N-Cubic Sets Applied to Linear Spaces

Abstract

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.

Cubic Pythagorean Hesitant Fuzzy Linear Spaces and Its Relevance in Multi Criteria Decision Making

“…In recent times fuzzy linear spaces have been gaining importance and their extensions include Interval valued fuzzy linear spaces, cubic linear spaces [13], cubic Γ n−normed linear spaces [7], N−cubic sets applied to linear spaces [8], cubic picture fuzzy linear spaces [9], cubic Pythagorean fuzzy linear spaces [10]. The purpose of this paper is to introduce the notion of cubic Pythagorean hesitant fuzzy linear spaces, combining interval-valued Pythagorean hesitant fuzzy linear space and Pythagorean hesitant fuzzy linear space, and to discuss properties with examples.…”