Trends, probability functions and fuzzy right ideals for dd-algebras

In this paper, we introduce the notion of a trend (probability function) on a dd-algebra, and obtain an equivalent condition defining a trend π0π0 with condition (j) on a standard BCKBCK-algebra. We obtain an example of dd-algebra such that any function φ:X→(0,1)φ:X→(0,1) with ∫0∞φ(z)dz<∞ is a fuzzy co-right ideal.