Abstract

BCK/BCI-algebra is a class of logical algebras that was defined by K. Iseki and S. Tanaka. BCK-algebras have a lot of generalizations. One of them is d-algebras. Near set theory which is a generalization of rough set theory. This theory is based on the determination of universal sets according to the available information of the objects. Based on the image analysis, the near set theory was created. ¨Ozt¨urk applied the notion of near sets defined by J. F. Peters to the theory of d-algebras. In this paper we introduce upper-nearness d-ideal, upper-near (upper-nearness) d#- ideal, upper-near (upper-nearness) d∗-ideal. We explored what conditions we should put on the ideal for quotient nearness d-algebra to become an nearness d-algebra again. More- over, we introduce quotient nearness d-algebras with the help of upper-nearness d∗-ideals of nearness d-algebras. Finally, we present a theorem involving the canonical homomor- phism and the structure of the kernel for nearness d-algebras. Thus, we aim to make preliminary preparations for proving isomorphism theorems for nearness d-algebras.