Plithogenic Cubic Vague Sets

Abstract

To measure the level of accuracy of crisp, fuzzy, intuitionistic fuzzy sets and neutrosophic
set various mathematical tools are available. The generalization of these four sets is Plithogenic set.
In this paper, for the first time we introduce the concept of plithogenic cubic vague set and its
generalization, plithogenic fuzzy cubic vague set, plithogenic intuitionistic fuzzy cubic vague set,
plithogenic neutrosophic cubic vague set. It is the combination of cubic vague set and plithogenic set.
It aims to address the problems involving multiple attribute decision making. This concept is suitable
and the accuracy of the result is precise as the set is described by more value of attributes. An attribute
value v has a corresponding (fuzzy, intuitionistic fuzzy, neutrosophic) degree of appurtenance d(x,v)
of the element x to the set P, with respect to some given criteria. Its corresponding internal and
external sets are also discussed with examples. Further, P-union, P-intersection as well as R-union
and R-intersection are introduced for plithogenic cubic vague sets which acts as a tool to study some
of their properties. Some examples of the newly developed concepts in our everyday life is offered in
this article.