Abstract
Bu çalışmada, BL-cebirleri üzerindeki çarpımsal co-türev operatörleri tanıtılacak ve incelenecektir. Aynı zamanda, çarpımsal co-türev operatörlerinin çarpımsal iç operatörler ve modal operatörlerden daha genel operatörler oldukları vurgulanacaktır. Ayrıca, BL-cebirleri ve bu cebirlerin regüler elemanlarının oluşturduğu cebirler üzerinde tanımlı çarpımsal co-türev operatörleri arasındaki ilişkiler betimlenecektir. Dahası, BL-cebirleri üzerindeki herhangi bir çarpımsal co-türev operatörü 𝟋’ e bağlı olarak BL-cebirleri üzerinde 𝟋-süzgeçler (𝟋-türetim sistemleri) tanıtılacaktır. Ek olarak, BL-cebirlerinin bazı kümelerinin 𝟋-süzgeçler (𝟋-türetim sistemleri) oldukları gösterilecektir. Sonra, BL-cebiri üzerindeki herhangi bir çarpımsal türev operatörü 𝟋 ve BL-cebirinin herhangi bir 𝟋-türetim sistemi yardımı ile bölüm BL-cebiri tanımlanacaktır. Son olarak, 𝟋-operatörü yardımı ile bölüm BL cebiri üzerinde yeni bir operatör tanımlanacak ve bu yeni operatörün çarpımsal bir co-türev operatörü olduğu gösterilecektir.
References
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Abstract
In this study we establish and investigate multiplicative co-derivative operators on BL-algebras. We also indicate that multiplicative co-derivative operators are more general operators than multiplicative interior operators and modal operators on BL-algebras. Furthermore, we describe relations between multiplicative co-derivative operators on BL-algebras and on the algebras of their regular elements. Moreover, 𝟋-filters (𝟋-derivative systems) will be introduced on BL-algebras depending on any multiplicative co-derivative operator 𝟋 on BL-algebras. We also show that some sets of BL-algebras are 𝟋-filters (𝟋-deductive systems) on BL-algebras. Next, we will define quotient BL-algebra by means of any multiplicative co-derivative operator 𝟋 on BL-algebra and any 𝟋-derivative systems on BL-algebra. Finally, we will define a new operator on the quotient BL-algebra with the aid of the operator 𝟋 and show that the new operator is a multiplicative co-derivative operator on the quotient BL-algebra.
Keywords
BL-algebras multiplicative interior operator modal operator multiplicative co-derivative operator.
References
- Hájeck, P., Metamathematics of Fuzzy Logic, Trends in Logic - Studia Logica Library, Volume 4, Kluwer Academic Publishers, Dordrecht, (1998).
- Rasiowa, H. and Sikorski, R., The Mathematics of Metamathematics, Panstwowe Wydawnictwo Naukowe, (1963).
- Rachůnek, J. and S̆vrc̆ek F., MV-algebras with additive closure operators, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 39, 183-189, (2000).
- Hamal, A., Additive derivative and multiplicative coderivative operators on MV-algebras, Turkish Journal of Mathematics, 43, no. 2, pp. 879–893, (2019).
- Macnab, D. S., Modal operators on Heyting algebras, Algebra Universalis, 12, 5–29, (1981).
- Zou, Y. X., Xin, X. L. and He, X. L., On annihilators in BL-algebras. Open Mathematics, 14, 324–337, (2016).
- Mi Ko, J. and Kim, Y. C., Closure operators on BL-algebras, Communications of the Korean Mathematical Society, 19 (2), 219-232 , (2004).
- Rachůnek, J. and Svoboda, Z., Interior and closure operators on commutative bounded residuated lattices, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 52, 121–134, (2013).
- Borzooei, R.A. and Paad, A., Integral filters and integral BL-algebras, Italian Journal of Pure and Applied Mathematics, 30, 303–316, (2013).
- Kondo M., Modal operators on commutative residuated lattices, Mathematica Slovaca, 61, 1-14, (2011).
- Khorami, R.T. and Saeid, A.B., Some unitary operators on hoop-algebras, Fuzzy Information and Engineering, 9, 205–223, (2017).
- Bělohlávek, R., Boolean Part of BL-algebras, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 42, 7-11, (2003).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | October 11, 2021 |
| Publication Date | July 8, 2022 |
| Published in Issue | Year 2022 Volume: 24 Issue: 2 |