N-Cubic Sets Applied to Linear Spaces

The concept of N-fuzzy sets is a good mathematical tool to deal with uncertainties that use the co-domain [−1, 0] for the membership function. The notion of N-cubic sets is defined by combining interval-valued N-fuzzy sets and N-fuzzy sets. Using this N-cubic sets, we initiate a new theory called N-cubic linear spaces. Motivated by the notion of cubic linear spaces we define P-union (resp. R-union), P-intersection (resp. R-intersection) of N-cubic linear spaces. The notion of internal and external N-cubic linear spaces and their properties are investigated.