The first author is supported by the “CSIR” Council of Scientific and Industrial Research.Pythagorean fuzzy sets assist in handling more uncertain and vague data than fuzzy sets and intuitionistic fuzzy sets. The notion of cubic pythagorean fuzzy sets is defined by combining interval valued pythagorean fuzzy sets and pythagorean fuzzy sets In this paper, based on the notion of cubic Pythagorean fuzzy sets we initiate a new theory called cubic pythagorean fuzzy linear spaces. Inspired by the notion of Cubic linear spaces we also present P(resp. R)-union and P(resp. R) intersection of cubic pythagorean fuzzy linear spaces. The concept of internal(resp. external) cubic pythagorean fuzzy linear spaces and its properties are examined.Publisher's Versio
