A bridge construction from Sheffer stroke basic algebras to MTL-algebras

İbrahim Şentürk

Öz


In this study, we bridge over from Sheffer stroke basic algebras to MTL-algebras by means of defining all operations only via Sheffer stroke operation.  We also give some equalities and inequalities which are used in this construction.  Furthermore, we deal with construction relations between other algebraic structures as BL-algebras, MV-algebras and Gödel algebras and Sheffer stroke basic algebras. 


Tam Metin:

PDF

Referanslar


Tarski A., Ein beitrag zur axiomatik der abelschen gruppen, Fundamenta Mathematicae, 30, 253–256, (1938).

Oner, T., Senturk, I., The Sheffer stroke operation reducts of basic algebras, Open Mathematics, 15(1), 926-935, (2017).

Esteva F., Godo L., Monoidal t-norm based logic: towards a logic for left-continuoust-norms, Fuzzy Sets Syst., 124, 271-288, (2001).

Vetterlein T., MTL-algebras arising from partially ordered groups, Fuzzy Sets Syst., 161, 433-443, (2010).

Noguera C., Esteva F., Gispert J., On Some Varieties of MTL-algebras, Log. J. IGPL., 13, 443-466, (2004).

Wang, J., Xin, X. and Saeid, A., Very true operators on MTL-algebras, Open Mathematics, 14(1), 955-969, (2016).

Sankappanavar, H. P., and Stanley B., A Course in Universal Algebra, Graduate Texts Math 78, (1981).

Chajda I., Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium Mathematica, 44, 19–23, (2005).

Łukaszuk A., Grabowski A., Short Sheffer Stroke-Based Single Axiom for Boolean Algebras, Formalized Mathematics, 12, 363–370, (1975).


Refback'ler

  • Şu halde refbacks yoktur.


Telif Hakkı (c) 2020 Ibrahim SENTURK

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.