We study certain things connecting strong bi-ideals of bi-near subtraction semigroup in a sub commutative $S$-bi-near subtraction semigroup. A bi-ideals $B$ of $X$ is strong bi-ideals if $X_1B_1^2\subseteq B_1$ (or $X_2B_2^2\subseteq B_2$) denotes $XB^2\subseteq B$.

In this paper, we introduce the notion of hybrid bi-ideals in semigroups and investigate some of their important properties. We also give various equivalent conditions for a semigroup to be regular and hybrid structures to be hybrid bi-ideals of S.

In this paper, we introduce and study the prime, strongly prime, semi prime and irreducible fuzzy bi-ideals of a semi group. We characterize those semi groups for which each fuzzy bi-ideal is semi prime. We also characterize those semi groups for which each fuzzy bi-ideal is strongly prime.

The notion of a G-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a G-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered G-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered G- semigroups analogous to the characterizations of (0-) minimal and maxi- mal ordered bi-ideals in ordered semigroups considered by Iampan [5].

Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study the intiuitionistic fuzzybi-ideals in ordered semigroups and investigate the basic theorem of intuitionistic fuzzy bi-ideals. To provide the characterizations of regularordered semigroups in terms of intuitionistic fuzzy bi-ideals and to discuss the relationships of left(resp. right and completely regular) ordered semigroups in terms intuitionistic fuzzy bi-ideals.

In this paper we introduce the concept of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R is also a spherical interval-valued fuzzy bi-ideal of gamma near-ring R. Further we discuss about the relationship between bi-ideal and spherical interval-valued fuzzy bi-ideal of gamma near-ring R.

In this paper, we investigate the relationship between symmetric bi-semiderivations and Lie ideals of a prime ring. Additionally, we extend some well-known results concerning symmetric biderivations of prime rings to symmetric bi-semiderivations.