In this note, we introduce the concept of a fuzzy filter of a BLalgebra,with respect to a t-norm briefly, T-fuzzy filters, and give some relatedresults. In particular, we prove Representation Theorem in BL-algebras. Thenwe generalize the notion of a fuzzy congruence (in a BL-algebra) was definedby Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.We prove that there i...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinateideals are given. Not only we give some characterizations of fuzzy obstinate ideals, but also bring the extension theorem of fuzzy obstinate ideal of an MV -algebra A. We investigate the relationships between fuzzy obstinate ideals and the other fuzzy ideals of an MV -algebra. We ...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

in this note, we introduce the concept of a fuzzy filter of a blalgebra,with respect to a t-norm briefly, t-fuzzy filters, and give some relatedresults. in particular, we prove representation theorem in bl-algebras. thenwe generalize the notion of a fuzzy congruence (in a bl-algebra) was definedby lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.we prove that there i...