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Cubic Intuitionistic Fuzzy Sets and its Fundamental Properties
Harish Garg and Gagandeep Kaur

Traditionally, the information related to an element is collected either by an intuitionistic fuzzy set (IFS) or interval-valued IFS (IVIFS) which may lose some useful information and hence may affect on the decision results. To overcome this loss, in this paper, we present a new concept of the cubic intuitionistic fuzzy set (CIFS) by extending the concept of the IFSs. As a generalization of the IFSs and IVIFSs, CIFS is a strong and valuable tool to represent the imprecise information by embedding both the features of IFSs and IVIFSs instantaneously. Further, based on its inherent property, we further define the internal (external) CIFS, P(R)-union and P(R)-intersection of CIFSs. The several desirable properties of these operations are defined along with their proof.

Keywords: Cubic intuitionistic fuzzy set; internal (external) cubic intuitionistic fuzzy set; P-(R)- union; P-(R) intersection

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