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2012•Journal of Shandong UniversityRequires access

Researches on some properties of L-fuzzy quantale

Shaohui Liang

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Abstract

The definition of L-fuzzy frame is generalized to L-fuzzy quantale,and some equivalent charaterizations of L-fuzzy quantale are given.The concept of L-filter and L-filtered quantale are introduced.It is proved that every L-filter can generate an L-filtered quantale,and there is an honest functor from L-FilQuant to L-FQuant.Finally,the concept of L-fuzzy ideal and L-fuzzy prime ideal are introduced,and their properties are discussed.

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What this paper is about

The definition of L-fuzzy frame is generalized to L-fuzzy quantale,and some equivalent charaterizations of L-fuzzy quantale are given.The concept of L-filter and L-filtered quantale are introduced.It is proved that every L-filter can generate an L-filtered quantale,and there is an honest functor from L-FilQuant to L-FQuant.Finally,the concept of L-fuzzy ideal and L-fuzzy prime ideal are introduced,and their properties are discussed.

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Available abstract

The definition of L-fuzzy frame is generalized to L-fuzzy quantale,and some equivalent charaterizations of L-fuzzy quantale are given.The concept of L-filter and L-filtered quantale are introduced.It is proved that every L-filter can generate an L-filtered quantale,and there is an honest functor from L-FilQuant to L-FQuant.Finally,the concept of L-fuzzy ideal and L-fuzzy prime ideal are introduced,and their properties are discussed.

Key concepts: Mathematics, Prime (order theory), Fuzzy logic, Pure mathematics, Ideal (ethics), Functor, Frame (networking), Filter (signal processing)

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