Nobuaki Kuroki

On fuzzy ideals and fuzzy bi-ideals in semigroups

Abstract In this paper we give some properties of fuzzy ideals and fuzzy bi-ideals of semigroups, and characterize semigroups that are (left) duo, (left) simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi-ideals.

Rough ideals in semigroups

Abstract We shall introduce the notion of a rough left [right, two-sided, bi-] ideal in a semigroup, which is an extended notion of a left [right, two-sided, bi-] ideal in a semigroup, and give some properties of such ideals.

On fuzzy semigroups

Abstract We give some propertes of fuzzy ideals and fuzzy biideals of a semigroup and characterize a regular semigroup, a semigroup that is a semilattice of left (right) simple semigroups, a semigroup that is a semilattice of left (right) groups and a semigroup that is a semilattice of groups in terms of fuzzy left, right and two-sided ideals and biideals.

Fuzzy semiprime ideals in semigroups

Abstract In this paper we shall introduce the notion of fuzzy semiprimality in a semigroup, which is an extension of semiprimality in it, and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality.

The lower and upper approximations in a fuzzy group

In this paper, we first point out that there are still some incomplete theorems in [11] although some authors have showed several incorrect statements in the literature. We then present the improved versions of the incomplete propositions.

Fuzzy semiprime quasi-ideals in semigroups

Abstract We give some properties of fuzzy quasi-ideals of a semigroup, and characterize a completely regular semigroup and a semigroup that is a semilattice of groups in terms of fuzzy semiprime quasi-ideals.

Fuzzy generalized bi-ideals in semigroups

Abstract We introduce the concept of a fuzzy generalized bi-ideal of a semigroup, which is an extension of the concept of a fuzzy bi-ideal (and of a nonfuzzy bi-ideal and a nonfuzzy ideal of a semigroup), and characterize regular semigroups and both intraregular and left quasiregular semigroups in terms of fuzzy generalized bi-ideals.

Fuzzy congruences and fuzzy normal subgroups

Abstract A complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by A. Rosenfeld and W. J. Howie. In this paper, we shall introduce the concept of fuzzy congruences on a groupoid and a group, and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups.

On fuzzy quotient rings induced by fuzzy ideals

Abstract In this paper we define fuzzy quotient rings induced by fuzzy ideals and study the relation between fuzzy quotient rings and fuzzy ideals.

Regular Fuzzy Expressions

The concept of regular expressions was introduced for the purpose of representing the languages accepted by deterministic finite automata. This is necessary in the analysis and synthesis of finite automata since the languages accepted by finite automata are usually infinite.