In this paper, we define the notion of a bipolar general fuzzy automaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolar general fuzzy automaton. Then we obtain some relationships between them.

The notion of pseudo-annulets is introduced in Stone lattices and characterized in terms of prime filters. Two operator α and β are introduced and obtained that their composition β ◦α is a closure operator on the class of all filters of a Stone lattice. A congruence θ is introduced on a Stone lattice L and proved that the quotient lattice L/θ is a Boolean algebra.

In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

in some multi-attribute decision making (madm) problems, various relationships among the decision attributes should be considered. this paper investigates the prioritization relationship of attributes in madm with trapezoidal intuitionistic fuzzy numbers (trifns). trifns are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. fir...

Varius concepts related to the category of fuzzy closure spaces have been introduced, and relations among them are studied by several authors [4-8]. in this paper, we introduce the weak fuzzy closure operators which need not preserve unions, showing that many concepts and properties of the category of closure spaces (FCS) can be proved under such weakened conditions. Initial structures of weak ...

We study closure operators and closure structures in a fuzzy setting. Our main interest is the monotony condition of closure operators. In a fuzzy setting, the monotony condition may take several particular forms, all of them equivalent in the bivalent case. We study closure operators, called fuzzy closure operators with truth stresser, satisfying the monotony condition which can be linguistica...

It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...

In this talk I will give a overview on the connections between closure operators and choice operators and on related results. An operator on a finite set S is a map defined on the set P(S) of all the subsets of S. A closure operator is an extensive, isotone and idempotent operator. A choice operator c is a contracting operator (c(A) ⊆ A, for every A ⊆ S). Choice operators and their lattices hav...