Cubic near-ring

Abstract

Y. B. Jun et al introduced a remarkable structure namely cubic sets that combines fuzzy set and interval-valued fuzzy set. Motivated by the above theory our aim in this paper is to introduce the notion of cubic near-ring. The notions of R-intersection, R-union, P-intersection and P-union are investigated. We prove that R-intersection of two cubic near-ring is again a cubic near-ring. It is shown by means of counter examples that the R-union, P-intersection and P-union of two cubic near-ring is not a cubic near-ring.