Top

Soft Computing

Published in:

07-03-2020 | Foundations

On pseudo-eBE-algebras

Authors: Shokofeh Sayyad, Hojat Babaei, Akbar Rezaei

Published in: Soft Computing | Issue 10/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we define the notion of a pseudo-eBE-algebra as an extension of a pseudo-BE-algebra, and it is studied in detail. The construction of an eBE-algebra from a pseudo-eBE-algebra is given. Further, the notions of filters and ideals are considered. The classes of distributive and commutative pseudo-eBE-algebras are introduced and investigated. We prove that for a distributive pseudo-eBE-algebra filters coincide with ideals. Also, some types of filters are defined and the relationship between these is investigated.

next article Probabilistic norms on the homeomorphisms of a group

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Borzooei RA, Saeid AB, Rezaei A, Radfar A, Ameri R (2013) On Pseudo-BE-algebras. Discuss Math General Algebra Appl 33:95–108MathSciNetCrossRef

Borzooei RA, Saeid AB, Rezaei A, Radfar A, Ameri R (2015) Distributive pseudo-BE-algebras. Fasc Math 54:21–39MathSciNetMATH

Ciungu LC (2014) Non-commutative multiple-valued logic algebras. Springer, ChamCrossRef

Ciungu LC (2016) Commutative pseudo-BE-algebras. Iran J Fuzzy Syst 13(1):131–144MathSciNetMATH

Ciungu LC (2018) Commutative deductive systems of pseudo-BCK-algebras. Soft Comput 22(4):1189–1201MathSciNetCrossRef

Ciungu LC (2019) Commutative deductive systems in probability theory on generalizations of fuzzy structures. Fuzzy Sets Syst 363:113–137MathSciNetCrossRef

Di Nola A, Georgescu G, Iorgulescu A (2002) Pseudo-BL-algebras—Part I. Multiple Valued Log 8:673–714MathSciNetMATH

Di Nola A, Georgescu G, Iorgulescu A (2002) Pseudo-BL-algebras—Part II. Multiple Valued Log 8:715–750MATH

Georgescu G, Iorgulescu A (1999) Pseudo-MV algebras: a noncommutative extension of MV-algebras. In: The proceedings of the fourth international symposium on economic informatics, 6–9 May, Bucharest, Romania, pp 961–968

Georgescu G, Leustean L (2002) Some classes of pseudo-BL-algebras. J Aust Math Soc 73:127–153MathSciNetCrossRef

Georgescu G, Iorgulescu A (2000) Pseudo-BL-algebras: a non-commutative extension of BL-algebras. In: Abstracts of the fifth international conference FSTA. Slovakia, pp 90–92

Georgescu G, Iorgulescu A (2001) Pseudo-BCK algebras: an extension of BCK-algebras. In: Proceedings of DMTCS’01: combinatorics, computability and logic. Springer, London, pp 97–114

Huang Y (2006) BCI-algebras. Science Press, ChinaMATH

Iorgulescu A (2006) Classes of pseudo-BCK algebras—Part I. J Mult-Valued Log Soft Comput 12:71–130MathSciNetMATH

Iorgulescu A (2008) Algebras of logic as BCK-algebras. ASE Education, BucharestMATH

Iorgulescu A (2018) Implicative vs. groups and generalizations. Matrix Rom, BucharestMATH

Jun YB, Kim HS, Neggers J (2006) On pseudo BCI-ideals of pseudo-BCI-algebras. Math Bec 58:39–46MathSciNetMATH

Kim HS, Kim YH (2007) On BE-algebras. Sci Math Jpn 66:113–117MathSciNetMATH

Kim YH, So KS (2012) On minimality in pseudo-BCI-algebras. Bull Korean Math Soc 27(1):7–130MathSciNetCrossRef

Kühr J (2003) Pseudo-BL-algebras and DRl-monoids. Math Bohem 128:199–202MathSciNetMATH

Kühr J (2007a) Pseudo-BCK-semilattices. Demonstr Math 40:495–516

Kühr J (2007b) Pseudo-BCK–algebras and related structures. Habilitation thesis, Palackú University in Olomouc

Mukkamala SR (2018) A course in BE-algebras. Springer, BerlinCrossRef

Rachůnek J (2012) A non commutative generalization of MV-algebras. Czechoslov Math 52(127):33–44MathSciNet

Rao MS (2015) Prime filters of commutative BE-algebras. J Appl Math Inform 33(5–6):579–591MathSciNetCrossRef

Rezaei A, Saeid AB, Radfar A, Borzooei RA (2014) Congruence relations on pseudo-BE-algebras. Ann Univ Craivova Math Comput Sci Ser 41(2):166–176MathSciNetMATH

Rezaei A, Saeid AB, Radfar A (2016) On eBE-algebras. TWMS J Pure Appl Math 7(2):200–210MathSciNetMATH

Rezaei A, Walendziak A, Saeid AB (2018) Some remarks on commutative and pointed pseudo-CI algebras. Mathematica Aeterna 8(4):269–277

Rezaei A, Saeid AB, Saber KYS (2019) On pseudo-CI-algebras. Soft Comput 23(13):4643–4654CrossRef

Walendziak A (2015) Pseudo-BCH-algebras. Discuss Math Gen Algebra Appl 35:5–19MathSciNetCrossRef

Walendziak A (2017) On branchwise commutative pseudo-BCH-algebras. Annales University Mariae Curie-Sklodowska Lublin-Polonia LXXI(2):79–89MathSciNetCrossRef

Title: On pseudo-eBE-algebras
Authors: Shokofeh Sayyad
Hojat Babaei
Akbar Rezaei
Publication date: 07-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 10/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-04810-1

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 10/2020

Linking granular computing, big data and decision making: a case study in urban path planning

Firms’ pricing strategies under different decision sequences in dual-format online retailing

Assessing the quality of mobile graphical user interfaces using multi-objective optimization

Modeling and state of health estimation of nickel–metal hydride battery using an EPSO-based fuzzy c-regression model

Selfish herd optimization algorithm based on chaotic strategy for adaptive IIR system identification problem

Combining quality function deployment with simple additive weighting for interval-valued fuzzy multi-criteria decision-making with dependent evaluation criteria

Premium Partner