Some results on Fermatean fuzzy linear space

Abstract

The Fermatean fuzzy set expands upon the Pythagorean fuzzy set, asserting that the combined value of the membership degree cube and non-membership degree cube falls within the unit interval [0, 1]. This paper introduce the notion of Fermatean fuzzy linear space (FFLS) as an extended interpretation encompassing both intuitionistic and Pythagorean fuzzy linear space. We provide evidence that the intersection of two Fermatean fuzzy linear spaces remains a Fermatean fuzzy linear space. But the union of two Fermatean fuzzy linear space need not necessarily be a Fermatean fuzzy linear space. To justify this statement we have a provided a counter example for it. Further, we define the concept of a Fermatean fuzzy level linear space and explore the cartesian product of a Fermatean fuzzy linear space. This structure investigates the image and inverse image of a Fermatean fuzzy linear space along with their associated properties.