Anti Fuzzy BG-ideals in BG-algebra

Yıl 2019, Sayı: 27, 1 - 10, 01.03.2019

Muhammad Uzair Khan Raees Khan Syed İnayat Ali Shah Muhammad Luqman

Öz

In this paper, we introduce the concept of anti fuzzy BG-ideals in BG-algebra and we have discussed some of their properties. Relation between anti fuzzy BG-ideal and cartessian product of anti fuzzy BG-ideals is developed.

Anahtar Kelimeler

BG-algebra, sub BG-algebra, BG-ideals, anti fuzzy BG-ideals, anti fuzzy BG-bi-ideal

Kaynakça

• [1] S. S. Ahn and H. D. Lee, Fuzzy Subalgebras of Bg-Algebras, Communication of the Korean Mathematical Society 19 (2004) 243-251.
• [2] K. T. Atanassov , On Intuitionistic Fuzzy Sets Theory, Published by Springer-Verlag Berlin Heidelberg, 2002.
• [3] K. T. Atanassov, More on intuitionistic Fuzzy Sets, Fuzzy sets and systems 33(1) (1989) 37-45.
• [4] K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, (Deposed in Central Sci. -Techn. Library of Bulg. Acad. of Sci., 1697/84) (1983)(in Bulg).
• [5] C. S. Hoo, Fuzzy ideals of BCI and Mv-algebras, fuzzy sets and system 62 (1994) 111-114.
• [6] Q. P. Hu and X. Li, On proper BCH-algebras, Mathematica Japonica International Society for Mathematical Sciences Japonica 30 (1985) 659{661.
• [7] Q. P. Hu and X. Li, On BCH-algebras, Mathematics Seminar notes 11 ( 1983) 313-320.
• [8] K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980) 125-130.
• [9] Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK- algebras, International Journal of Mathematics and Mathematical Sciences 24(12) (2000) 839-849.
• [10] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Scientiae Mathematicae Japonicae Online1 (1998) 347-354.
• [11] K. H. Kim, Intuitionistic Fuzzy Ideals of Semigroups, Indian Journal of Pure and Appllied Mathematics Math. 33(4) (2002) 443-449.
• [12] C. B. Kim and H.S. Kim, On BG-algebras, Demonstratio Mathematica 41(3) 497-505.
• [13] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa. Co., Seoul, ( 1994).
• [14] R.Muthuraj, M.Sridharan and P. M. Sitharselvam, Fuzzy BG-Ideals in BG-Algebra, International Journal of Computer Applications 2 (2010) 26-30.
• [15] Neggers and H. S. Kim, On B-algebras, Mathemati·cki Vensik, 54 (2002) 21-29.
• [16] Neggers and H. S. Kim, On -d-Algebras, Mathematica Slovaca 49(1999) 19-26.
• [17] A. Rosenfield, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971) 512-517.
• [18] M. W. Rysiawa, Anti Fuzzy flters of pseudo-BL-algebras, Commentations Math- ematicae 51(2) (2011) 155-165.
• [19] T. Senapati, M. Bhowmik, M. Pal, Intuitionistic fuzzifications of ideals in BG- algebras, Mathematical Aeterna 2(9) (2012) 761-778.
• [20] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338-353.