Abstract
In this paper, we introduce the notion of obstinate filter in hoop algebras and study the relationship between this notion and other types of filters in hoops, we show that every obstinate filter is a fantastic and perfect filter and collect all of the relationships in a diagram. Finally, we define the notion of locally finite hoop and we show that if
Get full access to this article
View all access options for this article.
References
1.
Aglianó
P.
,
Ferreirim
I.M.
and
Montagna
F.
, Basic hoops: An algebraic study of continuous t-norms , Studia Logica 87 (2007 ), 73 –98 .
2.
Akram
M.
and
Nawaz
S.
, Fuzzy soft graphs with applications , Journal of Intelligent and Fuzzy Systems 30 (2016 ), 3619 –3632 .
3.
Blok
W.J.
and
Ferreirim
I.M.A.
, Hoops and their implicational reducts , Banach Center Publ 28 (1993 ), 219 –230 .
4.
Blok
W.J.
and
Ferreirim
I.M.A.
, On the structure of Hoops , Algebra Universalis 43 (2000 ), 233 –257 .
5.
Blount
K.
and
Tsinakis
C.
, The structure of residuated lattices , International Journal of Algebra and Computation 13 (04 ) (2003 ), 437 –461 .
6.
Borzooei
R.A.
and
Aaly Kologani
M.
, Filter Theory of hoop algebras , Journal of Advanced Research in Pure Mathematics 6 (4 ) (2014 ), 72 –86 .
7.
Borzooei
R.A.
and
Aaly Kologani
M.
, Local and perfect semihoops , Journal of Intelligent and Fuzzy Systems 29 (2015 ), 223 –234 .
8.
Bosbach
B.
, Komplementäre, halbgruppen, axiomatik und arithmetik , Fundamenta Mathematicae 64 (1969 ), 257 –287 .
9.
Bosbach
B.
, Komplementäre, halbgruppen, kongruenzen und quatienten , Fundamenta Mathematicae 69 (1970 ), 1 –14 .
10.
Büchi
J.R.
and
Owens
T.M.
, Complemented monoids and hoops , unpublished manuscript .
11.
Cignoli
R.
,
Esteva
F.
,
Godo
L.
and
Torrens
A.
, Basic fuzzy logic is the logic of continuous t-norm and their residua , Soft Computing 4 (2000 ), 106 –112 .
12.
Esteva
F.
,
Godo
L.
,
Hájek
P.
and
Montagna
F.
, Hoop and fuzzy logic , Jornal of Logic and Computation 13 (2003 ), 532 –555 .
13.
Georgescu
G.
,
Leustean
L.
and
Preoteasa
V.
, Pseudo-hoops , Journal of Multiple-Valued logic and Soft Computing 11 (1-2 ) (2005 ), 153 –184 .
14.
Hájek
P.
, Metamathematics of fuzzy logic , Kluwer Academic Publishers , Dordrecht , 1998 .
15.
Haveshki
M.
,
Borumand
A.
and
Eslami
E.
, Some types of filters in BL-algebras , Soft Computing 10 (2006 ), 657 –664 .
16.
Kondo
M.
, Some types of filters in hoops , Multiple-Valued Logic, (ISMVL), 41st IEEE International Symposium on IEEE , 2011 , pp. 50 –53 .