New type of fuzzy ideals in BCK/BCI algebras
Languages of publication
In this paper, we expose pythagorean fuzzy sets in BCK-algebras. Also we define pythagorean fuzzy subalgebra, pythagorean fuzzy ideal in BCK-algebra and investigate some properties of these ideals. Some interesting examples are given. Homomorphism of pythagorean fuzzy set in BCK-algebras are introduce. Moreover we combine the pythagorean fuzzy set and rough sets in BCK-algebras. The concept of rough pythagorean fuzzy ideals in BCK-algebras are introduce.
-  K. Attanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986) 87-96
-  Azmat Hussain,Tahir Mahmood, Muhammad Irfan Ali, Rough Pythagorean Fuzzy Ideals in Semigroups. Computational and Applied Mathematics. 38(2) (2019). DOI: 10.1007/s40314-019-0824-6
-  R. Biswas and S. Nanda, Rough groups and rough subgroups. Bull. Pol. Ac. Math. 42 (1994) 251-254
-  D. Dubois, H. Prade. Rough fuzzy sets and fuzzy rough sets. Int. J. General Syst. 17(2-3) (1990) 191-209
-  K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras. Math. Japon. 23 (1978) 1-26
-  Y. B. Jun, Chracterization of fuzzy ideals by their level ideals in BCK(BCI)-algebras. Math. Japon. 38 (1993) 67-71
-  M. Kondo, Congruences and closed ideals in BCI-algebras. Math. Japo. 48 (1997) 491-496.
-  N. Kuroki, Rough ideals in semigroups. Inform. Sci. 100 (1995) 139-163.
-  N. Kuroki and J. N. Mordeson, Structure of rough sets and rough groups. J. Fuzzy Math. 5 (1997) 183-191
-  N. Kuroki and P. P. Wang, The lower and upper approximations in a fuzzy group. Inform. Sci. 90 (1996) 203-220
-  C. R. Lim and H. S. Kim, Rough ideals in BCK/BCI-algebras. Bull. Pol. Ac. Math. 51 (2003) 59-67
-  J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa, Seoul, 1994.
-  J. N. Mordeson, Rough set theory applied to (fuzzy) ideals theory. Fuzzy Sets and Systems Volume 121, Issue 2, 16 July 2001, Pages 315-324. https://doi.org/10.1016/S0165-0114(00)00023-3
-  Z. Pawlak. Rough sets. Int. J .Inform. Comput Science 11 (1982) 341-356
-  Z. Pawlak, Rough sets and Intelligent data analysis. Information Sciences, 147 (2002) 1-12
-  Sun Shin Ahn and Jung Mi Ko, Rough fuzzy ideals in BCK/BCI-algebras. J. Computational Analysis and Applications 25 (2018) 75-84
-  Q. M. Xiao and Z. L. Zhang, Rough prime ideals and rough fuzzy prime ideals in semigroups. Inform. Sci 176 (2006) 725-733
-  Yager. R. R, Pythagorean fuzzy subsets. Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada (2013) 57-61
-  L. A. Zadeh, The concept of a linguistic variable and it’s application to approximation reasoning I. Inform. Sci 8 (1975) 199-249
-  L. A. Zadeh, Fuzzy sets. Inform. Control 8 (1965) 338-353
-  Young Bae Jun, Kyoung Ja Lee, Chul Hwan Park. New types of fuzzy ideals in BCK/BCI-algebras. Computers & Mathematics with Applications Volume 60, Issue 3, August 2010, Pages 771-785. https://doi.org/10.1016/j.camwa.2010.05.024
Publication order reference