On Fuzzy Ideals of BL-Algebras
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-17
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
In this paper we investigate further properties of fuzzy ideals of a BL-algebra.
The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated.
We give a procedure to generate a fuzzy ideal by a fuzzy set.
We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω 0 = 1 and | Im ( ω ) | = 2 .
We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras.
Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice.
Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.
American Psychological Association (APA)
Meng, Biao Long& Xin, Xiao Long. 2014. On Fuzzy Ideals of BL-Algebras. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1050934
Modern Language Association (MLA)
Meng, Biao Long& Xin, Xiao Long. On Fuzzy Ideals of BL-Algebras. The Scientific World Journal No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1050934
American Medical Association (AMA)
Meng, Biao Long& Xin, Xiao Long. On Fuzzy Ideals of BL-Algebras. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1050934
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050934
