Free object in the category of Lfuzzy left Rmodules determined by Lfuzzy set

Purpose The purpose of this paper is to study free Lfuzzy left Rmodule, using the language of categories and functors for the general description of Lfuzzy left Rmodules generated by Lfuzzy set. In the language of categories and functors, an Lfuzzy left Rmodules generated by Lfuzzy set is called a f...

Full description

Saved in:
Bibliographic Details
Published in:Kybernetes 2009-04, Vol.38 (3/4), p.506-512
Main Authors: Tang, JianGang, Luo, MaoKang, Liu, Miao
Format: Article
Language:English
Subjects:
Cybernetics
Fuzzy logic
Systems theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Purpose The purpose of this paper is to study free Lfuzzy left Rmodule, using the language of categories and functors for the general description of Lfuzzy left Rmodules generated by Lfuzzy set. In the language of categories and functors, an Lfuzzy left Rmodules generated by Lfuzzy set is called a free object in the category of Lfuzzy left Rmodules determined by Lfuzzy set. Designmethodologyapproach Category theory is used to study the existent quality, unique quality and material structure of Lfuzzy left Rmodules generated by Lfuzzy set. Findings The paper gives the uniqueness, structure and existence theorems of free object in the category of Lfuzzy left Rmodules determined by Lfuzzy set, and the authors prove that the fuzzy free functor is left adjoint to the fuzzy underlying functor. Research limitationsimplications Some property of free Lfuzzy left Rmodules will need to be further researched. Originalityvalue The paper defines a new class of Lfuzzy left Rmodules, i.e. free Lfuzzy left Rmodules, research and explore free Lfuzzy left Rmodules in theory.
ISSN:0368-492X
DOI:10.1108/03684920910944227