Given a lattice (X,≤,∧,∨) we define a multi-valued operation ∧ which is analogous to a t-norm (i.e. it is commutative, associative, has one as a neutral element and is monotone). The operation is parametrized by the set Q, hence we actually obtain an entire family of such multi-valued t-norms. Similarly we define a family of multi-valued t-conorms ∨ . We show that, when P, Q are chosen appropri...

Let X be a completely regular Hausdorff space, E a Banach lattice, and μ an E-valued countably additive, regular Borel measure on X. Some results about the countable additivity and regularity of the modulus |μ| are proved. Also in special cases, it is proved that L1(μ) = L1(|μ|).

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

The current paper discusses the uncertainty reasoning method based on gradational lattice-valued firstorder logic Lvfl. For some representative uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process based on lattice-valued first-order logic Lvfl are proposed. Emphasis is placed on the research of the consistent of L-type...

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic, defined by Hájek, is presented. Moreover, Titani’s axioms of lattice-valued set theory are interpreted in fuzzy set theory, under slight modifications of the fuzzy set theory axiomatics.

A b s t r a c t. The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives (" natural " implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. In this paper...

With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. ...

In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is independent of the valued field’s characteristic...