Hee Sik Kim

Pseudo d-algebras

We introduce the notion of a pseudo d-algebra as a generalization of the idea of a d-algebra. The class of pseudo d-algebras can be included in the class of coupled d-algebras. We show that the class of pseudo d-algebras behaves well with respect to standard mappings such as direct products and standard mappings such as homomorphisms. Indeed, we are able to prove a fundamental theorem of homomorphisms and we are able to identify kernel objects as d-ideals in this theory. We also discuss several large classes of examples of pseudo d-algebras which occur in different settings and we identify properties sufficient for or equivalent to membership in important subclasses of the class of pseudo d-algebras in these settings.

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.

Fuzzy subinclines (ideals) of incline algebras

The fuzzification of subinclines (ideals) in inclines are considered, and some related properties are investigated. We also state the product of fuzzy subinclines (ideals), and the projections of fuzzy subinclines (ideals). We discuss fuzzy relations, fuzzy characteristic subinclines (ideals).

Companion d-algebras

In this paper we develop a theory of companion d-algebras in sufficient detail to demonstrate considerable parallelism with the theory of BCK-algebras as well as obtaining a collection of results of a novel type. Included among the latter are results on certain natural posets associated with companion d-algebras as well as constructions on Bin(X), the collection of binary operations on the set X, which permit construction of new companion d-algebras from companion d-algebras X also in natural ways.

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

Some types of falling fuzzy filters of BL-algebras and its applications

The notions of falling fuzzy implicative, positive implicative and fantastic filters of a BL-algebra are introduced based on the theory of falling shadows and fuzzy sets. The relations between fuzzy implicative, positive implicative and fantastic filters and falling fuzzy implicative, positive implicative and fantastic filters are provided. Finally, we apply the concept of falling fuzzy inference relations to BL-algebras and obtain some related results.

DEFORMATIONS OF d/BCK-ALGEBRAS

In this paper, we study the effects of a deformation mapping on the resulting deformation d=BCK-algebra obtained via such a defor- mation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the stan- dard BCK-algebras of posets as opposed to the properties of the class of divisible d=BCK-algebras which appear to be of interest and which form a new class of d=BCK-algebras insofar as its not having been identied before.

Quotient structures of some implicative algebras via fuzzy implicative filters

In this paper we discuss quotient implicative algebras induced by fuzzy implicative filters, and establish the fuzzy fundamental homomorphism theorem for some implicative algebras.

Fibonacci sequences in groupoids

In this article, we consider several properties of Fibonacci sequences in arbitrary groupoids (i.e., binary systems). Such sequences can be defined in a left-hand way and a right-hand way. Thus, it becomes a question of interest to decide when these two ways are equivalent, i.e., when they produce the same sequence for the same inputs. The problem has a simple solution when the groupoid is flexible. The Fibonacci sequences for several groupoids and for the class of groups as special cases are also discussed.2000 Mathematics Subject Classification: 20N02; 11B39.

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 (C2+1)-free. In the case of lattices this condition means that the lattice is alsoN5-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.