On fuzzy B-algebras

The fuzzification of (normal) B-subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy B-algebra is given.     

TN-groupoids

In this paper we introduce the notion of TN-groupoids in an arbitrary groupoid, and discuss some properties in Bin(X), and obtain several results related with non-negativity of norms.     

Modular posets and semigroups

Posets and poset homomorphisms (preserving both order and parallelism) have been shown to form a category which is equivalent to the category of pogroupoids and their homomorphisms. Among the posets those posets whose associated pogroupoids are semigroups are identified as being precisely those posets which are (C ₂+1)-free. In the case of lattices this condition means that the lattice is alsoN ₅-free and hence modular. Using the standard connection: semigroup to poset to pogroupoid, it is observed that in many cases the image pogroupoid obtained is a semigroup even if quite different from the original one. The nature of this mapping appears intriguing in the poset setting and may well be so seen from the semigroup theory viewpoint.     

On L-fuzzy ideals in semirings II

We study some properties of L-fuzzy left (right) ideals of a semiring R related to level left (right) ideals     

On BO-algebras

In this paper, we introduce the notion of a BO-algebra, and we prove that every BO-algebra is 0-commutative, and we show that BO-algebras, 0-commutative B-algebras, BM-algebras, p-semisimple BCI-algebras and abelian groups are logically equivalent.     

New types of hyper MV‐deductive systems in hyper MV‐algebras

The notions of a (weak) hyper MV‐deductive system, a (?, ?; ?)‐hyper MV‐deductive system, a (?, ?; ?)‐ hyper MV‐deductive system, a (?, ?; ?)‐hyper MV‐deductive system, a (?, ?; ?)‐hyper MV‐deductive system and a (∩, ∩; ∩)‐hyper MV‐deductive system are introduced, and then their relations are investigated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On d-Fuzzy Functions in d-Algebras

In this paper we introduce the concept of d-fuzzy function which generalizes the concept of fuzzy subalgebra to a much larger class of functions in a natural way. In addition we discuss a method of fuzzification of a wide class of algebraic systems onto [0, 1] along with some consequences.     

On L-fuzzy Ideals in Semirings I

In this paper we extend the concept of an L-fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring R, and we show that each level left (resp. right) ideal of an .L-fuzzy left (resp. right) ideal of R is characteristic iff is L-fuzzy characteristic.     

Cycloidal algebras

In this paper we introduce for an arbitrary algebra (groupoid, binary system) (X; *) a sequence of algebras (X; *) _n = (X; °), where x ° y = [x * y] _n = x * [x * y] _n?1, [x * y]₀ = y. For several classes of examples we study the cycloidal index (m, n) of (X; *), where (X; *) _m = (X; *) _n for m > n and m is minimal with this property. We show that (X; *) satisfies the left cancellation law, then if (X; *) _m = (X; *) _n , then also (X; *) _m?n = (X; *)₀, the right zero semigroup. Finite algebras are shown to have cycloidal indices (as expected). B-algebras are considered in greater detail. For commutative rings R with identity, x * y = ax + by + c, a, b, c ∈ ? defines a linear product and for such linear products the commutativity condition [x * y] _n = [y * x] _n is observed to be related to the golden section, the classical one obtained for ?, the real numbers, n = 2 and a = 1 as the coefficient b.