In this paper, we give the concepts of essential bipolar fuzzy ideals in semigroups. We discuss basic properties and relationships between semigroups Finally, extend to 0-essential

The concept of a bipolar metric space is presented in this article. In fuzzy space, the notions continuous t-norms and symmetry $$t_s$$ -conorms employs important role. Requirements triangular norms are used to extrapolate with probability density function triangle inequality. Dual processes known as conorms. Continuous define paper. Besides, number topological functional properties have been s...

The first aim to this paper is introduce the notions of bipolar fuzzy soft metric space and (D-)metric space. In order define these concepts, concept points has been brought literature have examined in detail. Moreover, sequences cauchy were defined some their properties examined. addition all this, many examples are given better understand concepts features studied contribute a understanding p...