Muhammad Shabir - Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Young Bae Jun - Department of Mathematics Education and RINS, Gyeongsang National University, Chinju ۶۶۰-۷۰۱, Korea
Mahwish Bano - Department of Mathematics, Air University E-۹, PAF Complex, Islamabad, Pakistan

In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. We also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

Prime fuzzy bi-ideals, Semiprime fuzzy bi-ideals, Strongly prime fuzzy bi-ideals, Irreducible fuzzy bi-ideals, Strongly irreducible fuzzy bi-ideals