TY - JOUR
ID - 542
TI - SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Bakhshi, Mahmood
AU - Borzooei, Rajab Ali
AD - Department of Mathematics, University of Bojnord, Bojnord,
Iran
AD - Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Y1 - 2009
PY - 2009
VL - 6
IS - 4
SP - 73
EP - 87
KW - Generalized groups
KW - Fuzzy generalized subgroups
KW - t-norm
KW - Heyting
algebra
DO - 10.22111/ijfs.2009.542
N2 - In this paper, we deal with Molaeiās generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of all T-fuzzy generalized subgroups of ageneralized group G, and the set of all T-fuzzy generalized subgroups of thecorresponding quotient generalized group. Subsequently, we study the quotientstructure of T-fuzzy generalized subgroups: we define the notion of aT-fuzzy normal generalized subgroup, give some related properties, constructthe quotient generalized group, state and prove the homomorphism theorem.Finally, we study the lattice of T-fuzzy generalized subgroups and prove thatTF(G) is a Heyting algebra.
UR - https://ijfs.usb.ac.ir/article_542.html
L1 - https://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf
ER -