Fuzzy connectedness: New definitions and comparisons

Connectedness, ultra-F1 connectedness, ultra-F2 connectedness and strong F2 connectedness are defined for an arbitrary L-subset, their properties are studied, and comparisons with some existing fuzzy connectedness notions (such as strong F1 connectedness, Lowen's connectedness, Rodabaugh's connectedness, Zhao's connectedness, etc.) are discussed in detail. Some standard examples of L-topological spaces or L-cotopological spaces which satisfy our new connectedness axioms are also given.