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Soft Computing
Published in: Soft Computing 3/2017

13-02-2016 | Foundations

A new class of BL-algebras

Authors: Somayeh Motamed, Lida Torkzadeh

Published in: Soft Computing | Issue 3/2017

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Abstract

In this paper, we introduce the notion of right stabilizers in BL-algebras and define a class of BL-algebras, called RS-BL-algebra. Then we investigate the relationships between the right and left stabilizers in BL-algebras. After that we define the concept of semi RS-BL-algebras and we prove that semisimple BL-algebras and semi RS-BL-algebras are RS-BL-algebra. Moreover, every finite RS-BL-algebra is a semi RS-BL-algebra. Finally, we introduce the concept of a semi-stabilizer and a stabilizer filter in a BL-algebra and we state and prove some theorems which determine the relationships between this notion and the other types of filters of a BL-algebra.
previous article Interval type-2 fuzzy logic for dynamic parameter adaptation in the bat algorithm
next article Third-order reciprocally convex approach to stability of fuzzy cellular neural networks under impulsive perturbations

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Literature
Borumand Saeid A, Motamed S (2009a) Normal filters in BL-algebras. World Appl Sci J 7(Special Issue Appl Math):70–76
Borumand Saeid A, Motamed S (2009b) Some results in BL-algebras. Math Log Q 55(6):649–658
Busneag D, Piciu D (2003a) BL-algebra of fractions relative to an \(\wedge \)-closed system. Analele Stiintifice ale Univ Ovidius Constanta Ser Mat vol XI Fasc 1:39–48
Busneag D, Piciu D (2003b) On the lattice of deductive systems of a BL-algebra. Cent Eur J Math 1(2):221–237
Haveshki M, Mohamadhasani M (2010) Stabilizer in BL-algebras and its properties. Int Math Forum 5(57–60):2809–2816MathSciNetMATH
Haveshki M, Borumand Saeid A, Eslami E (2006) Some types of filters in BL-algebras. Soft Comput 10:657–664CrossRefMATH
Motamed S, Torkzadeh L (2012) Primary decomposition of filters in BL-algebras. Afr Mat 24:725–737
Turunen E (1999a) BL-algebras of basic fuzzy logic. Mathw Soft Comput 6:49–61
Turunen E (1999b) Mathematics behind fuzzy logic. Physica-Verlag, Heidelberg
Metadata
Title
A new class of BL-algebras
Authors
Somayeh Motamed
Lida Torkzadeh
Publication date
13-02-2016
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 3/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-016-2043-z

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