$\mathcal N$-Cubic Sets Applied to Linear Spaces

P. R. Kavyasree, B. Surender Reddy

The concept of $\mathcal{N}$-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 $\mathcal{N}$-cubic sets is defined by combining interval-valued $\mathcal{N}$-fuzzy sets and $\mathcal{N}$-fuzzy sets. Using this $\mathcal{N}$-cubic sets, we initiate a new theory called $\mathcal{N}$-cubic linear spaces. Motivated by the notion of cubic linear spaces we define $P$-union (resp. $R$-union), $P$-intersection (resp. $R$-intersection) of $\mathcal{N}$-cubic linear spaces. The notion of internal and external $\mathcal{N}$-cubic linear spaces and their properties are investigated.