Intuitionistic Fuzzy Magnified Translation of PS-Algebra

Year 2021, Issue: 35, 32 - 47, 30.06.2021

Mohsin Khalid Zafar Iqbal Rakib Iqbal

https://doi.org/10.53570/jnt.846542

Cited By: 1

Abstract

In this paper, the concepts of intuitionistic fuzzy α-translation (IFAT), intuitionistic fuzzy α-multiplication (IFAM), and intuitionistic fuzzy magnified βα-translation (IFMBAT) are introduced in the setup of PS-algebra. Some properties of PS-ideal and PS-subalgebra are investigated by applying the concepts of IFAT, IFAM, and IFMBAT. Intersection and union of intuitionistic fuzzy PS-ideals are explained through results and examples.

Keywords

Intuitionistic fuzzy α-translation, intuitionistic fuzzy α-multiplication, intuitionistic fuzzy PS-ideal, intuitionistic fuzzy PS-subalgebra, intuitionistic fuzzy magnified βα-translation

References

• L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
• K. Iseki, S. Tanaka, An Introduction to the Theory of BCK-Algebras, Mathematica Japonica 23 (1978) 1-20.
• K. Iseki, On BCI-Algebras, Mathematics Seminar Notes 8 (1980) 125-130.
• K. J. Lee, Y. B. Jun, M. I. Doh, Fuzzy Translations and Fuzzy Multiplications of BCK/BCI-Algebras, Communications of the Korean Mathematical Society 24(3) (2009) 353-360.
• M. A. A. Ansari, M. Chandramouleeswaran, Fuzzy Translations of Fuzzy β-Ideals of β-Algebras, International Journal of Pure and Applied Mathematics 92(5) (2014) 657-667.
• T. Priya, T. Ramachandran, A Note on Fuzzy PS-Ideals in PS-Algebra and Its Level Subsets, International Journal of Advanced Mathematical Sciences 2(2) (2014) 101-106.
• T. Priya, T. Ramachandran, Classification of PS-Algebras, International Journal of Innovative Science, Engineering and Technology 1(7) (2014) 193-199.
• S. Lekkoksung, On Fuzzy Magnifed Translation in Ternary Hemirings, International Mathematical Forum 7(21) (2012) 1021-1025.
• T. Senapati, M. Bhowmik, M. Pal, Atanassov's Intuitionistic Fuzzy Translations of Intuitionistic Fuzzy H-Ideals in BCK/BCI-Algebras, Notes on Intuitionistic Fuzzy Sets 19(1) (2013) 32-47.
• C. Jana, T. Senapati, M. Bhowmik, M. Pal, On Intuitionistic Fuzzy G-Subalgebras, Fuzzy Information and Engineering 7 (2015) 195-209.
• T. Senapati, M. Bhowmik, M. Pal, B. Davvaz, Fuzzy Translations of Fuzzy H-Ideals in BCK/BCI-Algebras, Journal of the Indonesian Mathematical Society 21 (2015) 45-58.
• K. T. Atanassov, Intuitionistic Fuzzy Sets Theory and Applications, Studies in Fuzziness and Soft Computing, Vol. 35, Physica-Verlag, Heidelberg, New York, 1999.
• T. Senapati, Translation of Intuitionistic Fuzzy B-Algebras, Fuzzy Information and Engineering 7 (2015) 389-404.
• Y. H. Kim, T. E. Jeong, Intuitionistic Fuzzy Structure of B-Algebras, Journal of Applied Mathematics and Computing 22 (2006) 491-500.
• T. Senapati, C. S. Kim, M. Bhowmik, M. Pal, Cubic Subalgebras and Cubic Closed Ideals of B-Algebras, Fuzzy Information and Engineering 7 (2015) 129-149.
• T. Senapati, M. Bhowmik, M. Pal, Fuzzy Dot Subalgebras and Fuzzy Dot Ideals of B-Algebras, Journal of Uncertain Systems 8 (2014) 22-30.
• T. Priya, T. Ramachandran, Fuzzy Translation and Fuzzy Multiplication on PS-Algebras, International Journal of Innovation in Science and Mathematics 2(5) (2014) 485-489.
• M. Chandramouleeswaran, P. Muralikrishna, S. Srinivasan, Fuzzy Translation and Fuzzy Multiplication in BF/BG-Algebras, Indian Journal of Science and Technology, 6 (9) (2013), 5216-5219.
• Y. B. Jun, K. H. Kim, Intuitionistic Fuzzy Ideals in BCK-Algebras, International Journal of Mathematics and Mathematical Sciences 24(12) (2000) 839-849.