Cubic Linear Diophantine Fuzzy Sets and Their Essential Properties

Abstract

Cubic sets and cubic intuitionistic fuzzy sets are effective tools for handling incomplete data. However, these ideas and others in the field of cubic sets are incomplete because they lack important reference parameters needed in complicated real-life situations. This means that the results are not satisfactory. We introduce the concept of cubic linear Diophantine fuzzy sets (CLDFS) to address the limitations of the existing notions. Compared to the existing concepts, CLDFS is a great tool that presents information incorporating the interval-valued linear Diophantine fuzzy sets and linear Diophantine fuzzy sets, providing a broader space. Moreover, the internal (external) CLDFS, P(R)- union and P(R)-intersection of CLDFS are defined. We discuss the essential properties of these operations and present their proofs. We also construct cubic linear Diophantine fuzzy aggregation operators and discuss their essential properties.