Department of Applied Mathematics with Oceanology and computer Programming , Vidyasagar University , Midnapore , West Bengal , India
Abstract
Fuzzy set theories provide strict mathematical frameworks using vague phenomena
and can be precisely and rigorously studied. The core theories in mathematics such as
algebra, topology, lattices and analysis are subject to fuzzi cation. Many researchers
have dealt with subalgebras, ideals, subimplicative ideals, P-ideals, H-ideals, implica-
tive ideals, hyper structure etc. and their fuzzi cation.
This study attempts to introduce a new class of algebraic structures in intuitionis-
tic fuzzy set and interval-valued fuzzy set. The concepts of doubt intuitionistic fuzzy
subalgebra/ideals, doubt intuitionistic fuzzy H-ideals, doubt intuitionistic fuzzy sub-
implicative ideals, doubt intuitionistic fuzzy P-ideals and doubt intuitionistic fuzzy
translations of doubt intuitionistic fuzzy sub-implicative ideals are introduced for
BCK/BCI-algebra and their properties are duly characterized.
The notion of direct product of two doubt intuitionistic fuzzy subalgebras and two
doubt intuitionistic fuzzy H-ideals of two BCK/BCI-algebras has also been discussed
and some related properties have investigated. We have also found that the direct
product of two intuitionistic fuzzy sets becomes doubt intuitionistic fuzzy H-ideals
and doubt intuitionistic fuzzy subalgebras if and only if for any t; s 2 [0; 1], upper and
lower level sets are H-ideals or subalgebras of BCK/BCI algebra X Y .
Results of doubt interval-valued fuzzy subalgebras and doubt interval-valued fuzzy
ideals in BCK-algebras and BF-algebras are also provided. Cartesian product of two
interval-valued fuzzy sets is de ned and its properties are established. The relation
between doubt intuitionistic fuzzy ideals and an upper level and lower level cuts of
BCK/BCI-algebra have also been explored.
Besides doubt intuitionistic fuzzy hyper lters in hyper BE-algebras have also been
established in the present work
