On free constructions.
On free -algebras
In the present paper we show that free -algebras can be constructed by applying free abelian lattice ordered groups.
On free modes
We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by ’A. Szendrei in Identities satisfied by convex linear forms, Algebra Universalis 12 (1981), 103–122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska:...
On free pseudo-complemented and relatively pseudo-complemented semi-lattices
On FU()-spaces and -sequential spaces
Following Kombarov we say that is -sequential, for , if for every non-closed subset of there is such that and . This suggests the following definition due to Comfort and Savchenko, independently: is a FU()-space if for every and every there is a function such that . It is not hard to see that ( denotes the Rudin–Keisler order) every -sequential space is -sequential every FU()-space is a FU()-space. We generalize the spaces to construct examples of -sequential...
On Fuchs' problem 76.
On full Suslin trees
On functions that cannot be mv-truth values in algebraic structures.
It is shown, in a general frame and playing with idempotency, that in order to have on a given lattice a Multiple Valued Logic preserving the lattice structure, the only t-norms and t-conorms allowing to modelize the truth values of a v b, a ^ b and a --> b are Min and Max, respectively, apart from ordinal sums.
On fuzzification of the notion of quantaloid
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...
On fuzzy -algebras
The fuzzification of (normal) -subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy -algebra is given.
On fuzzy binary relations.
A binary relation language is an important tool of the theory of measurements (see, for example, book [5]). Specifically, the theory of nominal and ordinal scales is based on theories of equivalent relations and weak orderings. These binary relations have a simple structure which can be described as follows (bearing in mind a context of the measurement theory).
On fuzzy ideals in Hilbert algebras.
On fuzzy input data and the worst scenario method
In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity....
On fuzzy intuitionistic logic
On fuzzy points in semigroups.
On fuzzy sets.
On fuzzy subbundles of vector bundles.
On fuzzy-quantities with real and integer values
On game ideals
On General And Reproductive Solutions Of Arbitrary Equations