Abstract
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.
References
- 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).
Abstract
Bu çalışmada, MTL-cebirlerini oluşturan tüm operatörleri sadece Sheffer stroke operatörü yardımıyla tanımlayarak, Sheffer stroke temel cebirlerden MTL-cebirlerine bir köprü inşası oluşturduk. Ayrıca, bu inşa süresince kullanılacak bazı eşitlikler ve eşitsizlikleri verdik. Bunun yanı sıra, BL-cebirleri, MV-cebirleri ve Gödel cebirleri gibi cebirsel yapılar ile Sheffer stroke temel cebirleri arasındaki yapı ilişkilerini de ele aldık.
References
- 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).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | January 10, 2020 |
| Submission Date | April 22, 2019 |
| Published in Issue | Year 2020 Volume: 22 Issue: 1 |