Research Article
Year 2023,
Issue: 44, 1 - 9, 30.09.2023
Abstract
References
- C. C. Chang, Algebraic Analysis of Many-Valued Logics, Transactions of the American Mathematical Society 88 (1958) 467--490.
- A. Di Nola, G. Georgescu, A. Iorgulescu, Pseudo-BL Algebras: Part I, Multiple Valued Logic 8 (5-6) (2002) 673--716.
- R. Cignoli, I. M. L. D'Ottaviano, D. Mundici, Algebraic Foundations of Many Valued Reasoning, Kluwer Academic Publication, Dordrecht, 2000.
- E. Turunen, S. Sessa, Local BL-algebras, Multiple Valued Logic 6 (1-2) (2001) 229--250.
- P. Hajek, L. Godo, F. Esteva, A Complete Many-Valued Logic with Product-Conjunction, Archive for Mathematical Logic 35 (1996) 191--208.
- P. Hajek, Mathematics of Fuzzy Logic, Springer Science and Business Media, Dordrecht, 1998.
- K. H. Kim, On Symmetric Bi-Derivations of BL-Algebras, Annals of Fuzzy Mathematics and Informatics 19 (2) (2020) 189--198.
- S. Alsatayhi, A. Moussavi, $(\varphi,\psi )$-Derivations of BL-Algebras, Asian-European Journal of Mathematics 11 (01) (2018) 1850016 19 pages.
- S. Motamed, S. Ehterami, New Types of Derivations in BL-Algebras, New Mathematics and Natural Computation 16 (03) (2020) 627--643.
- M. A. Öztürk, Permuting Tri-Derivations in Prime and Semi-Prime Rings, East Asian Mathematical Journal 15 (1999) 177--190.
- D. Yılmaz, B. Davvaz, H. Yazarlı, Permuting Tri-Derivations in MV-Algebras, Malaya Journal of Matematik 11 (02) (2023) 142--150.
- H. Yazarlı, M. A. Öztürk, Y. B. Jun, Tri-Additive Maps and Permuting Tri-Derivations, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 54 (01) (2005).
- M. A. Öztürk, H. Yazarlı, K. H. Kim, Permuting Tri-Derivations in Lattices, Quaestiones Mathematicae 32 (3) (2009) 415--425.
Year 2023,
Issue: 44, 1 - 9, 30.09.2023
Abstract
Basic logic algebras (BL-algebras) were introduced by Hajek. Multi-value algebras (MV-algebras), Gödel algebras, and product algebras are particular cases of BL-algebras. Moreover, BL-algebras are algebraic structures, and their principal examples are the real interval $[0, 1]$ with the structure given by a continuous $t$-norm and abelian $l$-groups. In this article, we consider a type of derivation structure on BL-algebras. We study $(\odot,\vee)$-permuting tri-derivations of BL-algebras and their examples and basic properties. We obtain results regarding the trace of $(\odot,\vee)$-permuting derivations on Gödel BL-algebras. Finally, the article presents that the results herein can be generalized in future research.
References
- C. C. Chang, Algebraic Analysis of Many-Valued Logics, Transactions of the American Mathematical Society 88 (1958) 467--490.
- A. Di Nola, G. Georgescu, A. Iorgulescu, Pseudo-BL Algebras: Part I, Multiple Valued Logic 8 (5-6) (2002) 673--716.
- R. Cignoli, I. M. L. D'Ottaviano, D. Mundici, Algebraic Foundations of Many Valued Reasoning, Kluwer Academic Publication, Dordrecht, 2000.
- E. Turunen, S. Sessa, Local BL-algebras, Multiple Valued Logic 6 (1-2) (2001) 229--250.
- P. Hajek, L. Godo, F. Esteva, A Complete Many-Valued Logic with Product-Conjunction, Archive for Mathematical Logic 35 (1996) 191--208.
- P. Hajek, Mathematics of Fuzzy Logic, Springer Science and Business Media, Dordrecht, 1998.
- K. H. Kim, On Symmetric Bi-Derivations of BL-Algebras, Annals of Fuzzy Mathematics and Informatics 19 (2) (2020) 189--198.
- S. Alsatayhi, A. Moussavi, $(\varphi,\psi )$-Derivations of BL-Algebras, Asian-European Journal of Mathematics 11 (01) (2018) 1850016 19 pages.
- S. Motamed, S. Ehterami, New Types of Derivations in BL-Algebras, New Mathematics and Natural Computation 16 (03) (2020) 627--643.
- M. A. Öztürk, Permuting Tri-Derivations in Prime and Semi-Prime Rings, East Asian Mathematical Journal 15 (1999) 177--190.
- D. Yılmaz, B. Davvaz, H. Yazarlı, Permuting Tri-Derivations in MV-Algebras, Malaya Journal of Matematik 11 (02) (2023) 142--150.
- H. Yazarlı, M. A. Öztürk, Y. B. Jun, Tri-Additive Maps and Permuting Tri-Derivations, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 54 (01) (2005).
- M. A. Öztürk, H. Yazarlı, K. H. Kim, Permuting Tri-Derivations in Lattices, Quaestiones Mathematicae 32 (3) (2009) 415--425.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | September 30, 2023 |
| Submission Date | April 29, 2023 |
| Published in Issue | Year 2023 Issue: 44 |
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