Fuzzy presubsets as non-idempotent and non-commutative classifications of subalgebras

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• 作者：Ulrich Hö ; hle ^{uhoehle@uni-wuppertal.de}
• 关键词：Quantale preordered set ; Quasi-presingleton ; Q-Fuzzy presubset ; Monad ; Classification ; Characteristic morphism ; Truth arrow
• 刊名：Fuzzy Sets and Systems
• 出版年：2012
• 期刊代码：55_01650114
• 类别：cp
• 出版时间：16 June, 2012
• 卷：197
• 期：Complete
• 页码：14-44
• 文件大小：336 K

摘要

In the framework of quantale preordered sets regular Q-fuzzy presubsets are identified with classifiable subalgebras. This identification is based on the monad T of quasi-presingletons which is an extension of the monad associated with the Cauchy completion of quantale preordered sets. Even though not every T-subalgebra is classifiable, the classifiable hull of T-subalgebras exists always. An application of these constructions is the internalization of the negation of the underlying quantale as truth arrow in the category of T-algebras.