Abstract

Given a set <TEX>${\Omega}$</TEX> and the notion of bipolar valued fuzzy sets, the concept of a bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroup is provided, and normal bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroups become bipolar <TEX>${\Omega}$</TEX>-fuzzy sub-semigroups are considered.