in quantale-valued order theory: forward Cauchy ideals (generated by forward Cauchy nets), flat ideals and irreducible ideals. Main results include necessary and sufficient conditions for forward Cauchy ideals to be flat or irreducible for integral quantales. (C) 2018 Elsevier B.V. All rights reserved.