TY - JOUR
T1 - On bipolar fuzzy gradation of openness
AU - Roy, Subhadip
AU - Lee, Jeong-Gon
AU - Samanta, Syamal Kumar
AU - Pal, Anita
AU - Selvachandran, Ganeshsree
N1 - Funding Information:
Funding: This research was supported by a Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07049321).
Publisher Copyright:
© 2020 by the authors.
PY - 2020
Y1 - 2020
N2 - The concept of bipolar fuzziness is of relatively recent origin where in addition to the presence of a property, which is done in fuzzy theory, the presence of its counter-property is also taken into consideration. This seems to be much natural and realistic. In this paper, an attempt has been made to incorporate this bipolar fuzziness in topological perspective. This is done by introducing a notion of bipolar gradation of openness and to redefine the bipolar fuzzy topology. Furthermore, a notion of bipolar gradation preserving map is given. A concept of bipolar fuzzy closure operator is also introduced and its characteristic properties are studied. A decomposition theorem involving our bipolar gradation of openness and Chang type bipolar fuzzy topology is established. Finally, some categorical results of bipolar fuzzy topology (both Chang type and in our sense) are proved.
AB - The concept of bipolar fuzziness is of relatively recent origin where in addition to the presence of a property, which is done in fuzzy theory, the presence of its counter-property is also taken into consideration. This seems to be much natural and realistic. In this paper, an attempt has been made to incorporate this bipolar fuzziness in topological perspective. This is done by introducing a notion of bipolar gradation of openness and to redefine the bipolar fuzzy topology. Furthermore, a notion of bipolar gradation preserving map is given. A concept of bipolar fuzzy closure operator is also introduced and its characteristic properties are studied. A decomposition theorem involving our bipolar gradation of openness and Chang type bipolar fuzzy topology is established. Finally, some categorical results of bipolar fuzzy topology (both Chang type and in our sense) are proved.
KW - Bipolar fuzzy topology
KW - Bipolar gradation of closedness
KW - Bipolar gradation of openness
KW - Bipolar gradation preserving map
UR - https://www.scopus.com/pages/publications/85084465489
U2 - 10.3390/math8040510
DO - 10.3390/math8040510
M3 - Article
AN - SCOPUS:85084465489
SN - 2227-7390
VL - 8
JO - Mathematics
JF - Mathematics
IS - 4
M1 - 510
ER -